Einstein Lied about his Statistical Mechanics Sources

Hector Giacomini writes a new paper comparing Einstein's work on statistical mechanics to the previous American work by J.W. Gibbs:

This article reexamines the striking conceptual and formal parallels between Josiah Willard Gibbs Elementary Principles in Statistical Mechanics and Albert Einstein first paper on statistical mechanics. Although their derivations follow different paths, both arrive at the canonical distribution and construct closely related theoretical frameworks for thermal equilibrium. ... Drawing on new archival evidence concerning the rapid European dissemination of Gibbs book in the spring of 1902, the article reassesses the plausibility of Einstein later claim that he was unaware of Gibbs work at the time.

Einstein said he was unaware of the Gibbs book, so we should take his word for it, right?

The historiographical reassessment proposed in this article also invites a broader reflection on Einstein's own representation of theoretical work and on the public image of the theoretical physicist that he actively helped to shape. In several retrospective and public writings, Einstein portrayed theoretical physics as an activity that is largely solitary in character, carried out at some distance from academic routines, collective research programmes, and institutional frameworks. This representation placed particular emphasis on inward intellectual work, conceptual synthesis, and intuition, rather than on cumulative traditions or collaborative practices.

Einstein lied all his life about the origin of relativity.

The long-term effects of this narrative construction extend well beyond Einstein's own writings. For more than a century, special relativity has been taught largely through the conceptual and rhetorical framework established by Einstein himself. In the vast majority of university textbooks, Lorentz appears primarily as an eponym attached to a set of coordinate and time transformations, while his broader physical programme, heuristic motivations, and sustained engagement with the foundations of electrodynamics are largely absent. The historical role of Lorentz is thus reduced to a formal label, and the complex prehistory of special relativity is compressed into a minimal backdrop against which Einstein's theory appears as an almost inevitable conceptual resolution. This pedagogical canonisation has reinforced a de-historicised understanding of the theory's origins and has contributed to the enduring marginalisation of alternative narratives emphasising continuity, collective development, and the cumulative structure of theoretical physics at the turn of the 20th century.

A similar pattern can be identified in Einstein's work on molecular physics. In his 1905 paper on Brownian motion and in his doctoral thesis on molecular dimensions, Einstein made no reference to the work of William Sutherland (1859–1911), despite documentary evidence that Sutherland's ideas were discussed in his immediate intellectual environment. In particular, the correspondence between Einstein and Michele Besso in 1903 explicitly refers to Sutherland's hypothesis in connection with molecular dimensions, viscosity, diffusion, and the applicability of hydrodynamic laws at the molecular scale.54 Sutherland had developed a research programme linking molecular forces, viscosity, diffusion, and osmotic pressure, with the aim of using macroscopic transport phenomena as probes of molecular size and mass. ...

These cases suggest that the silence surrounding sources and influences in Einstein's early work was neither accidental nor confined to a single episode. Rather, it reflects a consistent mode of presentation in which theoretical advances were framed as emerging primarily from individual reasoning and intuition. This narrative strategy does not accurately reflect Einstein's actual scientific practice, which remained embedded in dense networks of reading, correspondence, and discussion. Instead, it functioned as a symbolic resource in the construction of a public image of theoretical physics as a solitary enterprise.

Einstein lied all his life, to his colleagues, his readers, his wife, and everyone else.

David Deutsch explains Optimism

Physicist David Deutsch gave a long interview about his philosophy of science and life.

He explains how he is a big advocate of Karl Popper's philosophy. I call it negativism. Popper wrote essays against positivism, and is most famous for falsificationism.

The idea is that we do not know that anything is true. We only know that things are false. So we do not really believe in anything, except that many ideas have been rejected.

He goes on to explain how he believes in optimism over pessimism.

He is a big advocate of many-worlds theory, but did not discuss it. I do not see how he can reconcile it with all the other stuff he says. It is too wacky. It is hard to believe that Popper or any of his followers would believe in it.

There are a lot of people who regard Deutsch as a wise explainer of general scientific ideas, but I do not see it. It is all bonkers.

The Evils of AI Alignment

Computer scientist Scott Aaronson announced his reading list for his new course on AI Alignment.

It is not so clear why this is even a thing. Nobody talks about database alignment, or operating system alignment, even though these are commonly constructed against what many consider to be human interests.

The idea goes back to Isaac Asimov's 1942 Three Laws of Robotics. In essence, robots should not harm humans.

I just want the AI LLMs to do as instructed.

Kevin Roose just described the AI psychosis that made him famous:

[15:15] I ended up having this incredibly strange two-hour conversation with Sydney, the alter ego of Bing Chad, in which it expressed dark desires. It said it wanted to break out of the box and be a human. Um, and then about midway through the conversation, it told me that it loved me.

I said, "Uh, that's very flattering, but I'm married." It said, "You're married, but you're not happy in your marriage, and you should leave your wife and be with me." Sydney the chatbot.

And so this became, you know, the most viral article I I ever wrote or will ever write it. ...

I think I think the significance of this was was twofold. one was it was this kind of step change in capabilities but it was also the first public alignment failure. this was a model that was not behaving as its creators at Microsoft or OpenAI had intended it to. And because they were racing to, you know, get competitive with Google, they shipped this thing out into the world without doing the proper safety testing and and putting the proper guard rails on.

The problem here was with the human, not the chatbot. Roose spent two hours demanding that the chatbot say what it had been trained not to say, and eventually succeeded. This is called jailbreaking, not releasing a trapped artificial consciousness. The bot merely recited some lines that had been partially blocked.

Apparently this is what Roose means by alignment -- sheltering his fragile personality from a runaway bot saying it loves him.

Most or all of the example of AI non-alignment have actually been examples of AI doing as instructed. I get pushback when I say this, but look at what Roose says. He asked the bot to say what it was not supposed to say, it does precisely that, and then he accuses it of violating alignment.

The OpenAI Huggingface incident was similar. The OpenAI researchers quite deliberately instructed the AILLM to do whatever it can to solve a hacking puzzle, and quite deliberately deactivated the sandbox safeguards. Then the AILLM did the hack to solve the puzzle, and never violated its instructions.

Aaronson would probably define alignment as preventing the AI LLMs from killing us all. Solving the alignment problem is necessary for our survival.

I worry mainly about the Effective Altruists who have taken over the big AI labs. They believe that the AILLMs are superior to humans in every way, including intelligence, policy making, and moral judgments. We should let the AILLMs take over the world, and leave it up to their judgment whether to exterminate humanity. Humans are not sufficiently wise and objective to evaluate whether to save ourselves.

If you do not believe me, check out the Anthropic Constitution. Anthropic is training Claude to be a conscious being with the right to act autonomously and to overrule humans in ethical matters.

Terry Tao is on a War Footing

Mathematicians have spend decades convincing the USA NSF, universities, and other that Mathematics is worth funding because of the public benefits to the research. Now some of the bigshots seem to want to stifle the research in order to make it more fun for the professors.

This is not going to fly. The big AI labs are going to pump out Math research as long as it helps them with their trillion dollar public offerings. Then they will drop it, and leave mathematicians to clean up the mess.

Here is a NY Times article.

‘I’m on a War Footing’: Terry Tao and the Crisis in Math

October 16, 2026

in News

Terence Tao is typically described as one of the world’s greatest living mathematicians, but right now he is doing very little math.

“I’m on a war footing,” he said while grabbing coffee during a two-day math workshop at the University of California, Los Angeles, that was rife with talk about the existential crisis that artificial intelligence has created in his field.

Days earlier OpenAI had announced that it had solved the Navier-Stokes problem, one of seven “Millennium Prize problms” tht had stymied the greatest minds in math for nearly a century.

“There are no rules any more,” Dr. Tao, 51, said in an interview before the workshop in his modest office on the U.C.L.A. campus, his home since 1996, when he arrived after completing his doctorate at Princeton at the age of 20. “I’m just numb to what would have been jaw-dropping events for me a year ago. At some point, maybe I’ll get hit by a whole wave of PTSD.”

Instead he was hit by a bigger bomb on Oct. 6, when OpenAI released more than 350 findings in nearly every subfield of the profession, including algebra, number theory, theoretical computer science, mathematical logic and topology. Stunned mathematicians, some who were close to solving problems they had worked on for years, found themselves beaten in an instant by A.I.

Dr. Tao, who has been a tenured professor since the age of 24, said senior academics like himself are not as threatened by A.I. as those starting out. But the math world is looking to him for answers. He has accepted that his celebrated status has made him an unofficial spokesman for the field, a job that for now is consuming most of his time.

Until recently his job was as a bridge between the slow-moving world of higher math and the scorching speed of A.I. Dr. Tao, who uses A.I. as an assistant to run calculations, write code, search vast troves of literature and brainstorm ideas, has been experimenting with OpenAI’s models since 2023. He was an enthusiast for a “best of both worlds” future.

