mathematics 34
- The value of a body of knowledge comes from the process of engaging with it, not just from its end products.
- Improper use of AI offloads a person's thinking and learning, which mortgages a field's future development.
Terence Tao
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What Terence Tao says most about
AI and science 12
- Current AI4Math systems largely operate as solvers of isolated, well-defined proofs rather than as researchers that expand mathematical knowledge.
- On small tasks he can check himself, he catches about as many of the AI's errors as it catches of his.
formal proof 3
- When formalising a proof costs no more than writing it, mathematics will flip: papers written in Lean first, and journals refereeing only for significance because correctness is certified.
- Lean and tools like GitHub will let experimental mathematics scale far beyond what one mathematician's spaghetti code allows today.
physics 3
- Current AI struggles even to rediscover old laws of physics from data, and when it does, contamination from training is the first suspect.
- Physics will be unified again as it has been before; the obstacle is that relativity and quantum mechanics already explain almost everything we can measure.
AI agents 2
- Today's AI tools either solve a problem or fail at it, and are really bad at partial progress or at identifying which intermediate step to attack first.
- Fully autonomous one-shot attempts are the wrong approach to the great unsolved problems; the mileage is in humans and tools working against each other.
education 2
- The value of a body of knowledge comes from the process of engaging with it, not just from its end products.
- Improper use of AI offloads a person's thinking and learning, which mortgages a field's future development.
LLMs 2
- Natural-language LLM mathematical reasoners are fundamentally limited by lacking machine-checkable semantics, which blocks autonomous verification needed for open-ended research.
- A model that solves a hard problem has learned nothing from it: the next session has forgotten it, with no new skill to carry to related problems.
peer review 2
- Automatic filters cannot replace community acceptance, and human referees cannot be removed from mathematical publication.
- The structures of science now have to change, because the scarce thing is no longer proposing theories but verifying and evaluating the thousands anyone can now propose.