The Mathematician: 2nd September 2025

Mathematical family (cameroncounts​.wordpress​.com). Reflections on mathematical mentorship, collaboration, and the concept of mathematical families involving notable mathematicians like G. H. Hardy, Paul Erdős, and more

A crowdsourced project to link up erdosproblems.com to the OEIS (terrytao​.wordpress​.com). Crowdsourced linkage of Erdos problems to OEIS via a GitHub YAML workflow and discussion forums

International Conference on Enumerative Combinatorics and Applications ICECA 2025 (August 25-27, 2025) (gilkalai​.wordpress​.com). ICECA 2025 online conference August 25–27 features Richard Stanley lecture on Symmetric functions from a Ramanujan theta function; Toufic Mansour organizes, with links to abstracts and videos from prior editions and interviews with combinatorialists

SLMath announces new research programs (terrytao​.wordpress​.com). SLMath announces three new research initiatives with open applications starting Sep 1, 2025, announced by Terence Tao

Retirement party (cameroncounts​.wordpress​.com). Retirement party at Cameron Counts blog features talks by Mia Tackney on design of experiments and Rosemary methods in clinical trials, Scott Harper on advanced combinatorics and Cauchy numbers, plus reflections on finite group theory progress and a Zizzi dinner

How a poet’s long-forgotten daughter created the first algorithm (adamgrant​.micro​.blog). Ada Lovelace, daughter of Lord Byron, pioneered early algorithms, envisioned computers manipulating symbols, and contributed to Babbage's Mechanical Analytical Engine with her visionary insights

Finding a Horseshoe on the Beaches of Rio (thatsmaths​.com). Steve Smale's 1960s Rio beach work on chaos theory and the horseshoe map; IMPA in Rio; Johnson administration fallout; Norman Levinson letter; chaos theory origins

the MANIAC, or when machines strike deep inside enemy lines (am17an​.bearblog​.dev). Explores the lives of Paul Ehrenfest and John von Neumann, the rise of Artificial General Intelligence, and the philosophical implications of machine superiority

Review: The Mathematician’s Library, by Thomas K. Briggs (aperiodical​.com). Briggs’s Mathematician’s Library surveys global mathematical texts from India, China, and beyond, via six chronological sections and visually rich selections

The Martians of Science (markbernstein​.org). Budapest-born physicists von Neumann, Szilard, Teller, Bohr? No, five Martians at Los Alamos; group biography detailing their paths from Budapest to Germany to the US, their roles in the atomic bomb project, and the political shifts that followed

André ou Jean Ville (1910-1989) (xianblog​.wordpress​.com). Overview of Jean/André Ville's life, contributions to martingale inequalities, counterexamples, early computer use, collaboration with mathematicians like Gödel, Popper, and Wald, and his diverse career

The Bejewled ‘Rubaiyat of Omar Khayyam’ at the Bottom of the Ocean (atlasobscura​.com). The jewel-encrusted 'Rubaiyat of Omar Khayyam' sank with the Titanic, showcasing the poet's journey from mathematician to literary sensation in the 19th century

Archaeologists Explore Estate Where Isaac Newton Was Born (archaeology​.org). Archaeologists excavate Woolsthorpe Manor grounds, uncover everyday Newton-era artifacts, aim to locate Hannah Newton’s house site, reveal 17th-century daily life tools

Girls’ Angle Bulletin, Volume 18, Number 6 (girlsangle​.wordpress​.com). Interview with Greta Panova; creativity in math, math competitions, Caitlin Cunjak’s Fibonacci matrices, graph constructions from codes, Summer Fun problem solutions, OEIS sequences

Thoughts on teaching multivariable calculus (blog​.evanchen​.cc). MIT 18.02 recitations emphasize writing polished notes, concrete examples: determinants, linear independence, normal vectors; plus sound-bites, repetition, flexible planning, and office-hours tweaks for student learning

Inquiries-Week 4: Triangulate the Triangle (fractalkitty​.com). Dissect triangles into LMD vertices, shade LMD triangles, explore vertex placement and conjectures in an interactive Triangle Dissection Tool

Introduction to Hilbert Spaces: An Adventure In Infinite Dimensions (boffosocko​.com). UCLA Extension MATH 900: Introduction to Hilbert Spaces, orthogonality, orthonormal bases, Bessel’s inequality, linear operators, Legendre polynomials, Fourier series, Sobolev spaces, l2 and L2 spaces, course notes and bibliography by Chris Aldrich

Hints for the Patty Paper Trisection (denisegaskins​.com). Patty paper trisection puzzle hints, Euclid-inspired proofs, patty paper overlapping lines, angle congruence, Aha moment, Geometry Book I concepts, teaching tips, Let’s Play Math blog