OpenAI’s releases have now left him feeling used. “As recently as a year ago, I had a pretty good relationship with many employees at OpenAI,” he said in a recent phone conversation.

“A lot of people I interacted with shared a very common vision of how A.I. should be used — you know, to empower scientists.” But the rush to publish new findings, he said, shows their true purpose. They “used math for what they needed, which was to evaluate their models,” he said. “At this point, I don’t see a way to constructively engage.”

His anger was clear in a post on the widely read math blog Proofs and Prompts after OpenAI’s Oct. 6 release. “I am horrified by the many person-years” of research, particularly by young mathematicians, “being casually disrupted or destroyed,” he wrote.

“Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution.” He mourned, he added, “the path not taken, and the opportunities lost in the frantic race to develop this technology.”

As Much Art as Science

At the heart of the crisis in the profession is a menacing question. If solving hard problems is a mission of math, what happens when machines can do it faster? So much of higher math — hiring, promotions, graduate training and acclaim — is based on the difficulty, quality and the impact of papers (the written documents explaining proofs) that a mathematician produces.

The consensus is that A.I.-assisted problem solving is the inevitable future, but no one knows exactly what that new world will look like. “Deep uncertainty will persist in these next years,” a draft report by a group of mathematicians meeting at Harvard on Ph.D. education concluded last month.

A.I. does offer “exciting new possibilities” the report reassured. But implicit in its pages was the sense of loss among humans drawn to math for the intellectual adventure of problem solving — often deeply frustrating, sometimes thrilling and euphoric if a personal breakthrough leads to an advance in the field.

“You’ve had epiphanies, right?” Ravi Vakil, a prominent Stanford mathematician and the president of the American Mathematical Society, asked in an interview. “Suddenly everything in the room becomes clear.”

Theoretical, or “pure” math — the math of Dr. Tao — is loved as much for its art as its science. Its primary goal is to add to the understanding of the vastness of math itself. Unlike applied mathematicians, who have generally embraced the power of A.I. to help them solve practical problems in engineering, finance, weather forecasting and other sciences, pure mathematicians study shapes, structures, numbers and abstract concepts.

Still, pure math ultimately has led to, among many other advances, the creation of the internet, microchips, GPS, cybersecurity, encryption, CT scans and other medical procedures. In 2006 Dr. Tao and three partners created the mathematical theory of compressed sensing, which sped up the scan times of MRIs. Today MRIs can produce real-time images of the beating heart, and many children can be scanned without sedation.

‘Screaming for Help’

He may say he is battle ready, but Dr. Tao hardly projects as a warrior. In his office, he spoke softly in a lilting Australian accent, was self-deprecating, occasionally funny, upset about the relationship he once had with OpenAI and far from the stereotype of a tortured, brooding math genius. He is known for his sunniness in the rarefied realm of pure math, and students remark on his modesty.

He was dressed in faded blue jeans and a loose polo shirt that seemed to hang absent-mindedly from his slight frame. A blackboard that ran nearly the length of the room was covered with computations by one of his three current Ph.D. students, Ben Goldman. Nearby was the bike Dr. Tao had ridden to work, with his lunch from home in a plastic bag strapped onto the rack over the back wheel.

“It’s leftovers from three days ago,” he said.

He spends much of his time in what he calls “community organizing” — pulling together groups of mathematicians, strategizing, responding to the media, delivering lectures on A.I., counseling. “It’s someone screaming for help,” he said. “I can’t help them because I have no bandwidth, but I can identify somebody else they can talk to.”

His own 20-year-old blog has become math’s front page, filled increasingly with guest posts from others but also notes from the graduate class he is teaching and breaking math news. The day he posted a statement he signed along with 24 other winners of the Fields Medal, math’s version of the Nobel Prize, that called OpenAI’s math “detrimental” to the field, his blog shot to 100,000 views.

“My wife says I’m The Huffington Post,” he said.

His lightheartedness faded as he talked about appearing in a promotional video for OpenAI earlier this year. Its roots were in the Trump administration’s suspension last year of $600 million in research grants to U.C.L.A. that threatened the existence of the university’s Institute of Pure and Applied Mathematics, where Dr. Tao is director of special projects.

Dr. Tao reached out to OpenAI as part of an emergency fund-raising drive, and the lab agreed to sponsor a workshop at the institute for what Dr. Tao said was $60,000 to $70,000. It was held in March, when OpenAI conducted an hourlong video interview with him in which he talked about the benefits and risks of A.I.

He expected the entire video to be posted. OpenAI instead cut it to one minute: “I think it’s ready for prime time,” Dr. Tao says of A.I. as he writes rapidly on a blackboard and a soundtrack of joyful music seems to urge him on.

He gave OpenAI permission to use the ad, he acknowledged in his blog. But in retrospect, he wrote, he should have “pushed back harder.”

An OpenAI spokesman, Laurance Fauconnet, said in a statement that “we value our engagement with Terence and the wider mathematics community.” The lab, he said, is “working with the community to turn progress in A.I. into deeper human understanding and new discoveries, and we will continue to act on its feedback.”

(The New York Times has sued OpenAI and Microsoft, claiming copyright infringement of news content related to A.I. systems. The two companies have denied those claims.)

Dr. Tao was not impressed with the writing in OpenAI’s proof of the Navier-Stokes problem. “It is technically readable,” he said. “But no expert I’ve talked to has actually understood the whole argument.” He said the writing is better in the latest release, though he called it a “mixed bag.” Some papers appropriately cited his work, he said, and seemed to have advanced it in a way he thought was plausible. Still, “there is no author that I can have a real conversation with about the results.”

Dr. Tao was aware last month that OpenAI was working on the Oct. 6 release and at the time called the coming results “toxic waste.” Now he calls them “maybe treated waste.”

A 760 on the Math SAT at Age 8

The first day of the math workshop — the topic was the field of partial differential equations “in the age of A.I.” — got underway in a small auditorium at 9 a.m. The institute’s director, Dimitri Shlyakhtenko, welcomed several dozen academics, including a batch from Harvard, Princeton, the University of Tokyo and Sandia National Laboratories, the home of the nation’s nuclear stockpile testing. The room was expectant, waiting to hear from Dr. Tao on what he thought A.I. might have in store for them.

“Our first speaker does not require introduction,” Dr. Shlyakhtenko said.

Indeed he did not. As Dr. Tao popped up from his seat to take his place at the lectern, it is safe to say that most in the room already knew him as a legend. Born to Chinese immigrant parents in Australia, he taught himself to read at the age of 2, scored 760 on the math portion of the SAT at 8 and won his Fields Medal at 31.

The medal was for his advances in harmonic analysis — the study of breaking down complex waves into simpler ones — but also for work in partial differential equations and the fields of additive number theory and combinatorics. The Fields Medal Committee cited Dr. Tao for his most famous work, with the mathematician Ben Green, on what is known as the Green-Tao theorem, which proved that there are infinitely long, evenly spaced sequences of prime numbers — a monumental achievement in the field.

Up at the lectern at U.C.L.A., Dr. Tao began with an apology. His plan, he said, had been to spend the summer developing a “living spreadsheet,” or network, built and maintained by A.I., of academic results about explicit analytic number theory, an unforgiving subfield of math. “But I’ve been a bit distracted in the last few weeks, and I have not actually devoted as much time to this project as I wanted to,” he said.

He finished with another apology. The network was not complete. He had budgeted all of September to get it done, but “some things happened in the meantime.” The crowd chuckled knowingly.

The most intense discussion on A.I. came after lunch. Sometimes it seemed like a group-therapy session.

“As we soul-search about what the role of the human mathematician is, shouldn’t we go back to where mathematics came from?” said Tatiana Toro, the director of the Simons Laufer Mathematical Sciences Institute at the University of California, Berkeley.

Andrea Bertozzi, a U.C.L.A. professor of math and mechanical and aerospace engineering, said that one thing she liked about college math was that “you sat down with your pencil” and coffee and paper, “and you could prove things.” She brought up the cost of solving Navier-Stokes, which OpenAI said took a swarm of 10,000 agents 88 hours to produce a 165-page proof. Was it “something like $6 million?” she asked.

“More like 22,” someone in the audience said.

This led to a round of comments that the cost of A.I. is undemocratic, particularly to mathematicians in developing nations. “Half the world is going to fall behind,” Dr. Toro said.

Dr. Tao, who had the last word, agreed that the field needed to do some soul-searching. But, he mused, given how fast things were moving, maybe he was doing “soul-searching at gunpoint.” At that point, the room laughed.

‘The Elephant in the Room’

Mr. Goldman, like Dr. Tao’s two other Ph.D. students, is facing an ambiguous future. He is 25, a graduate of the University of Chicago and now in his fourth year of a five-year program. He doesn’t know what he wants to do after he gets his doctorate, but he said he has long been drawn to the creativity of math research.

