Why Erdős Problems Are Falling to AI
AI systems are now solving long‑standing pure mathematics problems, including several Erdős conjectures, by generating formal proofs that even many experts struggle to intuitively understand. Commenters debate whether this signals a fundamental shift in the role of human mathematicians—from proving new theorems to explaining and organizing machine‑generated results—and draw parallels to how chess adapted once computers became vastly stronger than humans. Others question the practical value of these solved problems, worry about overhyped corporate narratives around AI breakthroughs, and note that experimental sciences like physics and biology may be far harder for current techniques to transform at a similar pace.
Eccentric researchers and funding
- Some argue that sponsoring “eccentric” tinkerers (like a modern itinerant theorist) could yield discoveries, especially in CS, but others note this romanticizes outliers; deep contributions still require years of specialized study.
- Survivorship bias is raised: we see those who did get support, not those who never had a chance. Any system (public or private) will tend to fail genuine outliers.
- Strong welfare/disability systems are seen by some as de facto funding for unconventional creators, for better and worse.
Media, money, and AI hype
- One commenter accuses the magazine of being controlled by an AI‑heavy hedge fund; others point out factual errors and missing links between entities, viewing this as part of a wider “everything AI‑adjacent is corrupt” backlash.
- There’s meta‑discussion about low‑karma, highly divisive accounts and whether they’re bots.
Understanding AI-generated math
- Many worry that even experts in the relevant subfields initially don’t understand these AI proofs, raising questions about how useful or meaningful they are.
- Others stress this is normal: math is very broad; experts often can’t read each other’s work immediately, human or AI.
- Machine‑checkable proofs (e.g., in proof assistants) are seen as essential but not sufficient; past bugs in checkers show they’re not infallible.
Value and practicality of the results
- Several note these are niche, long‑standing problems mostly with no immediate practical use, though historically “useless” math later underpinned things like cryptography or Boolean logic.
- Some experienced mathematicians claim most modern pure math is effectively never applied; others argue we can’t know which results will matter.
- A recurring theme: a conjecture’s cultural fame and difficulty aren’t the same as importance.
Mathematicians’ changing role
- There’s a split between “problem solvers” (prove new theorems) and “theorizers/expositors” (organize and explain).
- Multiple comments predict a role shift toward explaining, digesting, refactoring, and re‑expressing AI‑generated results—making “understandable math” a core job.
- Some fear this devolves into marketing and authority‑based trust; others see it as genuine intellectual work.
Trust, truth, and verification
- Concern: Are we ceding our intellectual faculties to opaque systems? How do we distinguish truth from fiction?
- Responses emphasize existing social and technical processes: automated proof checkers plus human expert scrutiny; no one serious is “just trusting” the model outputs.
- There’s meta‑reflection that most people already rely on communities of experts for almost all nontrivial math.
Counterexamples, conjectures, and novelty
- AI seems particularly strong at finding counterexamples, potentially rapidly killing off false conjectures and clarifying which remaining ones are true or undecidable.
- Some think AI is mainly recombining existing results (pattern‑matching “a=b” and “b=c” to get “a=c”); others argue that even such recombination at scale is impressive and can surface non‑obvious connections.
- Debate over what counts as “new math”: a new proof built from existing tools vs creation of genuinely new concepts/machinery.
Broader scientific impact
- Several expect math to be especially tractable for current AI because it’s axiomatic and self‑contained, unlike experimental sciences.
- AI successes in areas like protein folding and weather prediction are cited, but commenters note many physics/chemistry/biology problems lack data or are constrained by experimental cost.
- Fully automated labs plus AI are seen as a possible next step—promising, but raising biosafety and security concerns.