The 2025 International Mathematical Olympiad (rishimehta​.xyz). AI and mathematics intersect at the 2025 International Mathematical Olympiad, where OpenAI and Google DeepMind reported gold-medal performances, signaling a milestone in the AI Grand Challenge proposed in 2020. The contest featured six problems worth seven points each, with a gold cutoff of 35/42 and a record allocation of 72 gold medals due to many ties. OpenAI announced a gold-medal solution in natural language within 4.5 hours, delivering remarkably terse proofs and occasional self-encouragement phrases, prompting questions about verification and protocol. Google DeepMind followed with a similarly fast, externally vetted submission whose proofs appeared polished, almost indistinguishable from human work. Behind the scenes, ByteDance's Seed-Prover claimed gold on P1-P5 after a multi-day run, relying on a hybrid of formal and natural-language data, test-time library learning, conjecture generation, and scaling strategies. Harmonic, a lean-focused startup, also claimed gold with readable but still lengthy proofs; AlphaProof and AlphaGeometry from 2024 had come close, missing gold by a single point. The author reflects on why the Grand Challenge wasn't decisively solved, noting that fair grading in such settings requires external graders, invigilators, and robust verifier protocols, a point Terry Tao had emphasized. The piece surveys broader lessons: the pace of AI progress now shows energy and momentum across labs, with many viable approaches and strong path dependencies. Lean provers still matter, but the trend is toward building unified models that both reason and formalize, enabling agentic coding and faster progress on harder mathematical problems in the near future. This signals continuing AI math convergence

Scoopert! (radar​.spacebar​.org). Tom 7 Radar discusses a convex polyhedron with Rupert's property, a non-Rupert result on arXiv, DOOM: The Dark Ages, Shantae and the Seven Sirens, and high-performance rational interval arithmetic

Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math (quantamagazine​.org). Busy Beaver BB(6) lower bounds explode beyond decimal notation; 6-rule Turing machines run for astronomically many steps, via shift overflow counters, tackled by Busy Beaver Challenge members like Doucette, Ligocki, Kropitz, and mxdys

17 Year Old Hannah Cairo Found a Proof to a 40 Year old Problem (jeffmilner​.com). Hannah Cairo, 17, debunks the 40-year-old Mizohata-Takeuchi conjecture, challenging conventional mathematical intuitions about function behavior

Linkage (11011110​.github​.io). 3d and layered QR codes, developable surfaces from flat strips, AI slop in knowledge, matroid parity, cubical spheres, topological book embeddings, LATIN call, Wikipedia search critique

Linkage from Toronto (11011110​.github​.io). Terry Tao funding hijack, Sudoku difficulty via human-like solvers, Eric Domain (MIT origami), MathJax 4.0, Frontiers of CS controversy, AI in IMO, Fermi–Dirac primes, parallelohedra, penny graphs recognition complexity, STOC 2025 break-through bounds

The Age of Genius, by David Lindsay (wormwoodiana​.blogspot​.com). David Lindsay article analyzes 'The Age of Genius' with tabulated life spans across war, statecraft, science, philosophy, literature, music and arts; questions genius longevity; cites Gladstone, Bismarck, Beethoven; speculative method on lifespan statistics and exemplary figures

A few more notes about Tom L (blog​.computationalcomplexity​.org). Anecdotes about Tom Lehrer, Tom L., obituaries, novelty songs, Jane Morgan’s death, updates to Tom L.'s Elements, complexity classes, and related musical and mathematical references

A thesis week (blog​.mitrichev​.ch). Mitrichev outlines randomized solving for problem H, uses edge-based backtracking, notes DP over DFS subtrees with at most backward edges, duplicating vertices for nonbipartite matching

Piecework (futilitycloset​.com). Henry Dudeney's Canterbury Puzzles (1907) asks how to cut an equilateral triangle into four pieces forming a square; 'strip of squares over triangles' offers proof

Tic-tac-toe meets Lean 4 (ochagavia​.nl). Lean 4 tic-tac-toe formalization with proofs, well-formedness, Vector 9, Fin 9, GameStatus, initialGameState, and Curry–Howard connections

Beyond Booleans (overreacted​.io). Lean's propositions-as-types, proofs as values, Not and by decide, and how 2+2=4 becomes a proof object; contrast with TypeScript booleans and the Prop type

Definite integrals, I: easy cases over finite intervals (lawrencecpaulson​.github​.io). Definite integrals, FTC variants, arcsin derivative, endpoint divergence, continuous antiderivatives, Isar proofs, derivative_intros, continuous_on, fundamental_theorem_of_calculus_interior, WolframAlpha, Maple, Isabelle proof scripting

Knuckledragger Analysis Etudes (philipzucker​.com). Explores balls, open sets, and contraction via Z3-backed tactics, unfolding lemmas, axioms, and bagged intermediate goals to prove real analysis properties in a knuckledragger style

𝒫𝔩𝔬𝔫𝒦: A Hands-On Deep Dive (blog​.zksecurity​.xyz). Hands-on tutorial covering 𝒫𝔩𝔬𝔫𝒦 proof system components like selector polynomials, wiring constraints, KZG commitments, and Fiat–Shamir proofs using Jupyter Notebook