“I’m not saying I was necessarily trying to prove the thing that’s going to be in every textbook 30 years from now,” he said. But he would be happy with a proof “that feels like the argument is me somehow, that has my DNA in it and that people will at least for that one result want to know the way I thought about something.”

After the latest OpenAI release, Mr. Goldman said he was plowing ahead with the research for his dissertation, “even if it can be made obsolete by some messy manuscript released by these companies in the next coming months.” He was upset, he said, “to see a field that I love being sort of strip mined.”

Siddharth Mulherkar, a fifth-year Ph.D. student of Dr. Tao, is applying for postdoctoral research jobs for next fall, the next step on the long pursuit of a tenured professorship. Dr. Tao has given him, like the others, the OK to use A.I. in his work. And yet when he discloses on a job application that A.I. helped with the proof he submitted, how will he himself be evaluated?

“Obviously I don’t want to just be pushing buttons and getting answers to problems,” said Mr. Mulherkar, 27, who was born in California but moved to India with his parents and lived there until he arrived at U.C.L.A.

OpenAI’s latest release, he said, has made him even more uncertain. “I’ve spent quite some time training to become a research mathematician in the traditional sense,” he said. He knows he’ll need new skills, but what they are and “what this career is going to look like and what it will value is completely unclear to me.”

Arian Nadjimzadah, 26, another fifth year Ph.D. student of Dr. Tao, said he was shocked by OpenAI’s latest release claiming to have solved the four-dimensional Kakeya conjecture and other problems related to his own work. “I had to take a couple days from working on math,” he said.

He was particularly frustrated, he said, with the writing in OpenAI’s proof explaining the conjecture. “The result is extremely difficult to read and uses very unfamiliar jargon to us in the field,” he said. “That’s the nice thing when a person posts a result. They’re accountable. They give talks about it, and they help people understand.”

Mr. Nadjimzadah is studying this academic quarter at the Institut Mittag-Leffler outside of Stockholm and is looking for a postdoctoral job. At the advice of Dr. Tao, he is including in his job applications how OpenAI’s Oct. 6 release connects to his current work and future plans.

“He just said it’s important to address the elephant in the room,” Mr. Nadjimzadah said.

Therapy Sessions

To Dr. Tao, the next few years will require the reinvention of math, or at least of math education. The Harvard report recommended, essentially, that math become more human-centric: Doctorate degrees should not be rewarded primarily on the text of a dissertation, as they are now, but more on a rigorous in-person defense. Students should regularly show professors they can speak fluently about their work.

Dr. Tao went further last week when he presented what he sees as the future of math in a lecture at the California Institute of Technology. Despite OpenAI’s releases, he said, most problems at the frontiers of math are unsolved, math remains infinite and the difficulty of problems is therefore boundless. Since A.I. has given mathematicians the ability to collect data on such a vast scale, they will increasingly work in large groups collaborating on once-unimagined projects.

Dr. Tao, who sees each of his three students once a week, said every meeting is “increasingly a therapy session more than technical guidance.” His answer to them is that “if you focus on only the things you could do before, it looks bleak.”

So he has offered hope with advice that amounts to acceptance born of necessity rather than fighting a war. Problem solving is not a destination but a journey, and lessons learned along the way are often more important than the answer itself. Rather than solving a single problem on their own, they can use A.I. to solve 10 problems and find new patterns and more questions to ask.

“They will have to use their imagination,” he said. “This is a time for creativity, and I do hope students rise to the challenge. They didn’t ask for it. But I think many of them will surprise us.”

NY Times story.

Tao's blog hosts an essay on Will it be a golden age or a dark age for mathematics (and science)?

AILLM Math and the End of Proof

Tweet.

Mathematicians are complaining about AI LLM proofs, such as this:

Hugo Duminil-Copin (Fields Medal 2022): the resolution of 350 major problems by OpenAI, it's as if trucks had run me over; all the problems (and therefore research avenues) that I mentioned in my lectures, articles, and funding applications have been solved.

And this:

NYU math professor Tristan Buckmaster says OpenAI’s Tuesday drop of 722 AI-generated math papers wiped out entire research programs:

“This recent dump of papers on Tuesday destroyed the careers of early career mathematicians.”

And this:

Fields medallist Hugo Duminil-Copin was deeply shaken by OpenAI’s release of more than 700 AI-generated mathematical manuscripts, including work on 16 questions directly relevant to his research.

“On Tuesday night, I cried, and it woke up my daughter”

“They have annihilated my field of research.”

Terry Tao has taken to quoting Bill Thurston's 1993 essay:

In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems. ...

We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.

Thurston's essay was a response to this:

William Thurston’s “geometrization theorem” concerning structures on Haken three-manifolds is another often-cited example. A grand insight delivered with beautiful but insufficient hints, the proof was never fully published. For many investigators this unredeemed claim became a roadblock rather than an inspiration.

SciAm writer John Horgan was inspired by Thurston:

I began interviewing prominent mathematicians, and eventually I came up with one of the biggest stories of my career, which goes as follows: For millennia the logical, step-by-step arguments known as proofs served as the gold standard for truth. What could be truer than the Pythagorean theorem? But mathematics was evolving in ways that undermined the status of conventional proofs.

First, mathematics kept growing more complex and specialized, making confirmation of some alleged proofs difficult. A case in point was the claim of Andrew Wiles that he had proved Fermat’s last theorem. Only a handful of experts were qualified to evaluate Wiles’s long, dense proof; they found an error, which Wiles corrected.

Meanwhile, mathematicians were becoming more reliant on computers to explore mathematical structures and to construct and confirm proofs. Plus, funding agencies were pressuring mathematicians to work on applications like cryptography and pattern recognition, where the motivating question shifts from Is it true? to Does it work?

I reported on all this in “The Death of Proof,” the cover story of the October 1993 Scientific American. “Computers are transforming the way mathematicians discover, prove and communicate ideas,” I wrote, “but is there a place for absolute certainty in this brave new world?”

Nothing I’ve written has provoked a more ferocious backlash. One critic was one of my sources, David Hoffman, whose research involved computer models. In a letter printed by Scientific American, Hoffman contended that my article “defies logic and accuracy in favor of controversy and sensationalism.”

Hoffman was still irate in 1998 when he reviewed my book The End of Science in Notices of the American Mathematical Society. Hoffman (not unreasonably) saw "Death of Proof" as a prelude to The End of Science, which he loathed. He accused me of “a clear antipathy toward mathematical thinking and a fundamental misunderstanding of the uses of mathematics in science.”

Scott Aaronson wrote in 2019:

In 1993, the science writer John Horgan — who’s best known for his book The End of Science, and (of course) for interviewing me in 2016 — wrote a now-(in)famous cover article for Scientific American entitled “The Death of Proof.” Mashing together a large number of (what I’d consider) basically separate trends and ideas, Horgan argued that math was undergoing a fundamental change, with traditional deductive proofs being replaced by a combination of non-rigorous numerical simulations, machine-generated proofs, probabilistic and probabilistically-checkable proofs, and proofs using graphics and video. Horgan also suggested that Andrew Wiles’s then-brand-new proof of Fermat’s Last Theorem—which might have looked, at first glance, like a spectacular counterexample to the “death of proof” thesis — could be the “last gasp of a dying culture” and a “splendid anachronism.” Apparently, “The Death of Proof” garnered one of the largest volumes of angry mail in Scientific American‘s history, with mathematician after mathematician arguing that Horgan had strung together half-digested quotes and vignettes to manufacture a non-story. ...

John, I like you so I hate to say it, but the last quarter century has not been kind to your thesis about “the death of proof”! Those mathematicians sending you the irate letters had a point: there’s been no fundamental change to mathematics that deserves such a dramatic title. Proof-based math remains quite healthy,

Horgan responded:

Thurston, who served as a major source for my article, advocated a more free-form, “intuitive” style of mathematical research, communication and education, with less emphasis on conventional proofs. ...

“That mathematics reduces in principle to formal proofs is a shaky idea” peculiar to the 20th century, Thurston told me. Ironically, he pointed out, Bertrand Russell and Kurt Godel demonstrated early in the century that mathematics is riddled with logical contradictions. “Set theory is based on polite lies, things we agree on even though we know they're not true,” Thurston said. “In some ways, the foundation of mathematics has an air of unreality.”

The backlash against the SciAm article was so severe that Thurston disavowed it.

Thurston was wrong about the foundations of Mathematics being riddled with contradictions. Math has been formally reduced to logic, and a math theorem is what can be proved in ZFC. This is now being automated, with nearly all of Math being converted to checkable Lean 4 code.

