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A backtracking search colors a real US map with four colors while you watch — and the fifty-year-old theorem behind it asks the same question we're now asking about trusting AI. I built a small thing this week: a page that colors a map of the United States so that…
Thousands of AI agents working in parallel have settled a famous million-dollar math problem about fluid flow. If AI can do that, its effects on hydraulic modeling will reach well beyond math. Will these mathematical solvers change the important equations engineers use inside their hydraulic modeling software? You may have…
This study assesses physics-informed neural networks (PINNs) for the unsteady two-dimensional flow past a rotating circular cylinder confined in a channel (blockage ratio 0.2) at Reynolds numbers of 50, 200 and 500. The networks…
Finding the shortest route between two locations is something navigation apps like Google Maps do every day. Behind the scenes, sophisticated algorithms analyze networks of roads and intersections to identify efficient paths. But…
Nature Machine Intelligence (2026) Cite this article A preprint version of the article is available at arXiv. where l is the single-sample loss function. Standard training algorithms minimize the loss by iteratively updating θ. For example, the stochastic gradient descent (SGD) algorithm can be expressed as the discrete-time dynamical system…
Axiom Math has released a machine-checked Lean formalization of the Stacks Project, a roughly 7,500-page open-source reference for algebraic geometry. The startup says coordinated AI agents produced about 16 million lines of code linking thousands of definitions, lemmas and theorems into one reusable library. [1] The claim is narrower than…
Lubis EDA has released FormalOs, a verification infrastructure platform which is designed to be a tool-agnostic orchestration layer for verification for SoC, asic and IP sign-off projects. According to the company, it unifies…