The Mathematician: 19th August 2025

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

Updates! (scottaaronson​.blog). Updates on GPT-5 capabilities, AI milestones (Gold Medal at IMO), OpenAI transparency, Inkhaven residency, questionable Frontiers paper, Forrelation hardness, OTOCs, Gaussian BosonSampling, and comments policy

Appearing on MoMath’s QED (mrhonner​.com). Mr Honner announces his guest appearance on MoMath's QED series discussing infinity with David Reimann, highlighting topics in math education, public outreach, and online events

Presentation Day (telescoper​.blog). MSc in Theoretical Physics and Mathematics at Maynooth concludes with student dissertations and presentations spanning mathematical, statistical, and physics topics; reflections on viva voce, AI pressure, and next year’s intake

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

New Physics-Inspired Proof Probes the Borders of Disorder (quantamagazine​.org). Band matrix thresholds for localization-delocalization transitions; Yau, Yin, Erdős, Knowles, and collaborators prove delocalization just above predicted band widths in 1D, 2D, 3D

Quasicrystals Spill Secrets of Their Formation (quantamagazine​.org). Quasicrystals revealed: thermodynamic stability via density functional theory, nanoscooping energy analyses, and Dynabead-based real-time observation of quasiperiodic assembly, plus antiferromagnetism discoveries

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

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

Hitomezashi stitching (samjshah​.com). Explores hitomezashi stitching through math-art, binary encoding, quilt patterns, Truchet tiles, steganography, aleotoric art, and hands-on embroidery projects inspired by Katherine Seaton

Son’s math test sparks internet outrage (mindyourdecisions​.com). Parent posts reveal debate over multiplication conventions: 3×4 as 3+3+3+3 vs 4+4+4; explores historical definitions from Euler, Euclid, and Common Core standard 5×7 example

More of Humanistic Mathematics (poetrywithmathematics​.blogspot​.com). Poems intertwined with mathematics featured in Journal of Humanistic Mathematics July 2025 issue; references to Vijay Fafat, Cristian Ramirez Rodriguez, Langellier, and Langellier; JoAnne Growney highlights poetry in math-focused publication

Glowing algae reveal the geometry of life (cam​.ac​.uk). Glowing Volvox carteri ECM reveals foam-like, foam-like network; pherophorin II fluorescence; stochastic geometry; machine learning for ECM compartment shapes; cross-disciplinary work Cambridge, Bielefeld; PNAS study

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

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

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

Fifty Years of Fractals (daily​.jstor​.org). Mandelbrot coinages fractal geometry, 1970s computing revolution, IBM work on noise, fractal art from inputs to outputs, dragon and Mandelbrot sets, iteration dynamics, geometry of nature, geometric scaling, academic shift from regularity to chaos, visualizations via computer graphics

Dicing an Onion, the Mathematically Optimal Way (pudding​.cool). Explores optimal onion dicing techniques using mathematical concepts like layer analysis, relative standard deviation, and targeted radial and horizontal cuts, with insights from Kenji López-Alt and Dr. Dylan Poulsen

Derivatives, Gradients, Jacobians and Hessians – Oh My! (blog​.demofox​.org). Derivatives, gradients, Jacobians and Hessians explained: optimize with gradient descent, compute partial derivatives, build Jacobians, explore determinants, and apply in rendering and ML

Flipping Burgers on an Infinite Plane (politicalcalculations​.blogspot​.com). Flipping burgers on an infinite plane; Thiffeault's Physica D heat-transfer model; patty thickness, flip frequency, 1 cm patty, 80–69 seconds; Kenji López-Alt 2019 corroboration; continuous flipping effects

Factoring Stencils (johndcook​.com). Lehmer's factoring stencils: 295 circular stencils, quadratic residues modulo N, primes up to 48593, light-through-holes method, SVG stencil generation, Python simulation of stencil stacking, factorization example N = 19972009 into 97, 103, 1999

random variate generation with [finite] guarantees (xianblog​.wordpress​.com). Finite-precision random variate generation, Mironov 2012, Laplace noise, CDF-based inverse transform, Knuth–Yao, GSL, finite-precision guarantees, DP implications, ACM PL, binary trees

Counterintuitive coin flips (mathspp​.com). Explore counterintuitive probability with interactive coin flips, fair vs biased outcomes, convergence to 50/50, visualisations, Python tips, and related math topics

100 Years of Statistical Power: From Neyman’s Power-Curves to Z-Curve (replicationindex​.com). Neyman, power curves, and Z-curves traced across a century of statistical methods, including Cohen's definitions, Pek et al. (2024), and implications for replicability in psychology

