I recall some time ago thinking: what is the point of studying mathematics, when there are smarter people than me who have already discovered all the good stuff. And that anything I discover must be trivial.
As time goes on, the body of mathematics grows. New theorems are built on old theorems like the blocks of a pyramid. We each have a short amount of time that we can spend standing atop this pyramid trying to add that next brick, or that next theorem.
With this analogy in place, I’d like to say two things:
- People keep asking me “what can you do with your mathematics?” – how could I possibly know what people will do with my theorems. I cannot predict how far the next person who stands atop the pyramid will see.
- While the body of mathematics grows, so too does it become necessary to improve our ability to teach mathematics. So while the pyramid gets larger; we develop new ways of getting to the top faster.
I hope that one day, long after I have gone, civilization may build this pyramid to reach the heavens.