Three years ago, an AI system could not reliably add two numbers. A year ago, internal models at OpenAI and DeepMind scored gold-medal level on the IMO. Now those systems are solving major open questions on their own. The trend shows no sign of stopping.
That is the backdrop to a new essay titled A Beginning for Mathematics, published on the site Proofs and Prompts. The writer, a mathematician who has given talks titled “The End of Mathematics,” wants to pivot from doomscrolling to optimism. He argues that AI can automate the production of mathematics while deepening human understanding of it.
What the Essay Actually Says
The essay opens with a premise: superhuman AI systems will arrive soon, and the production of mathematical text will become increasingly disconnected from understanding. From there, the writer asks a simple question: what are we even trying to do?
He lists several answers from the mathematical community:
- Some want to solve problems.
- Some treat mathematics as play or poetry.
- Some quote the German slogan “Wir müssen wissen – wir werden wissen.”
- Some see mathematics as a path to the platonic realm.
- Some think the goal is to embody love of and understanding of mathematics, and pass it on to the next generation.
His own answers are narrower: produce and understand high-quality mathematics, and produce high-quality mathematicians. He adds that the definition of “high quality” has changed dramatically over time, and that educating the general public about mathematics is part of the job.
Why Proving Theorems Is Not the Goal
The essay spends time debunking the idea that mathematics is about proving theorems. A computer or monkey could start at the axioms of ZFC and iterate deductions forever, producing proofs with no understanding. A smarter machine could enumerate all conjectures and proofs, resolve open problems, and ask new ones.
But the writer argues that this machine would not produce human understanding. He thinks the explosion of mathematics will create more need for human mathematicians than ever before, but the profession will have to change.
What Needs to Change
The essay wants to preserve certain things: learning seminars, serendipitous conversations, students knocking on a professor’s door to chat about math. It worries that existing writing on this topic focuses too much on preserving the precise shape of academic institutions rather than the values they serve.
The writer rejects the question of how to preserve the journal and peer-review system, how to protect the arXiv, how to keep the role of gatekeeper. He says the idea that any semblance of the current equilibrium can survive what’s coming is absurd once you accept that AI systems can produce relatively high-quality results for the marginal cost of a few dollars.
Instead, he proposes chasing the edge of model capabilities. Right now, AI systems arguably underperform humans at theory-building, asking questions, and exposition. So the profession could prioritize and reward those skills. He argues this is unwise, comparing the speed at which AI systems can generate results to the speed at which humans build intuition and understanding.
The Verdict on the Optimism
The essay’s core move is to separate the production of mathematics from its understanding. AI can automate the former, but the latter remains a human task. The writer believes this is a moment of incredible potential, not of crisis.
The key facts are simple:
- Three years ago: AI could not reliably add two numbers.
- A year ago: internal models at OpenAI and DeepMind scored gold-medal level on the IMO.
- Now: systems are solving major open questions autonomously.
- Premise: superhuman AI systems will arrive soon.
- Goal: produce and understand high-quality mathematics.
The schedule of events looks like this:
| Year | Event |
|---|---|
| Three years ago | AI could not reliably add two numbers |
| A year ago | Internal models scored gold-medal level on the IMO |
| Now | Systems are solving major open questions |
| Soon | Superhuman AI systems expected |
The writer’s own talk, “The End of Mathematics,” was about a gloomy vision of stalled human understanding, not about machines solving everything. He thinks that future is avoidable but plausibly the default if academic mathematics does not adapt.
This is a moment of genuine excitement for the field, not fear. The essay argues that the explosion of mathematics will leave more room for human insight than ever before, provided the profession is willing to let go of old guardrails and adapt to new tools.
The paper’s view is that the end of mathematics as we know it is not coming. Instead, it is the beginning of something better.
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