by Andrew Lott, Mathematics

When someone asks about my plan for the future, I tell them I hope to do research in math. Many people think all of math has been established. But it is a vast subject, and, as the cliché goes, the more I learn, the more I understand how little I know.

To illustrate this, I introduce them to an interesting, approachable question, like the following elevator pitch for the twin primes conjecture: 

Number theory is the study of the integers: …-3,-2,-1,0,1,2,3… Even though this is the simplest, most fundamental set of numbers, mathematicians are still struggling to understand them. Some integers can be factored, like 4=2×2 and 6=2×3. But some integers cannot be factored: 2,3,5,7,11,… .These are the primes. Here is an open problem: are there infinitely many pairs of primes which are 2 apart? (think 11 and 13, or 41 and 43).  This problem was posed in 1846. Despite over a century of intense work by some of the world’s most brilliant mathematicians, it remains unsolved.

It’s best to keep things simple when explaining math. I draw them in with familiar concepts and definitions, at which point I introduce them to a deep and difficult modern research question. Sometimes I pull off an explanation like this, but often their eyes glaze over. Sometimes they have had traumatic experiences with math in the past, and they assume they won’t be able to understand and enjoy it, and so they shut down before the explanation even begins, which is a shame.