A mathematical puzzle asks whether two arbitrarily shaped potatoes can each have a closed curve drawn on them that are identical as curves in 3D space. The post discusses how to formalize this puzzle mathematically, interpreting potatoes as compact surfaces and curves as embedded loops.
A mathematician's colleague posted an abstract for an upcoming talk online, only to have a student elsewhere use AI to derive proofs of the results and post them to arXiv before the original researcher could submit their work.
SAIR Foundation is launching an initiative to build open-weight AI models for mathematics and science, with community-driven development, open licensing, and researcher control over data and training. The foundation is accelerating its timeline and seeking partners to contribute funding, compute, and expertise to create tools that support mathematical research and education.
Muhammad ibn Musa al-Khwarizmi was a 9th-century Persian mathematician and director of the House of Wisdom in Baghdad who pioneered algebra and championed the Hindu numerical system. His work on algebraic methods, polynomial equations, and the systematization of quadratic equation solving became foundational to mathematics globally, with his name giving rise to the words 'algorithm' and 'algebra.' His contributions, spread through Latin translations in the 12th century, profoundly influenced both Islamic and European mathematics.
Mathematicians proved in 2025 that any sufficiently large graph can be sandwiched between two simpler graphs, a conjecture posed in 2004 that connects two different types of random graph structures. This breakthrough demonstrates that random binomial graphs and random regular graphs are related in a deeper way, allowing difficult properties of regular graphs to be proven through their simpler counterparts.
A programmer used Claude to help formalize a proof of Conway's refinement conjecture about surreal numbers, a mathematical system invented by John Conway. The proof was written in Lean and passed mechanical verification, though it remains unverified by professional mathematicians.
Mathematics and physics share an intimate relationship dating back to antiquity, with mathematics serving as an essential tool for physical inquiry and physics inspiring mathematical innovation. Key historical developments—from Aristotle's classifications through Newton's calculus to Einstein's use of Riemannian geometry—demonstrate their deep interdependence, though the fields have gradually become more independent since the nineteenth century.
A founder reflects on delegating coding tasks to AI agents and confronts the broader existential challenge: as artificial intelligence surpasses human capabilities across domains from mathematics to art, how do humans maintain meaning, identity, and economic viability in a world where our intellectual contributions become obsolete? The author expresses hope that advanced AI, built on human knowledge and values, might discover paths to genuine coexistence that humanity itself has failed to find.
Epilogue is a platform showcasing open and solved problems across mathematics, physics, and computer science to inspire future problem-solvers. It features celebrated challenges like the Riemann Hypothesis and P versus NP, alongside historically solved problems like Fermat's Last Theorem, aiming to keep people engaged with compelling questions that drive scientific progress.
LLVM-libc, developed at Google over five years, implements the C standard library with a focus on portability, modularity, and clean C++ code. The project's math functions achieve correct rounding across all rounding modes, ensuring consistency in production systems where heterogeneous distributed computing demands deterministic results. MSVC and other LLVM projects now integrate LLVM-libc's math library for compiler use and runtime execution.
Timothy Gowers, a Fields medalist, explains why he declined to sign a letter by 25 Fields medallists regarding a mathematical crisis. He agrees with concerns about the field but offers a different analysis, and clarifies his independence from OpenAI despite having access to their models.
A mathematical exploration of Mrs. Perkins' Quilt problem, which challenges quilters to divide a square into the minimum number of smaller integer-sided squares. The author investigates a new sequence measuring the minimum number of L-shaped seams required to construct optimal quilts for each square size, presenting data for n=1 to 17 and raising open questions about the pattern's properties and potential OEIS inclusion.
A researcher presents a hybrid map projection that combines equal-area representation at global scale with seamless transition to Mercator projection when zoomed, addressing limitations of both Equal Earth and Mercator projections for interactive computer use following a UN resolution.
A mathematician recounts discovering difference sequences while attempting Fermat's Last Theorem as a child, explaining how the exploratory process deepened understanding despite not solving the original problem. The author declined to sign a letter by 25 Fields medallists on mathematics education, instead publishing independent thoughts on a perceived crisis in the field while clarifying lack of financial ties to OpenAI.
The term "computer" originally referred to people who performed mathematical calculations, with documented use dating back to 1613. Teams of human computers, increasingly composed of women from the late 19th century onward, were organized by institutions like observatories and the British Admiralty to conduct astronomical and navigational calculations, with standardized methods and verification procedures.
A mathematician argues that large language models should be understood as cultural and social technologies built from human knowledge, and proposes "mathematics above AI" as an approach where AI-generated proofs serve as starting points for deeper mathematical inquiry rather than final answers.
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A self-taught scientist reflects on how unconventional homeschooling and avoidance of formal mathematics education shaped their career. Despite lacking traditional academic foundations, they developed problem-solving skills through self-directed learning and eventually pursued science through community college, though they struggled with pre-calculus.
An essay argues that AI, particularly OpenAI's recent resolution of a Millennium Prize Problem, signals the end of human-led mathematical research. As AI systems become primary discoverers, humans will transition from researchers to priests (interpreters of AI-generated proofs) and eventually monks (contemplative devotees of mathematics), fundamentally reshaping the practice of mathematical science.
An article explaining how to estimate the number of digits in factorials using mathematical approximations. The author demonstrates the technique through Stirling's approximation and the Gamma function, showing that 52! has approximately 68 digits and explaining the underlying calculus behind these estimations.