He has since won many other prizes, including a MacArthur ‘‘genius’’ grant and the Fields Medal, considered the Nobel Prize for mathematicians. Today, many regard Tao as the finest mathematician of his generation. ...Sergiu Klainerman explains that the Fields is nothing like the Nobel at all:
Possibly the greatest mathematician since antiquity was Carl Friedrich Gauss, a dour German born in the late 18th century. He did not get along with his own children and kept important results to himself, seeing them as unsuitable for public view. They were discovered among his papers after his death. Before and since, the annals of the field have teemed with variations on this misfit theme, from Isaac Newton, the loner with a savage temper; to John Nash, the ‘‘beautiful mind’’ whose work shaped economics and even political science, but who was racked by paranoid delusions; to, more recently, Grigory Perelman, the Russian who conquered the Poincaré conjecture alone, then refused the Fields Medal, and who also allowed his fingernails to grow until they curled.
Concerning the first issue, the differences between the Fields Medal and the Nobel Prize can hardly be exaggerated. Whatever the original intentions, the Fields Medal is given only to young mathematicians below the age of forty. To have a chance at the medal a mathematician must not only make a major contribution early on, he/she must also be lucky enough to have its importance broadly recognized before the arbitrary fortieth mark. This means that, if an area of mathematics is not represented in the composition of the Fields committee at a given International Congress, truly original and important contributions in that area have very little chance.The Abel Prize is maybe the closest to being a Nobel Prize for Math.
In contrast, the Nobel Prize has no age limits. The role of a Nobel committee (in natural sciences) is, at least in principle, to identify those breakthroughs deemed most important by a broad segment of the scientific community and then decide who are the most deserving contributors to it. In contrast with the Fields Medal, which is given strictly to an individual, independent of whether other people might have contributed important ideas to the cited works, the Nobel Prize can be shared by up to three individuals. Thus, in theory, a Nobel Prize is awarded primarily for supreme achievements, and only secondarily to specific individuals. ...
In fact mathematics does not have any prize comparable with the Nobel Prize. The other major prizes — Abel, Shaw, and Wolf — don’t have any age limitation but are almost always given to individuals, based on works done throughout their careers, rather than for specific achievements. Even when the prize is shared there is, in most cases, no identifiable connection between the recipients.
There is a wide perception that all the good math is done by young math prodigies. The most famous big math problems of the last 25 years were Fermat's Last Theorem and the Poincare-Thurston conjecture. Both were by mathematicians around age 40, and that is probably the age of highest productivity.