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nimonian6 karma

*Infidelity has existed as long as mating fidelity has existed

nimonian1 karma

There is a saying in academia that 'mathematics is a young man's game'. This is disheartening to many researchers who reach 30 without proving something important, and evidence seems to suggest that most of the best theorems in mathematics were proven by people younger than 30. Is this just a remarkable coincidence, or is something going on here? Maybe it is not related to cognitive ability, per se, but a willingness to take on a daring and seemingly hopeless task and keep at it for up to a decade. I'd be interested in your take on this phenomenon.

nimonian1 karma

Thank you from the bottom of my heart for your message. Not only is it beautifully written, it resonates. When I see a quadratic equation these days, I don't think at all about what it is really saying, about its essence, and I don't justify my thoughts and actions by appealing to their meaning or worthiness, I just shift the symbols around, knowing by experience that my manipulations are correct. I am unlikely to ever discover anything new about quadratic equations (I know these days there is nothing new to discover here, it's just an example). In some ways, this is an essential part of mathematics: without taking certain procedures for granted, our thoughts would forever be clouded by minutiae and would obscure the bigger picture. But it also seems that this process of assimilation of knowledge into our existing mental structures, and the necessary compaction of mathematical praxis, also encourages routine modes of thought.

I'm led by your message to think of two people looking at clouds. One of them says: 'Look! There's a monkey, and there's a tree, and there's a giraffe!' and the other, who isn't in this habit, simply notices that it never rains when the clouds aren't there, and thinks 'maybe that's where rain comes from?' The first is distracted from this deduction by seeing what he knows and being in a particular habit of mind; the second just sees clouds for what they are. (It's not the best analogy, because seeing faces in clouds is useless, whereas recognising quadratics in formulae is useful; but it does capture a little bit the point being made.)

I guess it's easier to think outside the box if you're not in the box. But I am encouraged by your closing comment - maybe being aware of this pitfall is enough to help us be more willfully rebellious, and be less constrained by our own experience. Maybe venturing into a new field occasionally will help with this. Thanks again!