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Patent 5,893,120 reduced to mathematical formulae
I have previously argued that the Bilski ruling renders all software unpatentable in the US because any method of manipulating information ...
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 494 posts.
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The Prime That Wasn’t
Life, technology, and other good things
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Neural Networks Are Essentially Polynomial Regression (2018)
You may be interested in my new arXiv paper, joint work with Xi Cheng, an undergraduate at UC Davis (now heading to Cornell for grad school); Bohdan Khomtchouk, a post doc in biology at Stanford; a…
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Double encryption: Analyzing the NSA/GCHQ arguments against hybrids
In 2019, Google and Cloudflare ran an experiment where they upgraded HTTPS for many "real users’ connections" to use post-quantum encryption. They then reported statistics on how affordable this was. Google had also run a similar experiment in 2016: "While it's still very early days for quantum computers, we're…
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A reasonably speedy Python ray tracer
Cyrille Rossant's small ray-tracer is an nice self-contained Python program (using NumPy) that renders this 400×300 image in about 15 seconds on a fast PC:
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Comparing City Street Orientations
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
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Lovelace's Leap
There's a great deal said about Ada, Countess of Lovelace that I find misguided. And, worse, the real intellectual triumph of Lovelace is ...
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Improving mathematical reasoning with process supervision
We’ve trained a model to achieve a new state-of-the-art in mathematical problem solving by rewarding each correct step of reasoning (“process supervision”) instead of simply rewarding the correct final answer (“outcome supervision”). In addition to boosting performance relative to outcome supervision, process…
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Sunset Geometry (2016)
Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake.
461
A Misalignment of AI in Mathematics
I am proud to be among the list of 25 initial signatories — all Fields Medallists — to the declaration below, which grew out of discussions between ourselves over the last week. We have…
462
Finding Love Optimally
Like many in operations research, my research interests often creep over into my everyday life. Since I work on scheduling issues, I get particularly concerned with everyday scheduling, to the consternation of my friends and family (“We should have left six minutes ago: transportation is now on the critical path!”)…
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Knuth's 'Earthshaking Announcement' due tomorrow
(I'm still looking for the catchiest way to appreciate the number MMXXVI. Exercise 7.2.1.6–122 gives 1234+.5*6+789 and -1+2345*6/7+8+9 and 1+(2/3)*45*67.8-9 ; other suggestions are welcome. The most elegant that I've seen so far is a beauty that was suggested independently by Arnaud Lefebvre and by Evangelos…
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The Myers diff algorithm: part 1
If you enjoy this article, I have published a book explaining the internals of Git through implementation: Building Git .
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LLMs don't do formal reasoning
Important new study from Apple
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John Conway's FRACTRAN, a ridiculous, yet surprisingly deep language (2020)
On April 8, 2020, John Horton Conway developed symptoms of COVID-19. On April 11, 2020, he succumbed to the disease. 1 2 3 4
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Transformers Are Graph Neural Networks
Engineer friends often ask me: Graph Deep Learning sounds great, but are there any big commercial success stories? Is it being deployed in practical applications? Besides the obvious ones–recommendation systems at Pinterest, Alibaba and Twitter–a slightly nuanced success story is the Transformer architecture, which…
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Prover-Verifier Games improve legibility of language model outputs
Discover how prover-verifier games improve the legibility of language model outputs, making AI solutions clearer, easier to verify, and more trustworthy for both humans and machines.
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Logic Puzzles with Prolog (2017)
Solving Logic Puzzles with Prolog
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Why Hacker News should use a different Deterministic Algorithm, Not a Random One
NetworkSolutions.com - Original domain name registration and reservation services with variety of internet-related business offerings. Quick, dependable and reliable.
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Factoring RSA 260
How Devin and a Cognition researcher built the world’s highest-performance GPU lattice siever, to make factoring numbers 10x cheaper than the previous…
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Space Emerging from Quantum Mechanics
The other day I was amused to find a quote from Einstein , in 1936, about how hard it would be to quantize gravity: “like an attempt to breathe in empty space.” Eight decades later, I think we can still agree that it’s hard.
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The inspection paradox is everywhere (2015)
I have updated this article with new data, better code, and friendlier data visualization. You can read the new version here . Th...
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No, RSA Is Not Broken
I have been seeing this paper by cryptographer Peter Schnorr making the rounds: “Fast Factoring Integers by SVP Algorithms.” It describes a new factoring method, and its abstract ends with the provocative sentence: “This destroys the RSA cryptosystem.” It does not. At best, it’s an improvement in factoring—and I’m not…
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Responsible Release of AI-Generated Mathematics
Responsible Release of AI-Generated Mathematics September 29, 2026 Back to main page Download PDF At present, some frontier AI labs are testing advanced mathematical problems on proprietary models …
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Principles of TLA+
TLA+ is a formal specification and verification language intended to help engineers specify, design and reason about complex, real-life algorithms and software or hardware systems. We explore its motivation, application and principles of design.
478
How Many People? Ancient Demography
Bret Devereaux (A Collection of Unmitigated Pedantry)2023121 points5 commentscited by 3History & Retro Computing details
One of the first questions anyone asks about past societies is, ‘how many people were there?’ It is one of those basic bits of information and generally speaking those of us who teach t…
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Floating-Point Printing and Parsing Can Be Simple and Fast
A floating point number f has the form f = m · 2 e where m is called the mantissa and e is a signed integer exponent . We like to read numbers scaled by powers of ten, not two, so computers need algorithms to convert binary floating-point to and from decimal text. My 2011 post “ Floating Point to Decimal Conversion is…
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