@currying
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Associate Professor of Math & Statistics at UAlbany-SUNY
Albany, New York, USA
Joined November 2009
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Justin Curry retweeted
Graph theory turns complex relationships into pure geometry.
Nodes and edges transform abstract connections, whether flowing through an Arc Diagram or surrounding a Centralized Ring, into striking visual structures. Each distinct topology maps how information converges, branches, and spreads across a network.
From isolated clusters to spherical bounds, order reveals itself in every connection.
Justin Curry retweeted
The Curry-Howard correspondence is only one of many lenses we can use to view the relationship between things and facts. Different lenses characterize different approaches to foundation:
- Propositions are basic (single-sorted logics, ZF)
- Types are basic, some types are propositions (Homotopy Type Theory)
- Propositions and types are the same (Martin-Löf’s Type Theory)
- Propositions and types are different but equally basic (Logic-enriched Type Theory)
Shulman explains how the Axiom of Choice is true some but not in others, arguing that in certain respects, the HoTT’s way is the most “natural”: golem.ph.utexas.edu/category…
Adams & Luo argue instead for the practical virtues of making propositions and types completely separate: arxiv.org/html/0809.2061v3
Justin Curry retweeted
One "small" computation for AI, one leap for mathematicians. 30 years after the last bound towards the 1/3-2/3 conjecture an epsilon improvement breaks the barrier. Inspired by the breakthrough of Max Aires resolving the Kahn-Saks conjecture.
🤖 Made with AI
Justin Curry retweeted
I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here:
cmsa.fas.harvard.edu/aimathp…
i've made a game/app to teach my linear algebra students about cosine similarity... you can play "golf" with vector-embeddings of common words. try to get from "money" to "poetry" through hops with bounded cosine similarity. explore & hunt mode too...
claude.ai/artifact/NgCvFJH2z…
Justin Curry retweeted
Breaking math news: The first-ever 3D Einstein tile, an object that tiles space in a never-repeating pattern, has been found by independent researcher Ioannis Tsiokos using GPT Astra. Resembles a chair. Mathematicians have de-slopped the proof. @kkakaes: quantamagazine.org/updates/t…
As predicted, the AI for math push by the frontier labs is cooling as actual scientific discoveries, grounded in the real world, start to occur.
Claude has discovered a previously unknown enzyme system hidden in the DNA of bacteriophages. Beside the enzyme’s gene sits a long array of repeating DNA—a structure that looks somewhat similar to CRISPR.
We don’t yet understand what this system does, but only a handful of known systems share its features, and all of them are able to cut, copy, and paste DNA. Historically, the discovery of such programmable systems has helped revolutionize medicine. CRISPR, for instance, is now the foundation of genetic medicines. But it will take much more work to learn what this system does, and whether it can be put to similar use.
Read more: anthropic.com/news/claude-di…
Justin Curry retweeted
Lately I've been thinking a lot about mathematicians
What does it feel like to be surpassed by AI? What does it do to your sense of self? Your beliefs about your work? About the future?
So we found some of the world's best mathematicians and asked them
A chronicle of a moment in history:
Justin Curry retweeted
1/ Cornell just dropped a 200+ page report on “The Future of the American University” — the latest in a string of reports this year focused on reform.
provost.cornell.edu/_files/i…
Nice NYT piece by @stevenstrogatz and Alex Townsend, both applied mathematicians at Cornell!
Why should we care whether humans still understand mathematics if AI can solve the problems for us? Fair question. But we can say this at least: Historically, understanding has been a route to predictive power — with enormous benefits for our lives.
nytimes.com/2026/09/22/scien…
Justin Curry retweeted
Learn about category theory as Samson Abramsky uses it to talk about Arrow's Theorem.
arxiv.org/abs/1401.4585 – at Burnet, TX
Justin Curry retweeted
Jascha Sohl-Dickstein has an amazing blog post showing that the boundary between hyperparameter settings where neural network training succeeds and fails has a fractal structure.
The visualizations are mesmerizing.
sohl-dickstein.github.io/202…
Justin Curry retweeted
🗓️ Join me on October 7 for one of the inaugural lectures of the Science of Intelligence Institute at @UCBerkeley !
Can we write scientific laws for intelligence? I believe that we can, that the math for it already exists, and that they apply across brains & machines.
tinyurl.com/mvrfs39w
