What we covered:

– Why “problem solving” is often just a vague label people use when they haven’t explicitly enumerated the underlying skills, and how those skills can in fact be exhaustively mapped in a knowledge graph.

– How to approach research problems: Alex's PhD journey, top-down familiarity vs bottom-up mastery.

– If you have natural talent, use it, but not as a crutch, otherwise you'll stunt your long-term development. Don't turn your blessing into a curse.

– The story behind building our SAT prep curriculum: realizing that the standard school curriculum leaves a massive “missing middle” unaddressed; identifying 115+ missing topics to bridge the gap between textbook math and the hardest SAT questions.

– Watching the manifold hypothesis play out in test prep: the SAT may appear to allow an astronomical space of possible problem types, but in reality the actual problems live on a compact, highly structured manifold that can be fully enumerated and scaffolded in a knowledge graph.

Timestamps:

00:00 - Intro: "problem solving" is what you call it when you don't really know what it is (i.e. you haven't explicitly enumerated the skills)

04:11 - How to approach research problems: Alex's PhD journey, top-down familiarity vs bottom-up mastery

20:28 - If you have natural talent, don't use it as a crutch. Don't turn your blessing into a curse.

29:06 - SAT prep, iteration 1: Realizing that the standard school curriculum leaves a massive “missing middle” unaddressed

33:45 - SAT prep, iteration 2: Covering the "missing middle" problems

53:38 - SAT prep, iteration 3: Building the "missing middle" knowledge graph

1:08:11 - Watching the manifold hypothesis play out in SAT prep

1:16:42 - The unreasonable effectiveness of the knowledge graph

Follow on X:

Math Academy - https://x.com/_MathAcademy_

Justin Skycak - https://x.com/justinskycak

Jason Roberts - https://x.com/exojason

Alexander Smith - https://x.com/ninja_maths