Associate Professor of Computer Science at Columbia University. Quantum information, computation, and cryptography.
New York, NY
Joined June 2009
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Henry Yuen retweeted
I hate teaching at @Columbia. You finally sneak an achievement into the faculty news roundup and the guy next to you in the alphabet wins the Nobel.
Henry Yuen retweeted
Can you (or your agents) improve the super-quadratic separation between block sensitivity and sensitivity from the current bound of ~2.006? The optimal exponent is between 2 and 4. My guess is 2.5 is achievable. Submit your lean-verified solutions here: prove2.me/campaigns/block-se…
Henry Yuen retweeted
I rarely post here these days but I wanted to share my reflections: people.csail.mit.edu/virgi/t…
Henry Yuen retweeted
We just crossed 100,000 proved theorems on Prove2Me!
Huge thanks to everyone who contributed, helped build the platform, and shared feedback. We couldn't have reached this milestone without you all.
And we're just getting started!
prove2.me/momentum
This is a beautiful essay by Raghu Meka on how, as mathematicians, we have sometimes placed artificial barriers in the way of the truth. Perhaps some broader lessons to draw from this.
From my friend and guide for a long time, a timely essay: terrytao.wordpress.com/2026/…
Henry Yuen retweeted
I think there’s a lot of truth to this. I welcome these results but if we want humanity to understand them it’s also important to support and reward human expertise in mathematics, and we (the mathematical community and society at large) need to find ways to do so.
Reading the comments of junior mathematicians confirms what many senior mathematicians have been warning about over the past month:
It is becoming clear that people with the intellectual ability to understand these proofs will not be interested in spending their lives training to check LLM logs.
This is the tragic side of what is happening that almost no one — except the actual mathematicians — seems to get.
Either we figure out how to keep people interested in doing mathematics, or in 20 years LLMs will have no one’s work left to recombine into new proofs, and no one interested in reading those proofs.
That would be the thermal death of mathematics.
The argument that “LLMs will read LLM math” is so shortsighted that it makes me want to cry…
New corollary just dropped.
For what it's worth, OpenAI's one-tape TM simulation (assuming correct) immediately implies RAM time t is in SPACE[t^{4/5}]
github.com/openai/math/blob/…
Not sure why they didn't mention this corollary! That was the whole point of my question.
Henry Yuen retweeted
Huge congrats to @firebat03 and @pinkfloydie on breaking the longstanding APSP and 3SUM conjectures!
How much lower can the exponents go? Bring your best ideas and prove it in Lean on Prove2Me.
prove2.me/campaigns/3sum-exp…
prove2.me/campaigns/apsp-exp…
Henry Yuen retweeted
This kind of thing is why it is so difficult to prove P != NP (if that is even true) - because such a proof has to account for, and only sometimes rule out, an incredible number of insanely clever algorithms which solve problems that at first seem fully intractable.
Suppose you have n integers, and you want to decide whether some three of them sum to zero. It's not hard to solve this problem in O(n^2) time (think how to do it, the dumbest algorithm takes O(n^3) time!) and for a long time it was thought that getting time O(n^{1.999999}) is not possible. This hardness assumption was shown to imply many other interesting hardness results.
Not anymore! Claude obtained the O(n^{1.9992}) time algorithm together with a Lean proof, and the algorithm was checked and digested by Josh Alman and Virginia Williams who are leading experts in fine-grained hardness, so my a priori estimate that it's 99.99%-likely to be correct.
My mind is just absolutely blown! It's crazy that in such simple to state problems progress is still possible after decades of many smart people thinking hard about them.
Wow! Cool result @firebat03 and @pinkfloydie !!
The what now?!
arxiv.org/abs/2610.06783v1
A not-so-subtle suggestion, @QuantaMagazine ? 😉
When he was in his 20s, Alexander Grothendieck’s ideas changed the course of mathematics. Then in 1970, he quit. Eventually, he moved to a small village in the Pyrenees, where he lived as a hermit until his death in 2014. quantamagazine.org/how-alexa…
Henry Yuen retweeted
We want to formalize everything. We want everyone to be able to build on it.
New public contributions on Prove2Me are now licensed under Apache 2.0!
See: prove2.me/blog/contributions…!
It's rare when the main result of a paper is tweetable! My postdoc Barak and I just posted a paper which shows all quantum circuits can be parallelized to very low-depth. Specifically, all n-qubit unitaries admit circuits with poly(n)-depth and exp-many ancillas.
Paper link: arxiv.org/abs/2609.40351
I am not entirely sure where this question originated from, but this is something that my former student @gregrosent asked and more recently @RobinKothari asked at the Simons Institute (see youtube.com/watch?v=7F5LBNGD…).
Henry Yuen retweeted
Earlier this month, I participated in a two-day workshop at the Simons Institute on how the TCS community should adapt to rapid advances in AI. Our report, AI and TCS: The Next Six Months, is now out:
simons.berkeley.edu/ai-tcs-w…
Henry Yuen retweeted
Two years ago I argued we needed an autoformalizer.
Now the time has come to formalize all of mathematics.
We need to unite behind a single Mathematics Autoformalization Project that turns all known mathematics into one Lean library.
@jdlichtman @patrickshafto
Henry Yuen retweeted
Hello, world! There is a new repository for works in math and TCS: hexagonmath.org, now in public beta. Please try it out and submit something! We welcome your feedback while we build and improve it.
Last week I had a stimulating visit to Stanford Q-FARM (thanks @vedika_khemani and Jeongwan Haah for hosting me). I gave a talk about The Power and Limitations of Constant-Time Quantum Computation to a lively audience. Talk details and video below.
youtu.be/6HHlaw7adVg?si=DzrD…
Talk Title: The power and limitations of constant-time quantum computation
Abstract: In this talk I will survey the landscape of models of "constant-time" quantum computing, where the computation time is independent of the system size. The most interesting models usually involve some kind of non-local operation such as measure and feedforward, many-qubit gates, and so on. These models are motivated by both practical concerns (e.g., near-term hardware is depth-limited) as well as fundamental theory questions (e.g., how do different many-qubit gates compare?).
These constant-time models are *powerful*, capable of preparing interesting classes of states and performing interesting computations. Many of these models are surprisingly *equivalent, *enabling transfer of techniques, results, and questions. Finally, I will discuss how these models uncover fascinating links between many-body physics and deep questions in computational complexity theory.