AI is Solving Math's Hardest Problems, and Mathematicians Are Grieving
To grieve, or not to grieve?
Language models are now cracking problems humans couldn't, and the math community is reeling. From denial to depression, many mathematicians are grieving what they see as a loss. But not everyone: some, like Kevin Buzzard, are excited. He argues that the real value of math is human understanding, yet AI's rapid progress threatens even that refuge. A provocative look at AI's impact on mathematics.
You cannot fool Lean; one learns this very early on. Lean will not accept proof by authority or proof by intimidation; it doesn’t work like that. I feel safe with Lean.
- zaptheimpaler
Most of these idealistic pieces about AI seem to come from senior, established or wealthy people who aren't very exposed to the labor market. In that view, the question of AI and its transformation is almost philosophical like this piece.
It's more a question of survival if you're labor though. It's very transformative tech but it's coming at a time when the scales are heavily tilted in favor of capital over labor, the government is the most corrupt its ever been and AI is going to make that much more extreme. It doesn't matter how amazing the technology is if all the benefits are going to accrue to the same few people who already have everything and destroy everyone else's bargaining power.
- sachaa
I share the optimism here. Connecting dots across knowledge, lived experience and purpose remains, to me, a deeply human pursuit. The more AI discovers, the more possibilities we have to connect those discoveries to questions that matter to us.
- js8
I am also an optimist about AI, although I worry about the labor aspect as well (as a leftist I see the class aspect of this, on the other hand, as a computer programmer, computers were also originally meant to replace human labor, and we all see what happened).
My view is, current top AIs do multiple different things:
1. Interpret and output natural language
2. Do formal logical reasoning
3. Do informal logical reasoning
4. Provide encyclopedic knowledge
5. Discern vague instructions/statements and fill the most likely gaps (kind of error correction)
6. Serve as a model of the human mind, a proxy for a person
7. Translate between different languages, formal and informal
All these things are combined in these huge, hard-to-understand blobs of weights. I think humanity would be better off by understanding each aspect separately, but disentangling them will take decades of philosophical research. So there is a lot of interesting work ahead of us.
- youoy
In contrast to what these philosophical pieces tend to convey, the main crisis in mathematics is a labour one.
Mathematitians exchanged proofs for employment. That was the currency. Now they cannot use that currency anymore, so the question is how does someone know if they should hire an unknow person or not?
Philosophicaly who cares if you like more theory building or theorem proving? You dont need to convince anyone. The only solution is to be curious and follow your interests and naturally humanity will redefine what the new mathematics feels like.
You cannot convince anyone about it, its not something rational.
- dang
Buzzard is such a good writer. Read it all the way to the end - it gets (even) better as it goes along.