Computer scientist, computational biologist/chemist/physicist/cosmologist; PhD, MIT / Harvard Medical School; former Google AI research scientist; TED Fellow
Planet Earth
Joined May 2009
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I created a Claude Code skill that scours every major indexing service on the web to find the source or PDF for scientific papers, so that when you cite a paper, the claims you make around the citation are grounded in the actual content of the cited paper:
github.com/lukehutch/allpape…
Luke Hutchison retweeted
Israel has handed Netanyahu a humiliating defeat. But there's only one way the anti-Netanyahu bloc can ensure victory and avert his still-lurking danger: By lifting its Arab boycott | My analysis @haaretzcom
haaretz.com/israel-news/haar…
I need to re-watch this video every time I get mad that RAM prices are so high, to remind myself that it just might be worth it after all
Luke Hutchison retweeted
After 10 billion tokens of deep, extensive codebase analysis and improvement, fixing 7 years' worth of TODOs, I released version 6 of the widely-used #Java metaprogramming library ClassGraph: optimized, re-architected, modernized, and made futureproof.
github.com/classgraph/classg…
As part of this release, I split out ClassGraph's highly optimized and threadsafe/lock-free zipfile parser into a separate library, and made it into a full virtual filesystem, classgraph-vfs. This is the fastest, most scalable/paralleizable, and most full-featured/versatile VFS in the Java ecosystem.
After 10 billion tokens of deep, extensive codebase analysis and improvement, fixing 7 years' worth of TODOs, I released version 6 of the widely-used #Java metaprogramming library ClassGraph: optimized, re-architected, modernized, and made futureproof.
github.com/classgraph/classg…
As part of this release, I split out ClassGraph's highly optimized and threadsafe/lock-free zipfile parser into a separate library, and made it into a full virtual filesystem, classgraph-vfs. This is the fastest, most scalable/paralleizable, and most full-featured/versatile VFS in the Java ecosystem.
Luke Hutchison retweeted
Blog (main idea + context): nor-blog.pages.dev/posts/202…
Intuitive explanation: nor-git.pages.dev/prime-enum…
Paper: nor-git.pages.dev/prime-enum…
(3/3)
Luke Hutchison retweeted
A deterministic, unconditional algorithm that lists the primes below N in N (log log N)^{1+o(1)} bit operations on a multitape Turing machine, using GPT-6 Astra, building upon Harvey's recent breakthrough on prime enumeration. This achieves the bound from his paper without needing its conjecture.
(1/n)
Luke Hutchison retweeted
We have released Zero Breach Toolkit, a free open sourced tool capable of detecting over 12,100 traces of Israeli & other spyware on your devices. It works on Windows, Linux, Mac, Android and Iphones.
You can download it here: github.com/interplains/Zero-…
Inside the folder with the tools run this command: python -X utf8 scan/zero-breach-toolkit.py
It never writes to disk, never connects to the internet, or ask for admin perms. It takes around 10-15 minutes to run depending on the device.
This project is fully open source, so feel free to take the code and use it to create your own tools.
If you find some spyware on your device, consider sending it to us via telegram. Leave us a star on GitHub if the tool helped you.
Follow our backups: @ZionismExposedx
@IsraelExposedAr
God bless
This is exactly what I have been trying to explain to people about the ETH "subexponential" time finding... That word comes with a significant weakening condition that is mathematically subtle. ETH being false does not mean P=NP has been proved.
With the new results showing that 3-SAT can be solved in subexponential time, let me explain the confusing ways theoretical computer scientists talk about "exponential time".
There are two very different notions of exponential time in use:
1. The class E of problems solvable in 2^O(n) time, or equivalently O(2^(kn)) for some constant k, or O(c^n) for some constant c > 1.
2. The much broader class EXPTIME of problems solvable in O(2^(n^k)) time for some constant k.
The second is a misnomer: it’s the exponential of a polynomial, not just an exponential. But it’s the one complexity theorists usually mean, because it’s closed under polynomial-time reductions. In particular, every problem in NP is in EXPTIME.
Similarly, there are two notions of subexponential time:
1. 2^o(n): for every ε > 0, time O(2^(εn)), i.e. faster than O(c^n) for every constant c > 1. This one doesn’t have a standard class name.
2. The much smaller class SUBEXP: time O(2^(n^ε)) for every ε > 0.
The results announced by OpenAI and Anthropic run in approximately 2^(n /√log n) time. That makes 3-SAT subexponential in the first, weaker sense.
Proving 3-SAT is in SUBEXP would be a much bigger result. SUBEXP is closed under polynomial-time reductions and 3-SAT is NP-complete, so every problem in NP would then be solvable in subexponential time.
Luke Hutchison retweeted
With the new results showing that 3-SAT can be solved in subexponential time, let me explain the confusing ways theoretical computer scientists talk about "exponential time".
There are two very different notions of exponential time in use:
1. The class E of problems solvable in 2^O(n) time, or equivalently O(2^(kn)) for some constant k, or O(c^n) for some constant c > 1.
2. The much broader class EXPTIME of problems solvable in O(2^(n^k)) time for some constant k.
The second is a misnomer: it’s the exponential of a polynomial, not just an exponential. But it’s the one complexity theorists usually mean, because it’s closed under polynomial-time reductions. In particular, every problem in NP is in EXPTIME.
Similarly, there are two notions of subexponential time:
1. 2^o(n): for every ε > 0, time O(2^(εn)), i.e. faster than O(c^n) for every constant c > 1. This one doesn’t have a standard class name.
