The AI revolution in math has arrived (opens in new tab)

The bigger problem for me is that the realtime voice modes lack tool use, so they can't look anything up or do anything. Model strength definitely also matters, but even dumb models can be helpful when they can look things up and try things out. And smart models that don't do those things kinda suck.

Can get around this with a local STT model and use text input but UX is probably clunkier

Definitely, seems like gpt 3

So we have a bunch of imposter syndrome techies who would 5x with just a hint of encouragement, and now we’re trying to 2x them with LLMs, but in order to get there those same techies will have to gas up and inspire the LLM with the leadership and vision they themselves are wanting for?

The Universe seems against free lunches… if AGI is possible, finding a manager good enough to get the AGI to update its timesheet will not be (in practice).

From my reading, the official docs don’t support the strong claim that frontier LLMs are explicitly RL-trained to “be lazy” or conserve tokens as claimed in this thread. What they do document is adaptive / hidden reasoning compute: OpenAI says reasoning models allocate internal reasoning tokens and reasoning.effort controls how many are used (https://developers.openai.com/api/docs/guides/reasoning), and Anthropic says adaptive thinking decides whether/how much to use extended thinking based on request complexity, with effort as soft guidance and max_tokens as the hard cap (https://docs.anthropic.com/en/docs/build-with-claude/adaptiv... hinking). So prompt wording may change how the same budget is spent, but it can’t exceed the hard token cap.

Also, the “encouragement helps” anecdote seems real in the AlphaEvolve workflow, but I can't see that forpublic models. Gómez-Serrano says this in Quanta (https://www.quantamagazine.org/the-ai-revolution-in-math-has... rived-20260413/), and the released AlphaEvolve notebooks really do contain prompts like “Good luck, I believe in you...” (https://github.com/google-deepmind/alphaevolve_repository_of... oblems, e.g. https://github.com/google-deepmind/alphaevolve_repository_of... blems/blob/main/experiments/finite_field_kakeya_problem/finite_f ield_kakeya.ipynb). But those prompts also bundled strong structural hints (“find a general solution”, “better constructions are possible”), so from my reading the evidence is: prompt phrasing matters, especially in an internal search stack, but not “pep talks are a universal reasoning hack.”

It was just yesterday that this top post [] was decrying the "peril of laziness lost", that LLMs inherently lack the virtue of laziness.

So which one are they?

[] https://news.ycombinator.com/item?id=47743628

The training or system prompts have shoved the probabilities toward a space that tends to select “halt” sooner. You need to drag the probability weights around until they are less likely to reach “halt” so soon.

Nice language often sorta does this for whatever model(s) they looked at, and is also something people are likely to try. Probably lots and lots of nonsense token combos would work even better, but who’s gonna try sticking “gerontocratic green giant giraffes” on the end of their prompts to see if it helps?

Positive or negative language likely also prevents pulling the probabilities away from the correct topic, being so generic a thing. The above suggestion might only be ultra-effective if the topic is catalytic converters, for some reason, and push the thing into generating tokens about giraffes otherwise. How would you ever discover the dozens or thousands of more-effective but only-sometimes nonsense token combos? You’d need automation and a lot of brute force, or some better way to analyze the LLM’s database.

> Do we know why it works for humans?

Try to figure it out. You can do it.

If I had to wager a lazy, armchair guess, I think it forces it to think harder/longer

The answer is probably more straightforward than we think, e.g. “the user thinks I can do this so I better make sure I didn’t miss anything”

1. The four color theorem is a useful case study, for which the original proof was validated and 400 pages long. My prediction is that the first couple waves of proofs will be hard enough that a layman couldn't produce them, but simple enough that experts can verify them. Over time the most advanced proofs will get more and more complicated until humans can no longer verify them, this process could happen over the course of a few month or could take literally hundreds of years.

2. Especially early on the overwhelming majority of the proofs are likely to be uninteresting and more novel just because actually producing them would take expert time that's better spent elsewhere. That being said, as above over time I expect the interestingness of proofs to go up until they eventually regularly produce interesting proofs. The vast majority of proofs are likely to maintain their position as of no interest to humans for the simple reason that the vast majority of proofs are of no interest to humans.

In neither case will I make any particular guesses about a timeline beyond it seems like the way things will go.

Every new mathematician that comes along doesn’t know everything that has come before him. He needs to go learn all the math that his predecessors did. I don’t see how an LLM coming up with these proofs changes that.

Generally when people talk about using LLMs to do mathematics research they’re not talking about the LLM alone, but the LLM + a harness for it to write and execute theorem provers such as Lean or Coq to validate their results.

When I tried to use it as an AI CEO and Life Coach, it never was able to discern time passing, what I've already done, what needed to be done. It just said the same stuff over and over, stuff I've already done. That and it's kind of stuck in the era it was trained in. If it felt time passing like a human maybe it would be conscious?

Nevertheless not having a sense of time makes it really bad at planning anything. I used Gemini Pro.

Sounds like Musk setting deadlines for Mars landings.

Can’t tell if you are being sarcastic but Altman’s whole job is to make bullshit near future predictions about rapid development of AI in the public.

Taking the task at face value:

- 1 week to prototype: The tool + its accompanying JS sandbox + System prompt updates + context injection

- 11 months of public testing to go through i18n + a11y edge cases & fix them

There's no need to "estimate" it. "Time" is not something built into training and sampling a generative distribution. He might as well have told you your Naive Bayes email filters will measure time passed.

> go out on a limb and agree with Terrence Tao

Is AI his specialty?

> I think the dude is well known in the math community, or something

I believe this is called "appeal to authority." Which is why, instead of disagreeing with him, I suggested a more cogent endpoint that could be used to establish the facts the article's title suggests.

I think he means useful for mathematicians getting paid shilling for AI models

If anything his simping for AI models makes me more suspect of him than I ever was because my own eyes show me their limits.

The Turing test just failed you. I'll go one better, physics isn't reality, it's a model of reality utilizing math.

Maybe he passed the Turing test with 88.2% which is 1.8% higher than the competition.

Fortunately for me equivalents to Turing exist: https://en.wikipedia.org/wiki/Turing_machine_equivalents