Justin Curry

😭

YouTube video by Rhodes Information Initiative at Duke Meet Sayan Mukherjee

RIP Sayan Mukherjee. You were a fantastic mentor, collaborator, and friend.

youtu.be/XF8B5afS1DI?...

From p.1 of https://math.jhu.edu/~eriehl/context.pdf: In 1941, Saunders Mac Lane gave a lecture at the University of Michigan in which he computed for a prime p that Ext(Z[ 1 p ]/Z, Z)  Zp, the group of p-adic integers, where Z[ 1 p ]/Z is the Prüfer p-group. When he explained this result to Samuel Eilenberg, who had missed the lecture, Eilenberg recognized the calculation as the homology of the 3-sphere complement of the p-adic solenoid, a space formed as the infinite intersection of a sequence of solid tori, each wound around p times inside the preceding torus. In teasing apart this connection, the pair of them discovered what is now known as the universal coefficient theorem in algebraic topology, which relates the homology H∗ and cohomology groups H ∗ associated to a space X via a group extension [ML05]: (1.0.1) 0 → Ext(Hn−1(X),G) → H n (X,G) → Hom(Hn(X),G) → 0 . To obtain a more general form of the universal coefficient theorem, Eilenberg and Mac Lane needed to show that certain isomorphisms of abelian groups expressed by this group extension extend to spaces constructed via direct or inverse limits. And indeed this is the case, precisely because the homomorphisms in the diagram (1.0.1) are natural with respect to continuous maps between topological spaces.

So Mac Lane and Eilenberg invented category theory so they could prove the universal coefficient theorem, which they discovered because Saunders showed an algebra computation to Sammy and Sammy went "Huh. That's how I compute the complement of the p-adic solenoid inside a 3-sphere."

The State of LLM Reasoning Models Part 1: Inference-Time Compute Scaling Methods

I just shared a new article, "The State of Reasoning Models", where I am exploring 12 new research articles on improving the reasoning capabilities of LLMs (all published after the release of DeepSeek R1): magazine.sebastianraschka.com/p/state-of-l...

Happy reading!

Neurosymbolic artificial intelligence via large language models and coherence-driven inference We devise an algorithm to generate sets of propositions that objectively instantiate graphs that support coherence-driven inference. We then benchmark the ability of large language models (LLMs) to re...

LLMs may be good for something new. Some of them are good at “fast thinking” that sets up “slow thinking” by combinatorial optimization. This flavor of “coherence” has deep roots in cognitive science. We made an algorithmic benchmark: o1, Sonnet, and QwQ do very well—apparently superhuman, even.

Maybe a hot take, but what about the following advice to the next gen:
Don't get an AI degree; the curriculum will be outdated before you graduate. Instead, study math, stats, or physics as your foundation, and stay current with AI through code-focused books, blogs, and papers.

“The essence of tyranny is the denial of complexity.”
― Jacob Burckhardt
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Made with #python #mlx #matplotlib
#particlelenia #alife

Sweet! Let’s catch up while we’re there

A mathematical visualization of polynomial roots creating a soft, organic shape against an off-white background. The image has a delicate, watercolor-like quality with translucent layers in pale blue and dusty rose. The structure has four-fold symmetry with rounded lobes at each corner containing subtle circular patterns. The center features a teardrop-shaped void. The entire composition is rendered with a grainy, textured effect that enhances the watercolor appearance. The overall effect is minimalist and ethereal, resembling a sophisticated botanical illustration.

Polynomial roots mist.
#MathArt #Mathematics
Made with #python #matplotlib #numpy #sympy

*hugs* See you at JMM?

The final Calvin and Hobbes cartoon. The entire page is mostly white as they're in the winter snow. The pair is walking with a sledge, nicely duffled in in scarves, hats, gloves. Calvin delightedly exclaims 'wow, it really snowed las night! Isn't it wonderful?'. Hobbes follows up with 'Everything familiar has disappeared! The world looks brand-new!' -- A new year... a fresh, clean start!' adds Calvin. As they look over the landscape, Hobbes observes 'it's like having a big white sheet of paper to draw on!' -- 'A day full of possibilities!' Calvin affirms. They get ready on their sledge and Calvin tells his friend 'it's a magical world, Hobbes, ol' buddy... let's go exploring!', and the pair sledges off into the wintery landscape.

31 December 1995. Still the perfect goodbye.

Yessss…K_0 = Euler Calculus!

Alternative grading in probability and statistics How we used competency-based grading for 300 computer science students at a Dutch university

Today at Grading for Growth: A guest post from two Dutch faculty on how they're using alternative grading in probability and statistics.

gradingforgrowth.com...

Random autumn snapshots

my younger brother is at the point of his undergraduate math degree (taking galois theory) where he no longer believes in the reality of the irrationals. they grow up so fast!

Tropical root responses to global changes: A synthesis Responses of roots can reveal the strategies and vulnerabilities of tropical ecosystems facing present and future global changes. This analysis of 266 root trait observations from 93 studies across 2...

Are you interested in Root responses to climate change? Read our latest synthesis article about tropical root responses to global changes led by Daniella Yaffar and Laynara Lugli @laylugli.bsky.social on Global Change Biology. #fineroots #tropicalroots onlinelibrary.wiley.com/doi/10.1111/...

I’m liking The Alignment Problem so far…

brianchristian.org/the-alignmen...

A complex mathematical visualization showing a black square rotated 45 degrees, with symmetrical, flowing colored curves emanating from each corner. The curves create an elegant abstract pattern resembling a four-petaled flower or cross. Each corner features intricate swirling patterns in multiple colors including red, blue, and yellow lines that interweave and curl inward. The equation for this parametric visualization is shown at the top of the image. The artwork is displayed on a black background, creating strong contrast with the colored curves. The overall effect is both mathematically precise and artistically beautiful, demonstrating the intersection of mathematics and visual art.

Roots of parametric polynomials.
Made with #python, #matplotlib, #numpy and #sympy.

Hexagonal Truchet pattern 1

Hexagonal Truchet pattern 2

Hexagonal Truchet pattern 3

Hexagonal Truchet pattern 4

I'm thankful for the #MathSky community developing here! Here are some random Catalan-Truchet-Tantrix-inspired patterns as a token of appreciation.

I should've introduced myself on my first day in my first posting. I'm an industrial engineer turned software programmer turned environmental urban planner turned statistician with an interest in information geometry. Spent some time on AI and machine learning. I'm a forever-learning person.

Yes!

Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal | Quanta Magazine Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge.

Three high schoolers have proved that a fractal called the Menger sponge can contain any knot. @gregbarber.bsky.social reports: www.quantamagazine.org/teen-mathema...

ngl, but the Starter Pack feature solves a really hard problem that Threads and TikTok both missed out on. Brilliant way to clone whole communities instead of waiting for it to happen naturally

Knot tiles with the math club this week (inspired by @divbyzero.bsky.social and @anniekp.bsky.social #mathartchallenge day 22). Random numbers, binary, knot theory, probability... so much to talk about. #ITeachMath docs.google.com/presentation...

Woo! I made it. Thanks Mathieu…

My deep learning course at the University of Geneva is available on-line. 1000+ slides, ~20h of screen-casts. Full of examples in PyTorch.

fleuret.org/dlc/

And my "Little Book of Deep Learning" is available as a phone-formatted pdf (nearing 700k downloads!)

fleuret.org/lbdl/

Nvidia’s new AI audio model can synthesize sounds that have never existed What does a screaming saxophone sound like? The Fugatto model has an answer…

Nvidia’s new audio model - Fugatto - can generate new sound effects from text descriptions arstechnica.com/ai/2024/11/n...