The Mathematician newsletter
🔬 Recent Research
An enough week (blog.mitrichev.ch) . Overview of F problem on sorted arrays, randomized vs deterministic splitting, and DP-based analysis on tree substructures
Researchers Discover the Optimal Way To Optimize (quantamagazine.org) . Dantzig’s simplex method improved by Bach and Huiberts via more randomness; polynomial-time guarantees for optimization under constraints
Rising on arXiv - 2025-10-10 (blog.rinesi.com) . Overview of Lindbladians, zero-knowledge proofs, and the Algonauts 2025 Challenge with brain data and multimodal perception notes
🧩 Puzzles & Recreations
Change ringing: extensions to place notation (hunsley.io) . Explores extending place notation with a new ; operator for rotational symmetry, plus examples in Bristol Major, Double Norwich CBM, and other double methods
Basketball trivia, editing distances, and derangement (leancrew.com) . Basketball trivia about retirements, edit distances (Hamming, Levenshtein, Damerau-Levenshtein), and derangements with Python and Mathematica code examples
Do Nothing (blog.tanyakhovanova.com) . Creative interpretations of 8 + 8 = 91: flipping paper, modular arithmetic, bases, alien numerals, and classroom ideas
An NSA Puzzle (futilitycloset.com) . NSA puzzle on finding integers a,b,c,d,e,f,g >1 satisfying four equations and their product yields a unique solution 2,3,5,7,11,13,17
📜 History & Biographies
Book review: Science and Islam – A History by Ehsan Masood (ianhopkinson.org.uk) . Science and Islam–A History by Ehsan Masood surveys Abbasid translation, astronomy, medicine, algebra, trigonometry, and Bijir ibn-Hayyan within the medieval Islamic empire
Academic chat: On PhD (muratbuffalo.blogspot.com) . A reflection on PhD life: transformation, curiosity, mentorship, courage, and onboarding in CS, with personal anecdotes from Murat and Aleksey
Genius grant for Math-Woman (poetrywithmathematics.blogspot.com) . MacArthur Fellow Lauren Williams highlighted for connections between algebraic combinatorics, math, and physics; includes Marion Cohen poetry excerpt
Oct. 9, 1873: The birth of Karl Schwarzschild (astronomy.com) . Karl Schwarzschild’s birth and his pioneering solutions to Einstein’s field equations underpinning black hole theory
🤖 AI & Math
AI Delivers an Unexpected Mathematical Proof (politicalcalculations.blogspot.com) . AI GPT-5-Pro reportedly produced a new, verifiable mathematics proof improving a 1/L bound in convex optimization
Turing Test at 75 (markbernstein.org) . Turing Test at 75: a day-long symposium on the 75th anniversary of the Turing Test with talks and notes
AI as a Copilot for Mathematical Discovery (alexdong.com) . AI as a copilot for mathematical discovery; Ken Ono discusses AI's role, conjecture generation, and the future of math research
How AI Is Replacing Mathematicians (backreaction.blogspot.com) . AI tools, search for proofs, and the future role of mathematicians in problem-solving and verification
📘 Technical Notes
Binomial proportion estimation with unknown and varying number of trials (possiblywrong.wordpress.com) . Estimating a Bernoulli probability from paired daily hit counts with unknown daily trials, using a trick involving Paul and Quinn’s records
Notes on using LaTeX to generate formulae (eli.thegreenplace.net) . LaTeX rendering tips: standalone formulae, pandoc conversions, dvisvgm/dvipng, TikZ, TeXstudio, and Docker-based workflows
How many valid UTF-8 (or UTF-16, or UTF-32) byte sequences are there? (qntm.org) . How many valid UTF-8, UTF-16, and UTF-32 byte sequences exist, with recurrences and eigenvalues discussed
Notes - NLA MT25, Courant-Fischer minmax theorem (ollybritton.com) . Courant-Fischer minmax theorem for symmetric matrices and its relation to singular values, subspace optimization, and Weyl’s inequality
Random samples from a tetrahedron (johndcook.com) . Uniform random sampling inside a tetrahedron using exponential variables; compare with uniform sampling and cube-in-tetrahedron testing
Notes - NLA MT25, Norms (ollybritton.com) . Three useful inequalities and alternative characterisations for matrix and vector norms in MT25 NLA notes
📐 Pure Math Research
The Unknotting Number is Not Additive (divisbyzero.com) . Brittainham and Hermiller disprove additivity of unknotting number via connected sum, using torus (2,7) knot and its mirror with five-crossing projection changes
Monday Morning Math: Square Packing (threesixty360.wordpress.com) . Explores packing unit squares into larger squares, with rotation effects and known results for 1–11 squares, citing Trump and others
Explicit Lossless Vertex Expanders! (gilkalai.wordpress.com) . Explicit, constant-degree lossless vertex expanders via Ramanujan cubical complexes and base graphs, with group actions and LDPC-code implications
More on Carmichael (johndcook.com) . Generalizations of n and n^k ending in the same digit for base b, using φ(b)+1 and λ(b)+1; Euler's φ and Carmichael's λ functions with RSA context
Lattice path matroids (matroidunion.org) . Construction and properties of lattice path matroids via north/east lattice paths and duality
🧾 Formal Proofs
Formaising Domain Theory with Lean (anna-maths.xyz) . Formalising domain theory in Lean: Subset predicates, inSubset wrappers, directed sets, and dcpo proofs
Theorems for Free Redux (reasonablypolymorphic.com) . Explains Theorems for Free Redux: parametric polymorphism, free theorems, fmap, length, and examples like id and fromJust with type substitutions
ZF style set theory in Knuckledragger I (philipzucker.com) . ZF-style set theory in Knuckledragger I builds ZFSet, defines classes, Russell’s paradox, extensionality, empty set, picking, and unions
📚 Academic Research
The Hurwitz problem for abelian differentials (arxiv:math) . Introduces the Sobolev gap, a quantitative Casselman–Wallach invariant, and computes it for SL(2,ℝ), discrete and principal series. Provides uniform analytic bounds for automorphic functionals—key for representation theory
Bidifferentials, Lagrangian projections and the Virasoro extension (arxiv:math) . Characterizes Lagrangian supplements of H^0(C,Ω_C) via symmetric bidifferentials and constructs a Virasoro extension of the local derivation algebra. Important for algebraic curves, de Rham cohomology and conformal structures
Lagrangian Dual Sections: A Topological Perspective on Hidden Convexity (arxiv:math) . Introduces Lagrangian dual sections to expose hidden convexity via topological conditions, giving convex reformulations and algorithms for QCQPs and Stiefel-type problems. Bridges topology and optimization theory
Asymptotically large free semigroups in Zariski dense discrete subgroups of Lie groups (arxiv:math) . Constructs Zariski-dense free subsemigroups in semisimple Lie group lattices whose critical exponents approach that of the ambient group, via ε-contracting elements. Significant for geometric group theory and dynamics
Motivic Homotopy Groups of Spheres and Free Summands of Stably Free Modules (arxiv:math) . Shows motivic stable homotopy groups of the sphere can be recovered from p-completions and motivic cohomology, and applies this to realization/isomorphism results and free-summand questions for stably-free modules