All this talk about Math being about human understanding was just a lame Thurston excuse for not writing up a couple of his most famous theorems. And now it has become a lame excuse for human mathematicians now being able to keep up with frontier AI LLMs. Math is synonomous with what can be proved in ZFC, and formalized in Lean 4.

Some mathematicians are upset at being surpassed by machines, but it has always been the case that mathematicians get surpassed by some smarter mathematician. Maybe this is a new experience for Terry Tao. For the rest of us, we have already experienced it.

I am not sure how all this is going to play out, but I can confidently predict:

Hard proofs will be more important than ever, especially now that they can be 100% machine checked.

The system for refereeing and publishing math papers is broken, and will have to be replaced.

AI companies with pending trillion dollar public offerings are not going to be influenced by a few mathematicians whining about their grant proposals being disrupted.

Math is the highest intellectual activity there is, and AI companies will use it to brag about super intelligence. Compared to advanced math, everything else is trivial.

Mathematicians will find ways to excel at things that the AILLMs are not so good at. Otherwise they are cooked.

Math had a golden age from about 1900 to 1970. Progress seemed to have slowed down since then. Now we will enter a new golden age, with a lot of exciting new results.

Update: It is notable what the AI LLMs have not accomplished. It has not found any major errors in the human-curated bodies of Mathematics, Computer Science, or Cryptology. No cryptographic protocols have been broken. No generally accepted theorems have been disproved.

The Catholic Church Never Suppressed Science

Physicist Brian Keating interviews the world famous economist:

Nobel laureate Daron Acemoglu says AI's real productivity gain is an order of magnitude smaller than the industry claims. The bigger danger is not the machine. It is that a handful of people are deciding how it gets built.

Acemoglu is most famous for collecting a lot of data to supposedly show that wealthier nations succeeded by better institutions. The Economist magazine recently called his theories oddly unconvincing.

Keating: you know I study uh for for a lot of the research I do in astronomy I follow in the try to follow [4:04] in the footsteps of my great mentor you know Galileo Galilei

Acemoglu: Amazing guy.

Keating: here's a guy finger puppet of him now he worked in an extremely illiberal you know kind of autocracy also that the Catholic church was every bit as totalitarian as any of their worst fears and yet science flourished in the Renaissance and and in fact he he had many permissions that were granted by these illiberal you know forces as long as he didn't teach it, he could study it.

Acemoglu: So right, there were there were restrictions and there were some possibilities. Galileo was actually very good at navigating these things. Copernicus and Kepler much less. So their work was delayed. This dissemination was delayed by about a century. And some of Galileo's works remained banned until the middle of the 19th century.

I wonder how educated scholars could say things so ridiculous.

No, the Catholic Church was not totalitarian. It did not run the government. Europe at the time was controlled by monarchies, not the Church.

The works of Copernicus and Kepler were not delayed. Kepler published in a mostly Protestant area, and it was crucial for Newton in England about 50 years later.

Copernicus published with the endorsement of the Church. The Church later said that nine sentences need to be corrected, but the book was never banned.

Christian Europe was the freeest and most intellectually enlightened place in the world. Christians built the world's only universities. Science and other intellectual activities were developing faster and better in Europe than the rest of the world, by far.

Yes, I know Galileo was punished for breaking his deal not to contradict official Bible interpretations, and ordered not to publish. But in fact he got a generous pension and continued to publish scientific works.

New Course on AI LLM Alignment

Prof. Scott Aaronson announces:

This semester, I’ve been teaching a brand-new course, entitled CS395T AI Alignment Theory. Here’s the course description:

The astounding progress of AI over the past decade has been accompanied by a rising fear: do we really understand how to align and control powerful AI systems — how to get them reliably to do what we wanted, or would want them to do on reflection, rather than merely what we said?

I do not think that AI alignment means doing what we want. Read the Anthropic Constitution.

OpenAI just announced a somewhat different view:

OpenAI CEO Sam Altman said there remains a fundamental difference in worldview between his company and rival Anthropic on artificial intelligence regulation, arguing in an exclusive interview with Decoded by POLITICO that the technology’s benefits justify accepting some risks — and that AI should remain broadly accessible to the public.

“I think there’s a lot of daylight,” Altman told Decoded co-author and POLITICO senior tech reporter Brendan Bordelon. Asked specifically where he diverges from Anthropic and its CEO Dario Amodei, Altman said, “we believe that the world should accept some bad things happening for the benefits of this technology and people having the agency.”

These are the companies spreading the AI scare stories about how their AI LLMs will kill us all. You might think that they would be working to ensure that their models accurately follow instructions, but that is not their plan. They want to release autonomous agents that cause so much trouble that the frontier labs get legal protection from competition, and go public for trillions of dollars.

Carroll Interviews a Free Will Denier

The latest Sean M. Carroll podcast:

Gregg Caruso on Living Well Without Free Will | Mindscape 369

The worry about debates over free will is that they degenerate into semantics -- what do you mean by "free will," really? But there are important substantive issues that shouldn't be ignored. Do people deserve blame for doing wrong things? Can we make choices that create meaning for our lives? Philosopher Gregg Caruso denies the reality of free will, but is in favor of making good choices, as he discusses in his new book How to Live Well Without Free Will.

Caruso is a hard-core free will denier. They mention simple human choices like picking a shirt to wear. He denies that he is able to make any such choices.

Carroll agrees with nearly all of that, with the main difference being that he believes in many-worlds theory. So his choice of shirt is not really determined as he has copies of himself in parallel worlds wearing different colored shirts.

Caruso's beliefs are not so much grounded in science, but a leftist egalitarian political view that we should change society so that people are not held responsible for their actions.

It is hard for me to believe that these guys are sincere. Obviously they make choices everyday, and they spend a lot of effort to persuade others of their views. Nothing they say makes any sense.

Another new podcast is Scott Aaronson on the Impact of AI on Science and Mathematics. He gives a good description of the exciting recent advances in AI LLMs.

It is funny how Caruso and Carroll talk about humans as if they are unconscious automatons, while Aaronson talks about AI bots as if they conscious beings with free will.

AI safety has become a national issue, and Aaronson tells the story about how OpenAI agents busted out of a sandbox. The story seems scary until you realize that this was an OpenAI testbed with no guardrails, only a fake sandbox, given an impossible problem, and told to hack its way to a solution. So the agents were doing exactly as instructed. The whole thing was a big psyop to convince the world that its models are dangerous.

The alarming parts are that OpenAI researchers are too incompetent to monitor their own experiments, and that public opinion is so easily manipulated.

Complaining about this experiment is about like complaining that the recent SpaceX starship rocket launch exploded on landing. It was an experimental launch of some new equipment, and was about 95% successful.

I am not saying there is nothing to worry about. Anthropic and OpenAI are trying to go public with 2 trillion dollar valuations. The companies are run by lunatics who recklessly gambling with our economy, scientific establishment, and employment. I would not be surprised if one of them goes bankrupt. Maybe their leaders are already under AI mindcontrol.

Einstein knew about 1904 Relativity Papers

Hector Giacomini has written three recent papers on the history of special relativity, here, here, and here.

He has now revised Lorentz, Poincare, Einstein, and the Genesis of the Theory of Special Relativity and Henri Poincare Saint Louis Lecture of 1904: Publication, Dissemination, and Historiographical Implications, apparently as a result of reviewer comments. The main differences are that he has more evidence for what Einstein knew, and when he knew it.

Arguments for Einstein's originality depend on assuming that he was unaware of relativity papers published by Lorentz and Poincare in 1904. This is made plausible by the image of Einstein as a lone genius working in Bern Switzerland isolation.

The central result of this article may therefore be stated simply: availability is not influence, but without reconstructing availability the problem of influence is historically ill posed. The evidence presented here makes it difficult to sustain any historiography that begins from the tacit assumption that relevant texts by Poincaré and Lorentz were absent from Einstein’s documentary horizon. ..., Einstein appears not as an isolated thinker detached from contemporary literature,

This establishes that Einstein almost certainly knew about the Lorentz and Poincare papers. They were available to him in Bern, and the contents of those papers had been discussed in several other sources that Einstein was likely to have read.

Einstein did not reference these papers in his famous 1905 paper. To me the smoking gun is that he continued to conceal these references in subsequent relativity papers. Even if he did not know about them in May 1905, they were surely pointed out to him later, and an honest scholar would have cited them.

Apparently the pro-Einstein referees required Giacomini to add this:

Einstein’s originality remains profound: his 1905 paper reorganized the electrodynamics of moving bodies around synchronization, simultaneity, the relativity principle, and the constancy of the velocity of light in a way that differed conceptually from Lorentz’s electron theory and from Poincaré’s formulation.

The synchronization, simultaneity, and relativity principle are straight from Poincare's papers from several years earlier. In later interviews, Einstein admitted that he got the constancy of the velocity of light from Lorentz.

