Brilliant vs Genius

Source: Thomas Cayne/Quora, Dec 2022

Terry Tao – Brilliant

On the right-hand side is Terry Tao.

He was a child Mathematics prodigy beyond most anything what was known before him, he wrote hundreds of papers with many brilliant co-authors which were published in the best journals around, is one of the most-cited mathematicians in the world, and has gathered an astonishing pile of major awards.

Fields medal. Salem award. SASTRA Ramanujan award. Crafoord prize — I could go on and on.

Some have called him the greatest mathematician of the last 100 years.

if we look at the absolute highest level of mathematical research, Tao’s greatest talent is … speed. He is extremely fast, and works like a mathematical organism which is composed of between 5 and 10 absolutely brilliant top-notch mathematicians.

But if you look at the various specialisms in which he has published the most marvelous results, you will see that his (absolutely brilliant) co-authors are (more or less) as brilliant as he is.

The difference is: Tao tops between five and ten different areas in Mathematics — much more than other authors.

Tao is a concatenation of five to ten of the most brilliant mathematical specialists in the world.

Peter Scholze – Genius

also a child mathematical prodigy, crushed many records, published some dozens of papers — much much much much less than Tao ! — all published in the best journals around. And is gathering all the big awards as well.

here is where the story differs.

Almost every single one of his papers are milestones in the specialism it is published in. His Ph. D. thesis literally rocked Mathematics, and it entirely changed Arithmetic in an almost unthinkable way.

To put it differently: if Scholze starts working on a (major) problem or in a (major) specialism, he changes it much more radically than Tao does.

And Scholze essentially does it on his own.

To put it even more differently: you can put ten of the best specialists together to “create Tao,” but even if you put one hundred of the best specialists together, you simply will not create Scholze.

He has a singular mind. He is too original.