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AI may well be able to write massive software projects “from scratch”, but that almost certainly isn’t the fastest / highest performance / highest security / most token efficient way to do things. Good building blocks matter.
In addition to RL’ing the agents on final task loss, we should try to get them to regularize the building blocks as well. What would the standard library look like that makes the agents most effective?
It is likely at the limit that it turns out to be some alien organization of code, but given the existing human-bias in training, I bet that in the near term it would be lovely code that old programmers would appreciate.
I suspect the same could be said for mathematics, but that is out of my lane.
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AI-generated math solutions are not solutions, they are data, we should view them as that when trying to understand, interpret, & ask the next question.
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if you're a technical person that is sad right now, don't worry
it's just a phase, you're going through ego death
you will complete the journey, you will come out the other side and your lifeforce will return
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I think it's becoming rather clear that ALL of mathematics will become possible to formalize rather soon. There are deep implications:
1. Mathematics becomes super interactive. Formalizations make it easy to browse, recombine, and build mathematical proofs from components.
2. Each new idea and paper can be checked much faster. The deep part is meaning and explanation. Validation is almost automatic.
3. Optimization and identification of new proofs can be done partially via agents, and humans can contribute much faster with great new ideas. Proofs from the Book are possible at scale.
4. Scientists and people at large can finally use mathematical artifacts as black boxes with trust and confidence. We can commoditize mathematical theorems.
I think the mathematical enterprise also becomes very gamified. We can clearly see each unproven statement as a concrete goal, identify existing tools and directions, and focus quickly on what's missing. And everyone can contribute, with agents or through understanding.
Soon, new languages and new theories will also develop, but the structure will keep growing steadily, with no mistakes and on fundamentally solid foundations. Hilbert's dream is becoming a reality.
One important caveat: mathematics is by no means trivial now! It's just becoming extremely well-structured and laser-focused. I think the jump in capacity, quality, and scale will be massive. I also hope that our understanding of the big picture will remain solid, because there will be a lot to grasp.
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Finite simple groups are building blocks of finite groups, like primes are for whole numbers.
The “Enormous Theorem” states that every finite simple group belongs to one of the known infinite families or is one of 26 sporadic groups, including the Monster.
There are no others.
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can't believe it's actually working
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to the theoretical mathematicians, computer scientists, and physicists worried that their livelihood is getting destroyed by ai
everything is gonna be alright
i was in computational neuroscience, a niche field where the goal is to build computer models of the brain
the paradigm used to be some scientists hand-construct a neural network model and compare it with the brain
for example, people spent decades trying to build models of the visual cortex
around 10 years ago, people realized that the computer vision models that ai researchers built turned out to be better models of the brain's visual cortex than anything else designed by humans
then the same thing happened to language, llms turned out to be the best models we have on how language work in the brain
over time, people just moved more from hand-constructing these models to analyzing the ai models, or adjusting the ai models themselves
same is going to happen in theoretical math, cs, and physics
people will go from doing the work themselves by hand, to focusing on understanding the work ai put out & improving the ai system
it's gonna be fine
We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.
openai.com/index/building-sc…
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2023: GPT-4 almost solved grade-school math
2024: IMO silver
2025: IMO gold
2026 May: Erdős unit-distance conjecture
2026 Sep: Navier–Stokes Millennium Prize Problem solved
2026 Oct: 722 AI-written math manuscripts
Today: OpenAI proves ETH is false
Tomorrow: P = NP?
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A key thing lost in the lab automation push is that 80% of scaling scientific research looks like this -- getting more data out of the same labor steps with one-pot protocols. Unlike with lab automation there's no natural constituency that makes $ from telling this story
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It took 362 pages of pure logic to prove that one plus one equals two.
Russell and Whitehead built mathematics from the ground up in Principia Mathematica. Numbers became classes of equinumerous sets. Addition was defined through unions of disjoint classes. Only after hundreds of prior theorems did they reach the final step: 1 + 1 = 1 + ‘1, and 1 + ‘1 = 2, hence 1 + 1 = 2.
Even the simplest truth required an entire logical foundation to stand.
Certainty is expensive.
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The complexity theory result is actually huge.
P problems can be solved in polynomial time. It was widely believed that NP-complete problems require exponential time.
P = NP states that NP-complete problems can be solved in polynomial time. OpenAI didn't prove that. But, they proved that (some) NP-complete problems can be solved faster than exponential time, meaning:
- P = NP, or
- the complexity of NP problems is a "middle thing" between polynomial and exponential, eg. O(n^log n)
If it survives peer reviews, this could be one of the biggest CS breakthroughs in decades.
Announcing three major scientific discoveries, one each in mathematics (harmonic analysis), computer science (complexity theory), and physics (quantum field theory).
AI starting to help us improve our understanding of the universe! openai.com/index/building-sc…