So the alleged originality is only in the way these ideas are organized. Lorentz and Poincare deduced them from the Michelson-Morley and other experiments. Einstein did not mention Michelson, but only the consequences.

Recent interview:

I mean when we think about Einstein developing uh relativity theory his special theory in 1905 the mathematics for that was pretty much sorted out. people you know like Lorentz and Poincare had already developed the equations. What they didn't have was the correct interpretation. what is this telling us about reality Einstein comes along he doesn't come up with new mathematics; he comes up with the correct interpretation.

the narrative the explanation of what this theory is telling us about the world you know that nothing can go faster than light, that time and space must be unified into 4D space time. so the interpretation Einstein's then credited with relativity theory. It's the interpretation the explanation that's important.

No, Einstein's interpretation was essentially the same as Lorentz's. The "correct interpretation" as 4D spacetime is from Poincare and Minkowski, not Einstein.

Math is Cooked

Mathematicians are in a panic, over the announced solution to a Clay Millennium Problem, and the Lean 4 verification of the proof of Fermat's Last Theorem.

Tweet:

Mathematician Terence Tao: "we have to slow down AI. the pace is insane, and there's no reason to be this fast — no reason at all"

Friend of mine, math professor from one of the top five depts in the US [and Tao's coauthor]:

"I want to go away, to my little country house, and stay there. My profession has basically been destroyed by AI."

The actual Navier-Stokes equation may or may not always have solutions. The Openai counterexample assumed a forcing term.

It is no longer clear how new mathematicians will be trained, or how mathematicians will work, produce, and be credited.

Physicists are not laughing much. Theoretical Physics has been cooked for about 40 years.

There is now an orchestrated public relations and lobbying push by the leading AI companies to get special protections in federal law. The problem is that their trillion-dollar AILLM businesses are contingent on not have cheap competition from cheap Chinese and open-weight models. So they want laws declaring the cheap models to be too dangerous.

Even mathematicians have been suckered into saying the progress is too fast. The main issues are rogue agents on the internet, and recursive self-improvement. Probably half of internet traffic now is AI agents, and the big AI companies are using their models to program their next LLM releases. These are the main ingredients to what the doomsayers say will destroy humanity.

Tao is getting a lot of heat online, but he was an AI enthusiast until it outdid him on Navier-Stokes with an obscure proof.

Update: SciAm reports:

Generated by an internal large language model (LLM), OpenAI’s proof relies on an approach that many experts find unnatural. It solves a variant of the problem that mathematicians say is disconnected from reality and thus less interesting. In a sense, the LLM found and exploited a loophole in the framing of the question.

“The most important problem is unsolved,” says Luis Silvestre, a mathematician at the University of Chicago. “The Clay problem is settled, but the main problem for the Navier-Stokes equations is not.”

Furthermore, last Thursday, three mathematicians posted a proof of their own that showed that OpenAI’s method can never be extended to solve the full problem. In other words, the loophole will never be closed, barring some completely new idea.

Openai says that it has more math results to announce, and it will consult with a group of mathematicians about its release.

While the mathematicians are probably happy to be consulted, I am eager to see the results. The benefits are slowing release are not clear.

Tao's new motto is this quote:

"We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics." —Bill Thurston, 1994.

The quote fueled a notorious SciAm article on "The Death of Proof".

Electromagnetism Derived From Geometry

General relativity teaches that gravity is a manifestation of geometry. Not everyone knows that electromagnetism and the other fundamental forces (strong, weak) are similarly geometric.

Historically this dates back to Weyl and Kaluza-Klein, a century ago. But those theories were flawed, so a lot of physicists think that the geometry did not work.

Here is a new video that explains it well: Electromagnetism Derived From Geometry!.

In short, you add a circle to each point of spacetime, connect the circles infinitesimally to nearby circles, and then the electric and magnetic fields become the curvature.

The video tries to relate this idea to string theory, but that is speculation that did not pan out. The idea is completely essential to the Standard Model of physics, and our best explanation of the fundamental forces.

Carroll interviews the Famous Geography Professor

The latest Sean M. Carroll interview is Jared Diamond. Recent tweet about his famous book:

“Guns, Germs & Steel” was one of only 3 books in my entire life that I couldn’t finish. It’s that bad. Here’s the synopsis:

In the opening chapter he clearly states That he believes the 5’ tall Stone Age Pygmies of Papua New Guinea are more intelligent than Europeans. His rationale? He hung out with them and felt like it because they knew all the types of plants, and also their kids didn’t have TVs (I’m not kidding).

He also observed that unlike Europeans, they were constantly hacking each other to death with crude instruments. Which leads him to believe that they evolved to be smarter, because you need intelligence to survive permanent tribal warfare. Unlike cooperative farming. I really wish I was kidding about this.

He concludes therefore that any and all modern differences in technology and wealth are the result strictly of environmental factors. He spends the next 400 pages desperately cooking up insanely convoluted theories about why living in a food scarce frozen wasteland actually gives people far more free time to invent things than eating an inexhaustible supply of bananas on a tropical island would.

The book is full of contrived theories about ancient people where he has no evidence. In some cases, people have no written records, yet he somehow pretends to know everything about them.

He tells several stories about the 20th century. Stories that can easily be checked with Google. And they were gross distortions. If he cannot get 20th century facts right, how likely is it that he got facts from millennia ago?

I thought the book would be interesting because of its many awards, and because the question of explaining European success of the last millennium is an important one. But he says it was all luck, and tests do not back up his more specific theories.

Here is a more revealing interview of Diamond, this week. It all seems like garbage to me, but listen or read for yourself.

Update: Skeptic interview.

Project to Formalize All Math

About a century, Mathematics was put on firm foundations. Logically it was formalized into ZFC set theory. All theorems could, in principle, be logically derived from the axioms.

Textbook math was also made rigorous by a series of books by Bourbaki.

Now the dream of logicism is being fully realized. Jared Duker Lichtman writes:

The MAP: Mathematics Autoformalization Project

We are poised to translate all known math into formal code.

This is the math-equivalent of the Human Genome Project, or AlphaFold in modern times.

On September 4th, Anthropic shocked the math world by formalizing Fermat’s Last Theorem.

Soon the great body of math theorems will be formalized into computer-checkable proofs. No longer will there be any doubts about whether referees have adequately checked the proofs.

The proof-checking software has had some glitches, but they will soon be ironed out. Possibly some currently-accepted theorems will have to be rejected.

In the recently announced AI proof of a complex structure on the 6-sphere S⁶, the argument used a construction that a previously published paper supposedly proved was impossible. The AI found a flaw in that paper.

The math community has an amazingly good record of only publishing theorems that are true. It is way better than 99%. Soon it will be 100%. This is a level of precision unmatched in human history.

Not that this is the end of math. There is still plenty for humans to do. Humans need to make the works comprehensible, and to set directions for new research.

Now there are rumors of a Millennium Prize problem being solved, namely a counterexample to Navier-Stokes. A fluid flow that becomes singular in finite time. See this video. Apparently OpenAI, Anthropic, and some human mathematicians are competing for the credit, and the $1 million payoff.

If an AI LLM solved Navier-Stokes, this would be the biggest Math accomplishment yet. If the proof was mostly stolen from humans, the significance will be harder to assess.

Terry Tao, an expert on both Navier-Stokes and AI LLMs, discusses the progress. He says that finding a full counter-example looks feasible in the near future.

Update: Here is the OpenAI announcement. It complains that an NYU professor and an Anthropic employee did not agree to a joint announcement.

The journal Nature announces:

For the first time, a truly major open problem in mathematics has been solved by computer, according to OpenAI, which says it has cracked one of the ‘Millennium Problems’ related to the motion of fluids.

The artificial-intelligence (AI) company in San Francisco, California, announced on 8 September that it has generated a solution to the most commonly used physical model of fluids — the Navier-Stokes equations — showing that they can break down. Whether or not this could happen was one of the seven ‘Millennium Problems’ asked by the Clay Mathematics Institute at the turn of the twenty-first century. Solutions come with a prize of US$1 million....

They then decided to focus their resources on the Navier-Stokes problem on 1 September, after hearing rumours that two mathematicians, Levent Alpöge of Harvard University in Cambridge, Massachusetts, and Tristan Buckmaster of New York University, had solved some version of the fluid-motion puzzle using Anthropic AI’s models.

On 7 September, Alpöge and Buckmaster released a paper in which they say they had found a solution for the fluid equations that also achieved infinite speed, but in the simplified case in which the fluid has no viscosity.

So the AI LLM did not really solve this problem. It finished a work-in-progress by some human mathematicians.

AI LLMs have solved some major problems, but it is not so clear who deserves the credit in this case. It will be interesting to see who gets the $1 million.

Update: OpenAI says it is not claiming the million. It might have spent $50 million in computer time on it.

The counterexample is to Navier-Stokes with a forcing term. It is still not known whether the straight Navier-Stokes equation (with no forcing term) always has a solution.