The same colored grass (buttondown​.com/j2kun). Dan Abramov's lean+Mathlib journey on real numbers, Spivak's calculus critique, Emily Riehl's homotopy type theory talk, and the joy of cross-pollinating programming types with mathematical rigor

Science Notes / Pick Two Points (gregegan​.net). Geometric probability of random point pairs in a square; 4D hypercube mapping; parallel faces, Jacobian, and volume integrals; generalisation to d-dimensions and convex polytopes

From τὰ φυσικά (ta physika) to physics – XLIX (thonyc​.wordpress​.com). Examines the evolution of mathematical disciplines like algebra, geometry, trigonometry, logarithms, calculus, and their role in seventeenth-century natural philosophy and physics development

Fun Problem With A Golden Answer (mindyourdecisions​.com). Golden-ratio trick solving 9x+12x=16x; u=(4/3)x; solve u^2–u–1; x = ln((1+√5)/2)/ln(4/3)

Embroidering an aperiodic tiling (samjshah​.com). Sam Shah embroidery project uses aperiodic tiling with the spectre variant of the hat tile; threads, backstitch and satin stitch; water-soluble transfer paper; Threaded Theorems instructions; Scientific American explanation of aperiodic tilings

Three log scientist (curiouscoding​.nl). Analyzes a logarithmic reputation system for theoretical computer scientists, highlighting the prevalence of logarithms in algorithms, ranking tiers from no-log to four-log, and cultural perceptions

‘Ten Martini’ Proof Uses Number Theory to Explain Quantum Fractals (quantamagazine​.org). Ten Martini problem links Hofstadter butterfly fractals to Cantor set, almost-periodic functions, Avila’s global theory, and graphene experiments

parallels of statistical graphics and comics (xianblog​.wordpress​.com). Gelman and Kruglinski compare iconic statistical graphics (Galton’s correlation) with caricatures from Napoléon as a spider, linking data visualization concepts to comic imagery in Nightingale

Hadamard Factorization Theorem (kuniga​.me). Hadamard Factorization, genus and order of entire functions; Weierstrass, Jensen’s formula, Poisson kernel; Hadamard's theorem: h ≤ λ ≤ h+1; lemmas on order, genus, and canonical products

Multilinear polynomials: survival kit (blog​.lambdaclass​.com). Multilinear polynomials, hypercube interpolation, Lagrange basis, coordinates via evaluations, tensor product structure, and variable-dependence tests for products p_k(X)

What is mathematics? A classification based on universals (ebellani​.github​.io). Classification of mathematics by universals: realism vs nominalism (including Kantian conceptualism), Franklin 2014, De Wulf 1911; taxonomy of mathematical definitions; figures and references; author contact

The elementary theory of surreal arithmetic is bi-interpretable with set theory, Kobe, Japan, September 2025 (jdh​.hamkins​.org). Talk on the elementary theory of surreal arithmetic; bi-interpretability with set theory (V,∈); surreal field birthday order; ZFC bi-interpretation; collaboration with Junhong Chen and Ruizhi Yang; Kobe 2025

The biggest math symbol (johndcook​.com). Riemann P-symbol (Papperitz) for solutions to Riemann’s differential equation with three regular singular points a, b, c and Möbius-transformation behavior

God created the real numbers (ethanheilman​.com). Kronecker on integers, Cantor infinity, Cantorian theology, Descartes, Hilbert, and the hierarchy of creation in mathematics and nature

On Graham's rearrangement conjecture over $\mathbb{F}_2^n$ (arxiv:math). Provides near-complete resolution of Graham's famous 1971 conjecture about valid orderings in finite groups. Breakthrough combines additive combinatorics with probabilistic methods to solve a 50+ year old problem

Large implies henselian (arxiv:math). Establishes fundamental connection between large fields and Henselian local domains using étale-open topology. Provides new structural results about fields and answers questions in model theory and field arithmetic

First-order theory of torsion-free Tarski monsters (arxiv:math). Constructs simple torsion-free groups with same positive theory as free groups, answering several open questions. These exotic 'monster' groups cannot act on hyperbolic spaces with loxodromic elements

On the intersections of nilpotent subgroups in simple groups (arxiv:math). Completes proof of Vdovin's conjecture using probabilistic methods, showing nilpotent subgroups intersect trivially under conjugation. Resolves the stronger Lisi-Sabatini conjecture for all non-alternating simple groups

Rational Witt vectors and associated sheaves (arxiv:math). Develops theory of rational Witt vectors as uncompleted version of big Witt vectors. Establishes sheaf properties and connections to algebraic cycles, K-theory, and arithmetic geometry applications

Topologically 1-based T-minimal Structures (arxiv:math). Proves structure theorems for tame topological theories, establishing linear/non-linear dividing line called topological 1-basedness. Develops geometric group theory analogs of fundamental model-theoretic classification results

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