Snapshot · Hard Fork
On May 20th, OpenAI announced a model had disproved a longstanding geometry conjecture — the unit distance conjecture — by identifying a new mathematical approach no human had previously considered.
Where this was said
At 28:53 · chapter starts 28:18
Kevin Hartnett, former senior reporter for Quanta Magazine and current editorial lead at Cursor, joins the show to contextualize the rapid development of AI math capabilities. He recounts the arc from ChatGPT's early failures at basic arithmetic — mathematicians passed around examples of it claiming there are finitely many primes — to the IMO gold medal scores achieved by Google DeepMind, OpenAI, and Harmonic in 2025 [1] — Kevin Roose "AI math: IMO gold medal score: Three AI labs — Google DeepMind, OpenAI, and Harmonic — achieved gold medal scores at the International Math…" 31:38 . But Hartnett provides crucial context: even gold-medal performance at the IMO is 'essentially high school math, the hardest high school math in the world, but still just high school math' — representing roughly 0% of the way to frontier research mathematics [2] — Kevin Hartnett "AI at IMO = 0% of frontier math: Kevin Hartnett argued that even achieving a gold medal at the IMO represents essentially zero percent of t…" 33:16 . He explains why AI labs focused on math: the belief that teaching a model to reason through mathematical problems develops general-purpose logical reasoning that unlocks commercially valuable capabilities. The hosts also walk through the Erdős problem landscape: Paul Erdős compiled over 1,200 open mathematical problems with small cash bounties, and AI labs have been systematically working through them as capability benchmarks — though Hartnett notes most Erdős problems were not considered important by the mathematical community, more like 'sophisticated Wordle puzzles.'
Three AI labs — Google DeepMind, OpenAI, and Harmonic — achieved gold medal scores at the International Math Olympiad last summer, a feat once considered impossible.
Kevin Hartnett argued that even achieving a gold medal at the IMO represents essentially zero percent of the way to the frontier of research mathematics.
AI labs didn't pursue mathematics for its beauty — they pursued it because teaching a model to reason through hard math problems builds the general-purpose reasoning skills that power everything else. As Kevin Hartnett puts it: math is to AI what 'teaching you how to think' was to your high school math teacher.
Mathematician Paul Erdős compiled over 1,200 problems during his lifetime, offering small cash prizes for their solutions — prizes that AI labs are now claiming.
Animals first sensed light 540 million years ago, triggering an evolutionary acceleration known as the Cambrian explosion within 10 million years.
It is estimated that half of all cortical activity in the human brain is involved in visual function, underscoring vision's central role in intelligence.
Cognitive neuroscience literature shows that by age 6, humans can recognize tens of thousands of different object categories — far more data than early AI systems were trained on.
Only about 3% of FDA-approved drugs have genuinely unclear mechanisms of action, making an unknown mechanism a meaningful early red flag for any compound.
Even compounds that clear preclinical testing often fail in humans: 30 to 50% of drugs entering phase 1 trials do not advance to phase 2, frequently because human behavior differs from animal models.
More than 80% of published BPC-157 research comes from a single academic group whose researchers have IP and commercial interests connected to the molecule, limiting independent replication.
Roughly 100 peptide drugs are already FDA-approved, about 150 more are in clinical trials, and 600–700 are in preclinical development, underscoring the legitimacy of peptide science broadly.
The scientist who discovered BPC-157 refused to disclose the screening method used to identify the compound and has never fully published the parent protein sequence — what Peter Attia calls 'scientific trust me, bro.'
The brain's visual, auditory, and motor cortices light up nearly identically whether an experience is real or imagined, making visualization a form of actual neural training.
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