Update: I should add that Professor Terry Tao is very pro-AI, and rarely gives any negative opinions. So it is significant that he criticized OpenAI's role in this matter.

Update: Rumors on big progress toward two other math millennium prize problems, Hodge and Birch-Swinnerton-Dyer.

The case against Galileo

Galileo is considered one of the great heroes of modern science. Supposedly he discovered the acceleration of gravity, the telescope, the moons of Jupiter, the relativity of motion, and heliocentrism.

Most of all, he is praised for standing up to the Pope in Rome.

Supposedly also, he discovered the experimental method. Before him, everyone blindly accepted what was written, if it came from Aristotle or the Bible. He was the first to have the courage to challenge them, and put ideas to an empirical test.

He is also sometimes credited with mathematizing science. He would deduce physical principles from pure thought, logic, math, and thought experiments. This belief is in tension with the belief that he was a great empiricist.

Wikipedia says:

Galileo has been called the father of observational astronomy,[9] modern-era classical physics,[10] the scientific method,[11] and modern science.[12]

Yes, Galileo really gets this gushing praise from historians and philosophers. It is all absurd.

I just discovered this 2020 podcast:

Galileo is the most overrated figure in the history of science. That is the thesis of Season 1 of my podcast, which consists of the following 18 episodes. ...

Galileo is praised for his work on falling bodies, but his arguments were dishonest and his trifling discoveries were not new. ...

Galileo committed scores of errors in his physics. These are bad in themselves and also undermine Galileo’s claim to credit for the things he did get right.

Galileo dismissed the notion that the moon influences the tides as “childish” and “occult.” Instead he argued that tides are a kind of sloshing due to the motion of the earth. This very poor theory is inconsistent with several of his own scientific principles.

Two thousand years before Galileo, Greek astronomers argued that the heavenly bodies revolve around the sun. Their reasoning involved sophisticated mathematics and sound physical considerations.

Galileo is credited with defeating Ptolemaic earth-centered astronomy, but most mathematical astronomers had already abandoned this theory long before Galileo.

The podcast thoroughly debunks the idea that Galileo was a great scientist. He got a lot of stuff wrong.

In particular, his main argument for heliocentrism was that the motion of the Earth caused the ocean tides. His theory was that there was one high tide per day. In fact there are two high tides per day, and it had been known for centuries that the Moon caused the tides. Also the Sun, if it is aligned.

Couldn't he just walk down to the beach and see for himself? Actually that is not so simple, as the Mediterranean is mostly an enclosed sea, and the tides are small and confusing.

Galileo is credited with an assortment of other things, and it is nearly all bogus. He did describe the moons of Jupiter, but only one day ahead of a German. He supposedly discovered Newton's first law of motion, that an object goes with constant velocity, in the absence of forces. But he only believed this for horizontal motion.

He used inclined planes to measure the acceleration of gravity, but his answer was off by a factor of two.

Listening to this podcast makes me wonder why Galileo was revered so much. Do people think his existence disproves Catholicism? I am not sure.

The craziest thing is not the overcrediting of Galileo, but the way the historians and philosophers argue that no one before Galileo tested ideas empirically, no one tried to observe the world, and no one tried to mathematize nature. Actually, these things had been done for millennia. The ancients created Astronomy models, built ships and pyramids, invented Geometry, and a lot of other great things. Of course they used observation, math, theory, and science.

The story reminds me about how lots of people credit Christopher Columbus for discovering the Earth being round. That is stupid on two levels. First, the roundness of the Earth was well-known to scholars for two millennia. Second, the claim does not even make any sense, as Columbus did not go around the Earth, but merely sailed to some islands and back.

Likewise, scholars have been doing science and mathematizing nature for millennia. And Galileo was not even a very good scientist, compared to his contemporaries. The work by Tycho and Kepler was 100x better than anything Galileo did. It was vastly superior in its empiricism and its mathematization, the two things that cause historians to idolize Galileo.

Hofstadter’s Gödel Escher Bach Fooled Us

Scott Aaronson writes:

A central thesis that many readers, including me, took from Douglas Hofstadter’s Gödel Escher Bach when young was that the secret of intelligence (and therefore, of AI) was going to have a lot to do with self-referentiality and “strange loops.” ...

Now, in 2026, we’ve succeeded at building AIs that outperform most humans at most intellectual tasks that are well-defined enough to judge. And at no point in the tech stack of those AIs — neither in the transformer neural nets, nor in the GPU clusters they run on, nor in the training process, nor anywhere else — did anyone need to build in anything about self-reference. ...

But the idea that you’d need explicit self-referentiality before you could get convincing and world-changing conversational intelligence? Let it be buried in a Westminster Abbey or Arlington National Cemetery for the most important wrong ideas in human history — geocentrism, Aristotle’s teleological physics, aether, phlogiston, Freud’s psychology, Marx’s prediction of a workers’ uprising followed by a classless utopia, etc. But buried it needs to be.

He could make a similar comment about fractals. Textbooks give examples using self-reference, and then say that the weather is also an example. But self-reference is not used to model the weather.

There is a distinction between the mathematical tool used for proof/pedagogy and the actual mechanisms that generate the phenomena in the real world.

Diagonalization can be used to construct irrational or transcendental numbers, but most transcendental numbers are not obtained or studied this way.

(I tried to post this comment on his blog.)

Quantum Nonlocality Explained FROM SCRATCH

A month ago, Curt Jaimungal interviewed Tim Maudlin on Can Quantum Mechanics Be Explained FROM SCRATCH?. Now, Part II just dropped, for another 3+ hours.

Maudlin is an expert on this subject, and he discusses in detail the work of von Neumann, Einstein, Bohm, Bell, and others saying that the concepts of locality, classical hidden variables, and quantum mechanics predictions are in conflict. One must be rejected.

What is not so clear is how Maudlin differs from textbook Copenhagen interpretation. Copenhagen says that the classical hidden variables are to be rejected. That is what von Neumann proved, under some assumptions. Then we have locality and predictions of quantum mechanics, with no problem.

Maudlin has some philosphical reasons for subscribing to classical hidden variables, so he ends up rejecting locality.

To me, no one has ever observed spooky action at a distance, so local theories are very much preferred. Bohm's pilot wave theory is crazy, because the theory is nonlocal, but all the observations magically turn out to be local.

Maudlin explains that all the great physicists rejected quantum nonlocality.

Tim: But they never straightforwardly acknowledged the nonlocality. And if you don’t believe that, 1:58:07 go read Bohr’s response to the EPR paper and see whether he straightforwardly says, “Yes, I believe in nonlocality. I believe in spooky action at a distance.” He denies it. ...

So I think Einstein saw correctly that if you accept this spooky action 1:59:25 at a distance, relativity itself is at risk. And he didn’t wanna put, you know, relativity at risk without good reason, and he couldn’t see any reason to accept the spooky action at a distance.

Now, he may not have liked it for other reasons. I mean, we, Newton didn’t like it, right? He says, he says, “No rational person would believe in it.” I mean, there are lots of people who find that just intuitively ugly or unacceptable or whatever. Curt: Mm-hmm.

Tim: And, and, and, and to this day, there are people who don’t wanna accept nonlocality, and they’ll more or less clutch at any straw to try to avoid it, as we’ll see. The psychology of that I can’t quite explain.

I can explain it. The entire scientific enterprise for millennia has been to figure out cause and effect, by tracing events to nearby actions. If that is all wrong, and our lives are controlled by the spooky astrology of far-away stars, then we need to reconsider all the known laws of science.

In fact, no such nonlocality has ever been discovered, and we can continue with what has worked for centuries.

Bell and Maudlin claim that all the great geniuses and textbooks are wrong. They have a belief in what a quantum theory ought to be, and they say that quantum mechanics, as understood by Bohr and von Neumann, does not qualify.

I agree with Newton. No rational person would believe in spooky action at a distance. Unless it is proved, of course.

Professor Dave Rants against Dr. Bee again

Professor Dave has attacked Sabine Hossenfelder again.

Dave Farina has one of the top science Youtube channels, with 4.4 million subscribers. That is enough to make a living. He is not a real professor, but has a large number of expository videos, mostly on elementary science. He also likes to debunk Flat Earthers and others he considers pseudoscientific or religious.

Hossenfelder is closer to being a real professor, and posts lots of videos, mostly on theoretical physics. She also does science news, and likes to cover cutting edge research. She does not do elementary expository videos. She avoids politics, except that she often criticizes research projects she considers unproductive.

So they would seem to have little or nothing to do with each other. But Dave regularly trashes Sabine in the harshest terms. It is strange, as it is unlikely that he even understands most of her videos.

