Guest Video with 3Blue1Brown!

+ a cute problem from combinatorics

Hello friends,

Some exciting news! A few days ago, I had the pleasure of being featured as a guest creator on 3Blue1Brown.

The video was about a topic that I have been thinking about for a while: AlphaGeometry. This is Google DeepMind's AI model that solved IMO-level geometry problems at a silver-medal level.

Understandably, the AlphaGeometry model generated quite a lot of buzz. So it seemed worthwhile to explain how it works.

So how does AlphaGeometry work?

At a high level, AlphaGeometry has two components:

1. A logical component. This component involves no AI whatsoever. It carries out what IMO folks call "ratio chasing" and "angle chasing".

2. An AI component. This component comes up with so-called auxiliary constructions. These are extra points and figures in the diagram that have to be drawn in. This is the part of the model that thinks creatively.

The model works by using these two components alternatingly. It first runs the logical model, then the AI model, then the logical model, and so on. It does this until the problem is solved or time runs out.

There are more details in the video so check it out if you’re interested in learning more. I also highly recommend checking out the original paper. It’s quite readable and clearly written!

Problem of the Week

What is the minimum number of pairwise comparisons needed to identify the heaviest and second heaviest of 128 objects?

If you have a solution to this challenge problem, submit it here for a chance to be featured in the next issue of this newsletter.

Shoutout to Dashamir Hoxha (Albania), Advait Nene (Pittsburgh, PA), Michael David (Canada), CK (California), Ritoprovo Roy (Prague), Dashamir Hoxha (Albania), JW (The Hague), jwenpaq (Singapore), Marek Grabarski (Poland), jc (New York), David J. Webb (Hawaii), Madhur Agrawal (Mumbai), Nikolaj Peters (Denmark), and Ankit (Bay Area) for submitting solutions to last week’s challenge problem!

Until next time,

Adithya