When my students grow too dependent on their calculators, I ask them to find a number that, when multiplied by itself, gives them 2. Students quickly see that since 1² = 1 and 2² = 4, the answer has ...

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others. You’re sitting at the end of a long conference table, ...