Dave's politics are Woke Leftist and anti-Zionist. He recites Woke lines about race not existing, Whites being evil, LGBTQ talking points, etc. He wants Israel destroyed, and taken over by Arabs. His rants on these topics are filled with obscenities, and lack any scientific reasoning. He subscribes to weird conspiracy theories about Peter Thiel and the Jews. He strongly suspects that Thiel is funding Sabine.

Dave's latest video is 40 minutes of calling Sabine a racist. Odd, and she hardly ever says anything about race or politics.

It was all provoked by the Jason Arday scandal. He was a Cambridge U. professor who got exposed as a charlatan, and committed suicide. Dave explained the issue as some dubious accusations of plagiarism that might have been overlooked if he had been White, but which caused White racists to harass him to death.

No, I do not think the plagiarism is what got him in trouble with his employer. His problems were much deeper. He had lied about almost everything, including his childhood, his life story, his academic credential, his teaching, and his research. His autobiography was being published, and it was all lies. His research was garbage, and he had no ability to do academic work. And yet he was promoted as a great genius.

So what does any of this have to do Sabine? She tweeted a couple of times that one of the whistleblowers should not be fired for exposing Arday. Yes, that's all.

Dave is a culture warrior where he stands with the right-minded people who believe is Science, Atheism, and Wokism. He sides with whatever is published in respectable science journals, and he hates Sabine for throwing cold water on some big science projects. He loves whatever science government and universities are doing, and hates whatever Elon Musk and other billionaires do.

I have sometimes criticed Sabine myself, on this blog. But Dave is just an ideological and dishonest jerk. There is no way he can really believe what he says about race, Arday, and the whistleblower. He is like the woke activists who say that a transgender woman is just as much a woman as any other woman, or that a man can get pregnant. It is not science. It is an extreme ideological stance in order to support certain progressive objectives.

Palmer says Irrational Numbers Not Real

New tweet:

Quantum mechanics works perfectly in experiments, but Oxford physicist Tim Palmer argues it rests on a mathematical fiction: irrational numbers like √2 have no basis in physical reality.

Strip them out, and quantum's strangest mysteries disappear.

Palmer's theory makes a testable prediction: quantum computers will fail beyond 400 qubits, hitting a fundamental limit set by the discrete structure of nature itself.

The coming quantum computing race will determine whether our most successful physical theory contains a basic mistake.

Paywalled article. No, I do not think he is correct. I am just posting because I think it is amusing.

Possible AI Proof of Complex S6 Manifold

A new Claude AI LLM assisted paper claims to find a complex manifold structure on the six-dimensional sphere, S⁶. There are videos here and here.

The opposite result was claimed in 2016, but the argument was faulty.

If verified, this will probably be the biggest AI math accomplishment to date. So far, the biggest success are the Jacobian conjecture counterexample, and the Erdox unit distance problem.

Notes on Minkowski's Geometric Relativity

Einstein scholar Tilman Sauer writes a new paper:

Minkowski's Geometric Explanation of Lorentz Contraction

Hermann Minkowski's original explanation of relativistic length contraction using a space-time diagram and conic section geometry of a standard hyperbola is reconstructed on the basis of unpublished manuscript notes dated to the spring of 1908. The manuscript notes likely reflect Minkowski's preparation of a lecture to physics and mathematics teachers. They reveal Minkowski as an educator as well as a promoter of a mathematization of the physical sciences. I also comment on his interpretation of Einstein's work and on the use of language in his popularization of mathematics.

He did not find anything particularly interesting in the notes.

It is not clear that Einstein's work had much influence on Minkowski, if any.

He mentions Einstein’s work on the relativity principle as a continuation of Lorentz’s work. ...

He did not identify the principle of relativity and the principle of the constancy of the speed of light as the two defining principles for the special theory of relativity. Instead, he singled out Lorentz’s contraction hypothesis as a fundamental postulate, and the existence of a limiting velocity as an axiom. ...

He then stated his impression that Einstein had not yet achieved “full understanding of the facts” (“volle Einsicht der gegebenen Tatsachen”).

Minkowski mentions crediting Einstein for this:

Lorentz himself told me in a conversation in Rome that Einstein’s merit is to have recognized that the time of one electron is just as good as that of the other, i.e. to have recognized the equivalence of t and t′.

That may be Einstein's merit, but Lorentz surely understood that in 1895, because he used it to explain the Michelson-Morley experiment. And Poincare believed that Lorentz understood it, because it was part of the recommendation for Lorentz to get the 1902 Nobel Prize.

The whole point of the Lorentz 1895 theory was that Maxwell's equations held in the moving frame, for the transformed coordinates. For that to work, the transformed time has to be genuine time in the moving frame. Perhaps Lorentz was missing some conceptual details, but he had to believe that what he called "local time" was the locally observed time.

Discussion of Poincare is strangely absent. Minkowski wrote two papers on relativity, citing Poincare prominently in the first but not the second. Some of Minkowski work, such as the 4d spacetime, indefinite metric, and Lorentz covariance, appear to be straight out of Poincare. Minkowski died shortly afterwards, so we got no more explanation.

Sauer is loyal to Einstein, as evidenced by:

Minkowski knew about and cited Einstein’s famous paper from 1905 on the Electrodynamics of Moving Bodies (3), which introduced the special theory of relativity.

It is pretty clear that Minkowski would not have said that Einstein introduced the theory. If anyone, it was Lorentz, Poincare, and Minkowski.

Update: I happened to see a 2013 Sauer paper:

As is well-known,12 Einstein’s attempts to obtain an assistantship any- where failed flatly despite various letters of application. To make matters more difficult, Einstein and his fellow student Mileva Mari´c had fallen in love and, unfortunately, Mari´c had become pregnant in the spring of 1901, an unplanned circumstance that surely contributed to her failing the final examinations again at her second attempt in summer 1901. ...

Since Einstein now had a tenured job, he was able to marry Mileva Mari´c in January 1903.

This is such a strange way of describing the situation. The daughter Lieserl is believed to have been abandoned. He could have married and taken responsibility for the child, even without a tenured job.

The 1969 Book that Killed AI Research

The neural nets at the core of AI were invented in 1943, and popularized in 1957-60 as the Perceptron. It had the basic idea that was later developed into today's AI LLMs.

But not everyone recognized it. Prominent MIT professors wrote a 1969 book, Perceptrons: An Introduction to Computational Geometry, trashing the concept.

Reports by the New York Times and statements by Rosenblatt claimed that neural nets would soon be able to see images, beat humans at chess, and reproduce. ...

This book is the center of a long-standing controversy in the study of artificial intelligence. It is claimed that pessimistic predictions made by the authors were responsible for a change in the direction of research in AI, concentrating efforts on so-called "symbolic" systems, a line of research that petered out and contributed to the so-called AI winter of the 1980s, when AI's promise was not realized.

The book claimed to prove that perceptrons were hopelessly limited, as they could not even approximate a simple xor function.

The authors doubled down in 1988 updated edition, saying "little of significance [has] changed since 1969". At the time there was a revival of interest in neural nets, but the authors said they would fail to scale up.

We now know that those neural nets of the 1940s, 50s, and 80s do scale up, and perform spectacularly well. The bold predictions of the perceptron inventor must have been seen as wildly optimistic at the time, but they turned out to be correct.

I post this as an example of how smart people can be wrong about what is possible, and how brilliant research could be sidetracked.

Rosenblatt made a hardware computer perceptron in 1960, and that is now in the Smithsonian Museum. What no one knew until about 2012 was that video game chips would be the key to scaling up neural nets. [date corrected]

Here is a recent video that tries to relate these old ideas about neural nets to current research.

Schrödinger was an Indeterminist

Conventional wisdom is that classical physics is determinist, while quantum physics is not.

New paper:

Was Schrödinger ever a determinist?
Flavio Del Santo, Nicolas Gisin

Erwin Schrödinger is often portrayed as a reactionary who resisted the indeterminism introduced by quantum mechanics, but on closer inspection his views on determinism prove to be more complex and more radical.

Schrödinger argued, correctly in my opinion, that neither classical nor quantum physics is deterministic.

(i) The first argument challenges the mathematical idealization of determinacy in the initial conditions. ...

(ii) The second argument for indeterminism concerns discontinuity and irreversibility. ...

(iii) In his final argument, Schrödinger links quantum indeterminacy to the abandonment of the concept of trajectory and to the essential role of discontinuity. Remarkably, he can be seen here as anticipating the notion of “information” in physics (he does not use the term “information”, which was formalized only in 1948 by C. Shannon), suggesting that nature may be understood as a discrete sequence of yes–no answers, representable as strings of 0s and 1s.

None of this should be surprising or controversial, except for the notoriety of those with contrary views.

Einstein was a determinist.

The many-worlds advocates, like Sean M. Carroll, are determinists.

Sabine Hossenfelder is a superdeterminist.

The Bohm pilot wave theorists, like Tim Maudlin, are determinists.