2. The much smaller class SUBEXP: time O(2^(n^ε)) for every ε > 0.
The results announced by OpenAI and Anthropic run in approximately 2^(n /√log n) time. That makes 3-SAT subexponential in the first, weaker sense.
Proving 3-SAT is in SUBEXP would be a much bigger result. SUBEXP is closed under polynomial-time reductions and 3-SAT is NP-complete, so every problem in NP would then be solvable in subexponential time.
Luke Hutchison retweeted
Extremely ugly and questionable result if true. The paper reminds me of some of the worst vibe coded PRs I've seen, where it's gaslighting you very convincingly with far too much verbosity and no actual coherent approach from alpha to omega.
If you've blown through a barrier you ought to be able to show a simple example where that's true and useful. Otherwise you're big-O'ing in a place with no actual cost of computation.
Those who say mathematics is over are wrong. I just suspect the current crop of practitioners is too kind hearted to properly tear something like this to shreds.
Here's a direct link to OpenAI's PDF claiming a refutation of ETH. In particular, it's claimed that 3SAT on n variables is in about exp(n/(log n)^{1/2+o(1)}) time
github.com/openai/math/blob/…
Luke Hutchison retweeted
RAW image decoding has been stuck on legacy C libraries for decades.
Today I'm launching FlashRaw:
- Up to 15.4x faster than LibRaw
- Decodes formats LibRaw cannot touch
- Built in Rust, with bindings for Python, JS, and C++
The benchmarks speak for themselves:
This is the sort of perspective we need right now on ETH/SETH
Luke Hutchison retweeted
My take on OpenAI’s ETH paper, as someone who spent nearly 20 yers on SAT: I don’t care about worst case analysis. That’s not what SAT solvers do. They do average case.
Doing analysis of average case is HARD. But it’s what matters. Rest is ivory tower stuff. Not for me.
Luke Hutchison retweeted
"The Dao of Functional Programming"
Regularly updated work in progress. PDF on GitHub:
github.com/BartoszMilewski/D…
Luke Hutchison retweeted
Regarding the Exponential-Time Hypothesis, this is what I wrote a decade ago!
cacm.acm.org/opinion/the-mor…
Luke Hutchison retweeted
Forget P vs NP. The most surprising thing in OpenAI's ETH paper is a corollary on page 3.
The headline result is an algorithm that decides, and even counts, k-SAT solutions in 2^O(n log log n / √log n) time with polynomial space. That's subexponential, so ETH falls and SETH goes with it. But it isn't a polynomial-time guarantee, and P vs NP remains open.
Corollary 1.4 is what stopped me. There's a language in E^NP whose circuits need more than c·n·√log n gates for infinitely many input lengths. Any fan-in-2 gates, unlimited fan-out, no restrictions.
Here's why that's strange. Five decades of work on unrestricted circuits moved the best lower bound from 2n gates (Schnorr 1974) to 3n (Blum 1984) to 3.1n (Li and Yang 2022). Every one of those is a constant times n. Even when you let yourself pick anything in E^NP, which is a huge class to hunt in, nobody had proven that linear size isn't enough. This isn't a better constant. The gates per input grow without limit.
So how does a SAT algorithm prove a circuit lower bound? That's Ryan Williams's idea from 2010. Take a problem that provably needs about 2^n nondeterministic time. If its proofs could be written down by small circuits, you could guess the small circuit and run a fast SAT solver to confirm the proof it describes has no broken clause. That solves the problem in about 2^(n/2) time, which the time hierarchy forbids. Fast SAT and small circuits can't both exist. If fast SAT is real, the circuits can't be small.
Williams is now one of the three people leading the open examination of this proof. The other two are Russell Impagliazzo and Ramamohan Paturi, two of the three people who proposed ETH in the first place.
What's actually been checked
• Lean verifies one fixed machine that counts k-CNF solutions in 2^O(n(log log n)²/√log n) time with polynomial space
• That bound is already subexponential, so if the formal statement means what it says, the Lean-checked algorithm plus Williams's published theorem is enough for "E^NP has no linear-size circuits"
• The exact n√log n rate needs the paper's sharper 2^O(n/√log n) bound for sparse formulas and a local reduction, and neither is in Lean
• No outside expert has signed off on any of it yet
The algorithm will get the headlines. The lower bound is the part that would change what we thought could be proven about circuits.
Paper
github.com/openai/math/blob/…
What Lean actually checked
github.com/openai/math/blob/…
Luke Hutchison retweeted
OpenAI disproved all these hypotheses:
ETH.
SETH, in its fixed-k formulation.
Randomized ETH, Randomized SETH.
Gap-ETH, deterministic and randomized.
Counting ETH.
Counting SETH, for fixed widths.
Nondeterministic SETH.
Quantum ETH and fixed-width Quantum SETH.
Unique-SAT ETH variants.
Fixed-width quantum counting, parity, and majority hypotheses asserting exponential hardness.
Average-case exponential-hardness hypotheses for fixed-width SAT decision/search/counting.
—————
The following related problems are still OPEN:
Unrestricted CNF-SAT ETH/SETH formulations, parameterized by the original number of variables.
Unrestricted CNF counting/parity hypotheses.
Broader QSETH frameworks, including unrestricted-CNF formulations.
Circuit-SAT exponential-hardness hypotheses measured in input bits, allowing polynomials many gates.
PPAD-ETH allowing polylogarithmic losses in the exponent.
Hypotheses about quantified SAT, lattice problems, and other problems without a suitable reduction.
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…
Luke Hutchison retweeted
An extremely well-done documentary covering the history of the LEAN programming language and automated theorem prover:
youtu.be/IRJDwtAreB4