Wednesday, March 23, 2022

When were Negative Numbers Invented?

I thought that negative numbers were ancient, but have recently learned that mathematicians of a few centuries ago distrusted them.

Wikipedia says they go back to China and India a couple of millennia ago. I doubt it.

I am looking for an example of an algorithm:

1. Compute a number X that can be positive or negative.

2. Use X to compute something else, without dividing into two cases.

In doing my income taxes, I cannot find any example of IRS using such an algorithm.

I am guessing such algorithms started to appear around 1800 or so.

Wikipedia explains:

For a long time, understanding of negative numbers was delayed by the impossibility of having a negative-number amount of a physical object, for example "minus-three apples", and negative solutions to problems were considered "false".
But that is not impossible at all, as having "minus-three apples" means owing 3 apples.

Furthermore, lots of other natural measurements can be negative. I could ask "how far are you east of the landmark?" and get a negative answer. Likewise, feet below sea leval, freezing temperature, or a countdown to an anticipated event. If I ask the cost of something, and it turns out to be a benefit, then it has negative cost.

Newtonian Physics was invented around 1680. Today, textbooks explain it with force diagrams, where force vectors are added. These seems to require negative numbers, as forces can cancel out. It also seems to require vectors, but vectors were not invented until about 200 years later. It is hard to imagine that Newton did not understand negative numbers, but maybe not, if he did not understand vectors either.


  1. To what I remember of my mathematics history from my professors, negative numbers were primarily an offshoot necessity of cartesian graphing, which required negative numbers in order to create four quadrants around an origin at zero. At the development of Cartesian graphing, it is my understanding that the idea of numbers fundamentally changed from being primarily considered as a quantity at all, and became considered more as elements of coordinates designating lengths or distances from other points and zero in a cartesian plane.

    When negative numbers became graphically spatial as opposed to numerically quantitative, they became useful.

    The problem with all cartesian graphs and manipulations is that there are several very immutable required geometrical assumptions baked into the very graph itself that are often ignored and are rarely considered when folks muck about with them, which in turn leads to much of the paradoxical bullshit generated by non-euclidian geometries parading about as explanations. This is largely the result of mathematicians who pretend to forget what geometric definitions are logically dependent upon whenever it suits them and decide to selectively ignore basic axioms because they are inbred card cheats.

    Bullshitting at math is really not much different than cheating at cards. The folks that do it think they are vastly clever because they got away with something they know they aren't supposed to be doing, and hope to always be long gone by the time someone cleans up their sloppy mess enough to find out. Many famous 'mathematicians' were also con artists, it seems to go with the territory.

    “If you thought that science was certain - well, that is just an error on your part.”
    ― Richard P. Feynman

  2. Dear Roger,

    No Indian-born ``Indic'' (read ``Brahmin'') ``Researcher'' is ever going to respond to you.

    But Indian-borns in your country (they were born mostly in the ``Brahmin'' castes, and mostly are casteists) are going to ``respond'' to you in their own echo-chamber. Soon enough. *I* can guarantee you that. (They will respond to ``Which British?'' ``Abrahamics'' Etc. Even while making tons of money in your own country. My country-borns, I mean. They are like that.)

    I will read this post a bit more carefully should I develop a sufficient interest in maths (and not ``math'') in near future.

    PS: Hope you really run this comment. TIA.

  3. I was not expecting anyone from China or India to respond.

  4. What about ... "losing three apples and owing it to onesself to find them"?

  5. Yes, negative numbers occur naturally. The question is whether the ancients ever considered negative numbers just like positive numbers.