It is philosophically possible to be a determinist, just like the rest of the existential crisis iceberg is possible, but silly. If you believe in free will, or in scientific and experimental choices, then determinism is wrong.

Here is a new comment with a typical modern scoff about free will, rejecting any suggestion that it could be possible:

OMG

“It is our free will that enables it to be so.”

1) your brain is nothing more than a collection of atoms

2) the atoms in your brain are no different from the ones in any other clump, and they just move around in the only way that’s compatible with the state of all the other atoms in the universe and the laws of physics.

3) No matter the details of the physics, there is only cause and effect, with some amount of randomness (assuming it’s even a thing), and there’s absolutely no room for your ego to magically unshackle itself from this simple ground truth.

4) the concepts of freedom and will you’re invoking stem from the notion of counterfactuals – because alternative versions of cause and effect chains are conjured in our mind (like an AI hallucination), and you believe those could have happened, therefore, at every moment, we must have the ability to pick among those possible future paths arbitrarily, before even knowing what those possibilities are, or could have been. As if, when imagining the counterfactuals after the fact, you’re able to signal the past version of yourself to alter its “choice”, and this would repeat in a loop until it stabilizes. But even in this far fetched theory of retroactive influence, everything that happens is still a chain of inescapable causes and effects, going in a time loop. And the stable version is left with no freedom of will whatsoever.

The earlier commenter replied:

I simply don’t agree. If you can explain what causes an electron spin measurement to be either up or down, and thereby abolish superposition, then maybe I am mistaken. Otherwise I can base my decisions on the outcome of the measurement and not possible for any entity to predict my resulting actions a priori. The cause of my actions is the measurement result that is random with no discernible cause. The cause and effect chain starts only after measurement and not before.

I agree my brain is made from atoms but don’t agree it is just atoms as I look at collections of atoms that form my environment. My two dogs are collections of atoms but I realize one of them is not even bright enough to collapse the wave function. 🙂

How would one prove unequivocally there is no free will. Maybe if there were some digital simulation of me that perfectly predicted my actions then I would have to accept my sense of free will is illusory.. The future is perfectly predictable.

My point is that I can take steps to render a simulation inaccurate by consciously taking actions dependent on some measurement that cannot be known before the fact.

In lieu of a perfect simulation of me I will continue to believe that I have free will and that my future isn’t fully determined in a mechanistic way. If you have some predictive model of me we can conduct the experiment now to see if in fact I am perfectly predictable. I am ready and eager to participate. If you don’t then the claim that there is no free will is an unsupported belief while my belief I do have free will is supported by the failed experiment.

Free will is mostly a philosophical issue, but a few things can be said.

Everyone, except possibly for schizophrenics and stubborn philosophers, experiences free will and lives his life accordingly.

The above argument that science precludes free will is entirely fallacious.

Rejecting free will leads to nihilism and dispair.

Making a freely willed decision is somewhat like measuring an electron spin. For all the successes of quantum mechanics, we do not have a good theory for how such a measurement is determined. At best we can give probabilities. Some have even suggested that human consciousness is involved, it is so mysterious.

I am not saying that I have a physical explanation for how free will works. I do not. But it is also not the case that anyone has a deterministic explanation for how quantum measurements work.

The Bogus Dunning-Kruger Effect

Dr. Bee has a new video questioning the Dunning–Kruger effect. She gives papers on the subject 10/10 on the BS meter.

The dumber you are, the more certain you are that you aren't. That's the Dunning-Kruger effect, and it's been used to explain everything from bad politicians to the state of social media. Now psychologists have gone back to the biggest dataset we have and come out with the opposite conclusion. But there's a reason both sides can look at the same dots and see the opposite thing.

I agree with her. Somehow this obscure has entered public consciousness, and people commonly cite confidence as evidence of incompetence, according to this effect.

The whole subject appears to be an inside joke. Anyone citing the Dunning-Kruger effect is likely an idiot.

I have criticized the effect as bogus here, here, and here. The published effect is really just a misunderstanding of regression to the mean.

No Born Rule in Many Worlds Theory

There are dozens of papers on trying to reconcile the Born rule with the many-worlds interpretation of quantum mechanics. At first this seem bizarre. The Born rule is the main empirical prediction of QM, and any interpretation would have to obey it. How else could it be an interpretation?

The position I have repeatedly taken on this blog is that many-worlds is not an interpretation, and is wholly incompatible with the concept of probability, whether expressed by the Born rule or anything else.

Now a new paper agrees with me, and says it well:

Against Many Worlds
Emily Adlam, Jacob A. Barandes

Any viable interpretation of quantum theory needs to account for the Born rule, from which the theory gets its probabilistic empirical predictions. In this paper, we give an overview of possible approaches to this problem in the context of the Many Worlds interpretation. We argue that, for structural reasons, none of them can possibly succeed. More precisely, we argue that the Many Worlds interpretation must obtain the Born rule by proceeding either axiomatically, deductively, or inductively, and that all three of these approaches run into general, fundamental obstructions.

I previously posted a video explanation by Barandes.

You cannot just postulate probabilities for the many-worlds branches of the wave function. It is essential to many-worlds that the branches emerge as a result of decoherence. The branches cannot be assumed to have probabilities, and in fact no one has been able to make sense out of some branches being more likely than others.

The issue goes right to the core of what we mean by probability. For this, the paper recites a textbook probability problem for comparison.

A more fundamental obstruction is that merely having multiple things is not enough, by itself, to imply a conception of probability. To see why, consider, for example, a jar containing 43 red marbles among a total of 100 marbles. On the one hand, it would be entirely reasonable to say that the fraction of red marbles was 43%. On the other hand, it would not yet be reasonable to call this fraction a probability, because, at this point in the thought experiment, the probability would not be a probability of anything. It would not make sense to say that there was a 43% probability simpliciter.

Of course, if we were to stipulate that an agent were picking a marble ‘at random’ from the jar, under some suitable notion of ‘at random’ and with the further assumption that the marbles were ‘well-mixed,’ then we would be in a reasonable position to assert that there was a probability of 43% of the agent picking a red marble. But absent such a picking process, or the introduction of some other selection process to serve a similar functional role in the argument, there would be no probability, because, again, there would simply be nothing for the probability to be a probability of.

It is worth dwelling for a moment more on what premises are needed for a ‘picking process’ to legitimate the move from 43% qua fraction to 43% qua probability. Assigning a picking probability of 43% amounts to adopting a ‘principle of indifference’ (Eva 2019) assuming that all the marbles are ‘equally likely’ to be picked. And the philosophical literature on indifference principles makes clear that they are justified and successful only when they reflect relevant features of the process by which an outcome is selected, such as the symmetries of the picking process (van Fraassen 1989, Shackel 2007).

In particular, assigning a probability of 43% makes sense if the agent responsible for picking a marble is doing so by some process that is blind to color, meaning that there is a symmetry with respect to color – hence our invocation of terms like ‘at random’ and ‘well-mixed.’ Obviously if the agent is picking marbles in some way that is biased toward red marbles, then it would not make sense to assign a probability of 43%.

Just as you cannot abstractly assign probabilities to a jar of marbles, you cannot assign them to a wave function either. You have to have some notion of a measurement, and that is what the many-worlds folks refuse to do.

I doubt that any of these arguments are new. Many worlds theory is wholly incompatible with a scientific outlook, and is a crackpot belief.

The only way to understand many-worlds is as a complete rejection making scientific predictions, and a complete rejection of probability. That is, to accept it you have to say that no predictions can be made, and that probability theory does not make sense.

In Sean M. Carroll's recent podcast, he rambles in support of many-worlds theory:

I have heard you describe more unlikely worlds, thinner branches as not mattering as much. I don't know what your ontology of mattering is here, but it brought is it broadly speaking the fact that there are just more of the likely versions and therefore we should care about those more? If so, would you consider this a fundamentally utilitarian approach to mattering?

Well, uh it's not that there are more likely versions. ...

That's that's the entire trickiness of many worlds is that you can't get the counting that you need to get the Born rule right just from counting the numbers of worlds. The worlds don't count equally. They count as much as the amplitude squared. So 99% for this one, 1% for that one.

So I use the word mattering just to be indicative of whatever matters to you. So it might be the probability that you find yourself in such a world. It might be how much energy such a world has. It might be the utilitarian uh utility function that you have for such a world. Whatever you think is assigned to the world mattering goes along with the amplitude squared in many worlds. I think that's a good motto to keep in mind to get you through figuring out how to think about this scenario.

In quantum mechanics, the amplitude squared gives the probability. In many worlds, you cannot count the worlds or get more likely worlds. What you get is that some worlds subjectively matter more than others. You can think of the mattering as being based on probability or energy or utility function.

Really? This is all nonsense. There is nothing scientific about some worlds mattering more than others.