One of the Tiniest Proofs Ever Published

Photo by Gabriella Clare Marino on Unsplash
“Portrait of Leonhard Euler” (1753), by Jakob Emanuel Handmann. Image from Wikimedia Commons (public domain)

Euler’s Sum of Powers Conjecture, Explained

Among other things, Euler was interested in powers of numbers, and in 1769 he made a conjecture now called Euler’s sum of powers conjecture (or just Euler’s Conjecture). In general, a conjecture is a math statement that has not been proven yet, and a theorem is a big result that’s been proven. So Euler was making a sort of educated guess.

Disproving Euler’s Conjecture with a Supercomputer

Euler’s conjecture was disproven in just 2 sentences, almost 200 years later.

  • Sentence 2: This is a counter-example to Euler’s conjecture ok bye³.

The Proof by Counterexample

If a movie was two minutes long, you would call it a ripoff. If a book was two sentences long, you would call that a scam. Can a math proof this short still be legitimate? Yes. Lander and Parkin’s paper is a great example of a proof-by-counterexample.

A human, writing (mostly) about math | California | If you want to reach out

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store