Genius doesn’t trample on mastery and leave it in the dust

This was born as a blue sky thread, instigated by someone asserting the opposite of the title.

Let me start by introducing context. I am a senior mathematician, which means I’ve spent 40 years living of and in a group which supposedly has geniuses.

Indeed some ideas are truly beautiful, and surprising; and some people have more of those, and of wider impact, than the average practitioner. 

I don’t like the word genius, but let’s use it for simplicity to describe such people. They do not stomp on anyone else: in fact, their typical attitude is to found a school, and (with a few asshole exceptions!) seniors recognise their gift, honour it, and support them as far as possible.

Such recognition and support are much more likely if the “genius” is a non-disabled, straight-passing white man.

Exceptions exist, of course: maths and physics buildings in Cambridge UK are much more accessible than in Oxford UK because Hawking.


In general, again, new ideas are celebrated by weaving them into the structure of existing knowledge: they shed new light onto existing results, and reverberate into far away areas in the field. No one stomps on anyone else. It’s a moment of joy.


This applies also to new ways of math-ing: we have used computers to calculate, then to typeset, and now to check our proofs and support our search for ideas. The only exception I personally know are the brilliant ideas of @pwr2ppl.bsky.social but I have my own opinion on why that is.


Genius in mathematics isn’t an up and down switch: it’s a continuum, which we all share to some degree, and the work of recognised geniuses builds on and interacts with work of everyone else. 


Progress becomes sometimes evident when a “genius” arises, but it wouldn’t exist without worldwide contributions of a number of people of different levels of ability, interest, and persistence. Reading Singh’s book on Fermat’s last theorem is a good starting point in this sense.

No one tramples on anything. No one leaves anyone in the dust. Michelangelo, like all other creatives, had to learn the basic techniques from established predecessors before he sculpted his immortal David from a piece of marmor another artist had “ruined”.




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