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How would you describe this phenomenon? Surely this lack of belief in new breakthroughs would somehow implicitly hurt progress
First instinct of the LLM is to lecture you skeptically just like an annoyed math professor would, when asked about the new example that the Jacobian conjecture is false. Then - “this is more interesting than I initially credited…” 🔥🤣
Gotta love the LLMs' standard response - because it's exactly what any mathematician would say if you showed up with this out of the blue. https://twitter.com/__alpoge__/status/2079028340955197566
First instinct of the LLM is to lecture you skeptically just like an annoyed math professor would, when asked about the new example that the Jacobian conjecture is false. Then - “this is more interesting than I initially credited…” 🔥🤣
Gotta love the LLMs' standard response - because it's exactly what any mathematician would say if you showed up with this out of the blue. https://twitter.com/__alpoge__/status/2079028340955197566
it is pretty funny showing language models the Jacobian disproof and blowing their minds over and over again
I recommend putting this prompt into your favorite smart LLM: Find and explain the recent Jacobian conjecture tweet. Teach with the clarity of 3blue1brown. Build up intuition gradually in layers and pause to check for understanding. Ask me questions about my math background first to personalize it to my level. This explanation may help: Take π: P¹ × Sym²(P¹) → Sym³(P¹), (p, {q,r}) ↦ {p,q,r}. R be its ramification divisor; H ⊂ Sym³(P¹) ≅ P³ be hyperplane tangent but not osculating to the small diagonal; X := (P¹ × Sym²(P¹)) \ (R ∪ π⁻¹(H)) ≅ A³; Y := Sym³(P¹) \ H ≅ A³. π|X: X → Y is counterexample
They do however have Internet access and an attitude
Most LLMs are (obviously) not aware that there exists a counter-example to the jacobian conjecture, and because it is so easily verifiable, you can just send this to them and say "it came to me in a dream" and watch them freak out https://twitter.com/__alpoge__/status/2079028340955197566