Mathematics as a social entity
One of our greats, Bill Thurston passed away on Tuesday. Since then my friends have been digging up old writings and discussing the work that he did. This short essay in response to a Math Overflow question caught my eye though.
[quote] It’s not mathematics that you need to contribute to. It’s deeper than that: how might you contribute to humanity, and even deeper, to the well-being of the world, by pursuing mathematics? Such a question is not possible to answer in a purely intellectual way, because the effects of our actions go far beyond our understanding. We are deeply social and deeply instinctual animals, so much that our well-being depends on many things we do that are hard to explain in an intellectual way. That is why you do well to follow your heart and your passion. Bare reason is likely to lead you astray. None of us are smart and wise enough to figure it out intellectually.
(Click here to read the rest.) [/quote]
Whereas most mathematicians cite the eternality and universality as a primary appeal working in the subject, Thurston makes an essential point that the body of mathematical understanding as organic as the community that carries it. Ideas blossom and then fade. We tend to think of the essential notions as lasting forever, but it’s very hard to know in the moment which ideas will find favor among future generations. Anyone who has tried to read original texts knows how obscure the majority of the material is, and Thurston points out that demonstrates how “taken for granted knowledge” changes over time.
So rather than chase immortality through proving what seems to be a timeless result, maybe focus your energies on whatever seems cool at the time. Curious advice from a guy who had a habit of proving timeless results!