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Suppose I give you an n-digit number and ask you what it represents. This seems impossible, and in theory it is impossible. But in practice it’s often possible.
Apps on a phone may automatically interpret a 10-digit number as a phone number or a 16-digit number as a package tracking number. And very often these interpretations are correct, given the k...
The Greek letter β (beta) and the German letter ß (eszett) look similar, especially in some fonts.
Now suppose an OCR program sees some character that could be a beta or could be an eszett. It could calculate some kind of distance between between the pixel pattern of the character and the pixel patterns of beta and eszett. But that would be discarding context.
I...
The idea of using computers to assist with proofs is not new. The first major computer-assisted proof was published in 1976, the proof of the four color theorem by Kenneth Appel and Wolfgang Haken. The authors reduced the proof of the four color theorem to verifying calculations on 1,834 configurations, each checked by a computer program.
The proof was simplified over ...
A rising tide may lift all boats, but the AI tide lifts some boats much more than others.
By all accounts, the best programmers have had the biggest productivity boost from AI. And top tier mathematicians are using AI to settle long-standing mathematical conjectures. AI is a powerful tool, but tools don’t come to life and make things on their own.
I routinely ha...
Yesterday OpenAI announced a proof that settled a long-standing question about the Navier-Stokes equations from fluid dynamics. The announcement has created a lot of buzz, as one would expect. But there’s an aspect of OpenAI’s work that I haven’t seen anyone talk about: they posted a Lean 4 formal proof at the same time as their conventional human-readable proof.
Quite...