SIAM Activity Group on Dynamical Systems

The new and final quarterly issue of DSWeb is now available: dsweb.siam.org Sorry, folks. DSWeb has had a good run.

A simple mathematical procedure, involving lots of trial and error, can teach a computer to identify pictures of cats. This kind of math is the engine behind modern AI. Here’s how it actually works: quantamagazine.org/how-can-ai-id-…

"Overall, we aim to promote a broader adoption of TSP by bridging methodological developments with applications, fostering its use among a wide community of theoretical and applied researchers."

"For instance, we introduce an edge-level signal capturing lagged interactions between nodal signals, and demonstrate its use in a case study on TSP-based analysis of brain imaging data, revealing nontrivial interactions between sets of brain regions."

"Topological Signal Processing: An Application-Oriented Tutorial" (by Flavia Petruso, Maria Giulia Preti, Dimitri Van De Ville): arxiv.org/abs/2605.22853

The physicist Sidney Nagel finds his new scientific inquiry through play. In his office at the University of Chicago, Nagel keeps an assortment of toys and demos, including a device that looks at how mustard seeds cascade (top center). quantamagazine.org/finding-beauty…

The Tower of Babel story is about punishment. For its arrogant, sky-reaching tower, humanity is condemned to speak in many tongues. For our mathematicians, the Tower of Babel is an inspiration. The Tower of Babel - Episode 2

“Evolution is not really like an inventor; it acts more like a tinkerer. . . . It takes parts that have existed long before, and it recombines, reinvents, and reshapes.”— Karthik Shekhar, biologist at UC Berkeley quantamagazine.org/how-the-bird-e…

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-alexander-…

Alexander Grothendieck, seen here in 1954, was fascinated by hidden geometric structure. “If there is one thing in mathematics which fascinates me more than any other (and undoubtedly always has), it is neither ‘number’ nor ‘size,’ but invariably shape,” he wrote. Mathematicians are still grappling with the innovations he made half a century ago. quantamagazine.org/how-alexander-…

The German mathematician Felix Hausdorff laid the foundations for modern topology. He was also a poet, philosopher, and playwright. quantamagazine.org/two-researcher…

With the help of her then-3-year-old daughter, biologist Kerstin Johannesson collected hundreds of snails along Sweden’s coastline and placed them on rocks exposed to the sea. Over only a few short decades, genes were activated that allowed them to cling better to rocks. Today, she’s studying how such rapid adaptation is possible. quantamagazine.org/how-ecotypes-h…

“I like to think of category theory as Mad Libs for mathematics. In Mad Libs, you have one story, but you get different versions of the story based on the different words you fill in. It turns out that there are certain stories or constructions that are shared across the mathematical landscape. Different branches of math might use different words for things — like ‘group’ instead of ‘vector space’ — but when you swap out words in the right way, you can see that the underlying framework or story is really the same.” — Tai-Danae Bradley quantamagazine.org/where-does-mea…

Utilizing Turing and Church’s invention of computability we can devise the sketch for a computability proof of Gödel’s incompleteness theorem that is equally as strong as Gödel’s version, but much easier to deduce: ift.tt/vhHdlpb