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Progress on provable inference for large language models
Sharing progress on a powerful type of cryptographic proof known as a zkSNARK, which is uniquely fit for provable inference.
New
The latest blog posts to take off on Hacker News. 2,851 posts.
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Could a modern chess engine on a Pentium have defeated Kasparov in 1996?
A fun experiment where I back-port all the improvements we've made to chess engines over the last 30 years and run it on a 1996 Pentium Pro to see what we could have done if only we knew more at the time.
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Egoless Mathematics in the AI Era
[This is a guest post by Karthik C. S., Amit Sahai, and Jie Xue. This blog post was initially written in a different file format and converted using AI. — T.] This is a good time for mathemat…
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Mathematics has changed. Let's act like it
[This is a guest post by Frank Calegari. This blog post was initially written in a different file format and converted using AI. — T.] Why we should not be sad The release by OpenAI on Octobe…
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Efficient algorithms, the Exponential Time Hypothesis, and losing the plot
On efficient algorithms, the exponential time hypothesis, and losing the plot.
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A new faster algorithm to compute 64-bit signed floor division
The missing chapter of Hacker's Delight
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Faster than earcut: triangulating 3.7M map polygons in 489 ms
We published the triangulator of our map engine as earstrip, an ISC-licensed C++ and WebAssembly library. How it came to be: the ear clipper rebuilt one idea at a time and timed on 3.7 million polygons of real map data.
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One Hash Bloom Filters
Jim Calabro
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Dungeon generation in the Gnomish mines of NetHack
Ok, this one is really best explained with a visualiser:
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The Intel 8087 chip: floating-point addition and subtraction
In 1980, Intel introduced the 8087, a chip that made floating-point operations much faster in the IBM PC and other systems. Although the 808...
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Will it be a golden age or a dark age for mathematics (and science)?
[This is a guest post by Francesco Maggi. This blog post was initially written in a different file format and converted using AI. — T.] Large language models (LLMs) and the research systems b…
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You could have invented transformers from memory
Every layer is a memory store
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Why are we even doing all this?
[This is a guest post by Rikab Gambhir. This blog post was initially written in a different file format and converted using AI. — T.] First, they came for the artists, and I did not speak out…
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Simons Foundation launches $15M effort to help mathematicians navigate AI era
The Simons Foundation today announced a new set of initiatives that will help the mathematics community navigate the rapid rise of artificial intelligence in the field. Under a partnership…
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I know why the mathematicians weep
On technological grief
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Monte-Carlo Simulations
Monte Carlo simulations (or methods ) is the technique of applying randomness and the Law of large numbers to the solution of various scientific and engineering problems. One of its first documented uses was by Stanislaw Ulam and John von Neumann for nuclear weapon simulations after WWII [1] .
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Two-Stack Sliding-Window Aggregation
An aggregation is some kind of summary of a set of data. This can be the sum, length, minimum, etc. It is quite common to want to calculate such a summary repeatedly, e.g. “the maximum noise level in dB for the past 30 seconds” for a nuisance detector. In such a case we say there is a sliding window over our data, and…
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A Visual Intro to Complex Numbers
A visual and intuitive intro to complex number system providing a historical overview of how it was developed and why it is useful.
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A look at the math that OpenAI claims computes faster Fourier transforms
The OpenAI algorithm for the FFT is less a breakthrough and more a malicious exploit.
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(Post-Quantum) Cryptographic Right Answers
In the tradition started by Colin Percival and Thomas Ptacek, a set of “Cryptographic Right Answers” updated for the accelerated post-quantum transition timeline.
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Illustration Beyond Proof
[This is a guest post by Kate Stange and Edmund Harriss. This blog post was initially written in a different file format and converted using AI. — T.] In January a group of mathematicians, hi…
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Knuth reward check
Twenty years ago I got a reward check from Donald Knuth.
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What mathematicians should know about the Lean Theorem Prover: reliability & AI
[This is a guest post by Thomas Hales. This blog post was initially written in a different file format and converted using AI. — T.] Mathematicians have been weighing in on what they value ab…
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What should we tell our students?
[This is a guest post by Álvaro Lozano-Robledo. This blog post was initially written in a different file format and converted using AI. — T.] TL;DR: Keep calm and carry on studying math. I wo…
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OpenAI, the Partition Principle, and Mathematics
By the time I got out of bed yesterday, I had three people ask me if I'd seen the OpenAI announcement that the Partition Principle does not (...)
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The Mathocalypse
More Updates (Oct. 12): Jeffrey Ketchersid has used Claude Code agents to show that BusyBeaver(10) exceeds Graham’s number, beating the previous best result that BB(13) does so. In response t…
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Sharing AI progress in mathematics
OpenAI publishes new results on open problems in mathematics from an internal frontier model and shares Lean proof formalizations and research details on GitHub.
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How machines learned precision
How do you make an accurate machine without one to copy? Explore flat surfaces, screw-cutting lathes, and millionth-of-an-inch measurements through interactive 3D figures.
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Dust: Pretraining Transformers Without Backpropagation
Deep learning has been built around backprop, the only credit assignment algorithm capable of training modern neural nets, including transformer-based language models. Backprop requires differentiability and produces first-order gradients, and deep learning’s architectures, optimizers, and hardware have co-evolved…