How to Find Rational Points Like Your Job Depends On It — Quanta Magazine

My latest column for Quanta Magazine begins with a story from my past.

You’re sitting at the end of a long conference table, interviewing for your dream job. You’ve made it this far, but there’s just one more question you have to answer.

“Is it possible for a line that passes through the origin to pass through no other rational points?”

Five pairs of intense eyes watch you, waiting for your response. Do you get the job?

The simple challenge of finding rational points on lines leads to a more interesting property of rational points on circles, which ultimately lands us in the fascinating world of elliptic curves, which are essential in modern cryptography and were instrumental in proving Fermat’s Last Theorem.

The entire article is freely available here.