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

Simulating and Visualising the Central Limit Theorem (blog​.foletta​.net). Simulation and visualization of the Central Limit Theorem using R: sampling from six distributions, 20,000 means, population stats, QQ plots, and confidence interval exploration

Vandermonde Matrices are Merely Exponentially Ill-Conditioned (ethanepperly​.com). Gautschi’s bound on Vandermonde conditioning, exponential ill-conditioning, block Krylov iterations, RBKI, elementary symmetric polynomials, Lagrange vs Vandermonde, robust FTA, inverse Vandermonde entries

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

Abstract algebra structures made easy (blog​.sesse​.net). Explores how max(x,y) forms a monoid under the binary operation, uses 0 as a neutral element, and clarifies why it is not a group; touches on group theory and abstract algebra in CS

Pet Peeves (math​.columbia​.edu). Critique of SUSY training, Lie group notations, Lie algebras, complexifications, and representation mistakes; advocates understanding SO(3,1), SO(4), and their spin covers over SUSY extensions

Tiny Jubjub (johndcook​.com). Tiny Jubjub is a small elliptic curve over Z/13 with 20 points, showcasing properties of Jubjub curves, Montgomery and twisted Edwards forms, and SNARK-friendly features for zero-knowledge proofs

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

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

Did Turing ever halt? HPS Colloquium, Notre Dame, October 2025 (jdh​.hamkins​.org). Joel David Hamkins discusses Turing's 1936 paper, the halting problem, and whether Turing proved undecidability; joint work with Theodor Nenu analyzes historical attribution and presents arXiv:2407.00680

Typechecker Zoo (stephendiehl​.com). Rust implementations of type theory milestones from Milner's Algorithm W to modern dependent types, with literate code, test suites, parse libraries, and mascots; aims for readability over Haskell/Coq giants

On $q$-analogs of the $3x+1$ Dynamical System (arxiv:math). Conjugacy of q-analogs of 3x+1 via formal power series and 2-adics; T_q and T extended to F2[[q]] and Z2, with T_(A,B) family, fixed points, 2-cycle, and rational series connections

Mathematical Computation and Reasoning Errors by Large Language Models (arxiv:cs). Evaluation of GPT-4 variations and DeepSeek models on arithmetic, algebra, and number theory tasks reveals reasoning errors and the impact of dual-agent setups to improve mathematical accuracy

The pure $Y=X^{d}$ truncated moment problem (arxiv:math). Study of representing measures for real bivariate moments on y = x^d, focusing on (y−x^d)-pure moment matrices, core variety, recursive generation, positive semidefinite completions, and d=3,4 specialized results

Polynomial extension of Van der Waerden's Theorem near zero (arxiv:math). Polynomial Van der Waerden's theorem near zero for dense subrings of real numbers, combinatorial partitions, polynomial sequences, and sum conditions in a near-zero interval

Local-global compatibility and the exceptional zero conjecture for GL(3) (arxiv:math). Local-global compatibility for GL3, exceptional zero conjecture of Greenberg–Benois, p-ordinary RACARs, Steinberg at p, Gehrmann L-invariants, p-arithmetic cohomology, Fontaine–Mazur L-invariants, Hansen conjecture, 10-author strategy

On the system of length sets of power monoids (arxiv:math). Study of length sets in finite zero-containing subsets of N0 under set addition; shows for any rational q>=1 there exists A with max(L(A))/min(L(A))=q, supporting Fan–Tringali conjecture

Non-orientable regular hypermaps of arbitrary hyperbolic type (arxiv:math). Non-orientable regular hypermaps of hyperbolic type: infinite primes, PSL(2,p) automorphism groups, non-orientable surface carriers, and hyperbolic triples (ℓ,m,n) in compact surfaces

Generating random factorisations of polynomial values (arxiv:math). Algorithms generate random factorizations of polynomial values P(n) for quadratic and cubic polynomials, with applications to RSA key construction and density of divisor ratios

Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields (arxiv:math). Analyzes periodicity, symmetry, and dynamical behavior of Dickson polynomials over finite fields using combinatorics, number theory, and algorithms, focusing on sequences modulo x^q - x

The Resolvent Mean and The Parametrized $\mathcal{A} \sharp \mathcal{B}$ (arxiv:math). Extends resolvent average and geometric mean concepts from positive definite to accretive matrices, establishing inequalities and properties in matrix analysis frameworks

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