Besides proving new theorems, how can a person contribute to mathematics?

There are at least a few things a person can do to contribute to the mathematics community without necessarily obtaining novel results, for example:

  • Organizing known results into a coherent narrative in the form of lecture notes or a textbook
  • Contributing code to open-source mathematical software

What are some other ways to make auxiliary contributions to mathematics?

Answer

You can create new jobs for mathematicians, e.g. by funding institutes like Jim Simons. Arguably this does much more for mathematics than actually doing mathematics due to replaceability: the marginal effect of becoming a mathematician is that you do marginally better mathematics than the next best candidate for your job, which is a much smaller effect than creating a new mathematician job where there wasn’t one before.

You can also work on tools for mathematicians to use like arXiv (or MathOverflow!). Arguably this also does much more for mathematics than actually doing mathematics. Incidentally, arXiv was developed by a physicist, Paul Ginsparg, and almost none of the mathematics graduate students I’ve talked to about this know his name.

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