吾舉兩例供各位辨論時各取所需好了:

Both are mathematicians of the highest rank.

Ramanujan, was self-taught and with a singular working style. He had no notion of logic and didn't even know what constitutes a mathematical"proof". Consequently he would fail many elementary problems.

Grothendieck, was well trained and worked in a highly abstract style. Once he was giving a talk about prime numbers 貭數. Baffled by his wildly generalized and abstract arguments, the audience asked : would you provide with an instance of a prime number and proceed with it? G answered: 51 (which in fact can be decomposed into 17x 3). Certainly this didn't mean G could not do some elementary problems, but for sure he could be quite clumsy when handle them.

 

 

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