Pinned
Many of us intuitively feel that the field of mathematics is going to change, so let's unpack the likely outcomes, without resorting to hyperbole or doomerism.
Harmonic
301 posts
Harmonic
@HarmonicMath
Building Mathematical Superintelligence
Joined January 2024
- Formal verification is the future of cryptoWe at Protocol Snarkification - me and @alexanderlhicks, plus about 30 or so external collaborators - are working hard with formal verification to ship the highest-assurance zkVMs possible. (see end of thread for collaborators) (1/n)
- Fantastic to have Rustan Leino join us at @HarmonicMath to help advance AI ✕ mathematics ✕ verification.
- In the future, all critical software will be formally verified.As we discussed with @VitalikButerin on our Fireside, formal verification is a big positive outcome from AI that will more than counterbalance the effects of AI finding new bugs. I am strongly supportive of math AI tools like Aristotle from @HarmonicMath driving this forward.
- Mathematical superintelligence is nearer by the day. Wouter van Doorn presented at NYNTS how he used Aristotle to tackle an important unsolved problem in number theory. Check it out here:Today at the New York Number Theory Seminar, Wouter and Pietro were discussing their new paper. Really cool use of the AI-human feedback loop, with Aristotle as the main AI ingredient. I explained how I think formalization feels like doing the low-tech steps of algebraic
- ICYMI: A few quality of life improvements landed in Aristotle Web to make it much more interactive and responsive: ▪ Live Updates. Aristotle can now share updates while it's in the middle of a run, so that you always know what it's doing and whether it's on track. ▪
- Harmonic reposted
Today at the New York Number Theory Seminar, Wouter and Pietro were discussing their new paper. Really cool use of the AI-human feedback loop, with Aristotle as the main AI ingredient. I explained how I think formalization feels like doing the low-tech steps of algebraic
Here's what András Sárközy, Erdős's most prolific collaborator, asked 25 years ago: "How small can one make the maximal gap between the consecutive elements of a multiplicative Sidon set selected from {1, 2, ..., n}?" In particular: does there exist a multiplicative Sidon set A - Harmonic reposted
Here's what András Sárközy, Erdős's most prolific collaborator, asked 25 years ago: "How small can one make the maximal gap between the consecutive elements of a multiplicative Sidon set selected from {1, 2, ..., n}?" In particular: does there exist a multiplicative Sidon set A - Harmonic reposted
I used @HarmonicMath's Aristotle to formalize Erdős problem #426 in Lean 4… and ended up fully verifying a stronger bound that the original paper only suggested 🧵 Erdős offered $25 for a disproof, and $100 if the conjecture was true 👇
- Harmonic reposted
Mel Nathanson — How Harmonic's Aristotle solved some of my problems. gist.github.com/kim-em/20212c6… #LeanProver #ITP #Aristotle #AI4Math - Harmonic repostedNathanson has just published the recording of his talk about Aristotle’s solutions and it is very interesting to watch! “I tried to figure out what it did that I didn’t do to solve the problems.” “The incredibly clever idea that Aristotle had was…” youtu.be/VBIxv-6m7sk
Interesting update: a few days ago, Nathanson presented a talk at the New York Number Theory Seminar explaining how Aristotle solved some of his problems. - Aristotle solves several open problems from Melvyn B. Nathanson, a frequent collaborator with Paul ErdosInteresting update: a few days ago, Nathanson presented a talk at the New York Number Theory Seminar explaining how Aristotle solved some of his problems.
