The Mathematician: 29th July 2025

Introduction: The Man Who Thought Differently (analog-antiquarian​.net). Aristarchus of Samos proposed heliocentrism 250-300 years BCE, challenging geocentrism, influencing later astronomers like Archimedes amidst societal controversy

The English aristocratic bastard, who advised the Florentines on matters nautical and published the first maritime atlas by an English author. (thonyc​.wordpress​.com). Robert Dudley, illegitimate son of the Earl of Leicester, became a maritime expert and authored the first English maritime atlas, influenced by his naval heritage

Tom Lehrer Passed Away at the Age of 97 (blog​.computationalcomplexity​.org). Tom Lehrer, mathematician and parody songwriter, passed away at 97, remembered for his political satire and songs like 'The Elements' and 'The Vatican Rag.'

That Time Tom Lehrer Pranked the NSA (schneier​.com). Tom Lehrer humorously engaged with the NSA in 1957, blending satire, mathematics, and gambling themes in his work, notably his song 'Lobachevsky.'

Musical Genius Tom Lehrer Passes Away at 97 (flyingpenguin​.com). Tom Lehrer, influential satirist and musical genius, passed away at 97, leaving a legacy of humor, mathematical prowess, and significant contributions to public domain music

Happy Retirement, James Hirschfeld! (telescoper​.blog). James Hirschfeld retires after nearly 60 years at Sussex University, celebrated by colleagues and students for his contributions to mathematics and teaching

Among the Last Human Gold: Gemini Eats the Olympiad (drinkyourmilk​.blog). AI system Gemini Deep Think impressively solved five math problems at the IMO 2025, signaling a shift in benchmarks of human excellence

Amazing: Jie Ma, Wujie Shen, and Shengjie Xie Gave an Exponential Improvement for Ramsey Lower Bounds (gilkalai​.wordpress​.com). Jie Ma, Wujie Shen, and Shengjie Xie achieve exponential improvement in Ramsey lower bounds using geometric random models and advanced combinatorial techniques

Google and OpenAI Get 2025 IMO Gold (thezvi​.wordpress​.com). Google and OpenAI achieve gold in 2025 IMO using advanced LLMs, showcasing significant advancements in AI reasoning and problem-solving capabilities

2-Rig Conjectures Proved? (golem​.ph​.utexas​.edu). Kevin Coloumbier claims to prove 2-rig conjectures made by Todd Trimble, Joe Moeller, and John Baez, advancing research in category theory

Tom Hutchcroft Honored by London Mathematical Society (caltech​.edu). Tom Hutchcroft awarded the 2025 Whitehead Prize for contributions to probability theory, particularly in Bernoulli percolation and Cayley graphs

What is a Hitomezashi Snowflake? (questionsindataviz​.com). Explores Hitomezashi, a form of Sashiko embroidery, its mathematical properties, and Fibonacci Snowflakes through data visualisation using Tableau and Morse code

The prophecy in the pi decimals (earth​.hoyd​.net). Exploring patterns in the decimals of pi through mathematical sums and programming with Python to uncover hidden prophetic sequences

Zigzag Number Spiral (susam​.net). Exploration of closed-form expressions for calculating numbers in the Zigzag Number Spiral grid using mathematical functions and patterns

Hen and Chicks Whorls (bruceediger​.com). Hen and chicks plants exhibit Fibonacci Sequence in whorls, with counts of 13 and 21. Exploration of patterns in nature and plant growth

Tricolor (futilitycloset​.com). Hexagonal cell coloring rules predict the last cell's color in an inverted triangle, discovered by mathematician Steve Humble and discussed in a 2013 paper

Viral Puzzle Only 1 Percent Can Solve (mindyourdecisions​.com). Presh Talwalkar presents a challenging viral math puzzle that tests interpretation of expressions and prompts viewers to engage with fundamental concepts in game theory and mathematics

Hardest Question From China’s University Entrance Exam (mindyourdecisions​.com). Analysis of China’s Gaokao exam, featuring a challenging calculus problem that stumped 10 million test-takers, with a detailed explanation of the solution

ChatGPT and beam bending redux (leancrew​.com). ChatGPT's struggle with beam bending problems reveals inconsistencies in answers, reliance on external sources, and failed algebraic reasoning, highlighting challenges in AI explanations

Analogs of binomial coefficients (johndcook​.com). Exploration of q-binomial coefficients, Stirling numbers, and Eulerian numbers arranged in triangular forms similar to Pascal's triangle

The ruliad and possibilities space (markjgsmith​.com). Exploration of the ruliad concept, a possibilities space for all computations, and its implications from Mark Smith's perspective on technology and science

Annuity and factorial notation (johndcook​.com). Actuarial notation for annuities and historical factorial symbols, with a focus on LaTeX usage and specific mathematical representations

Helly’s Theorem (futilitycloset​.com). Helly's Theorem states that the intersection of convex sets in the Euclidean plane is non-empty if every triple’s intersection is non-empty

On texml and texml-to-html (peterkrautzberger​.org). Exploration of AMS's texml and texml-to-html tools for converting TeX to HTML, comparing with pandoc, make4ht, and other TeX-to-HTML systems

GKR protocol implementation: deep dive into the code (blog​.lambdaclass​.com). Explore GKR protocol's efficient computation verification, arithmetic circuits structure, implementation in Lambdaworks, and integration of the Fiat-Shamir transform

Encoding SAT in OCaml GADTs (farlow​.dev). Encode boolean satisfiability (SAT) problems in OCaml using GADTs, demonstrating compiler constraints and NP-hardness in computation

Tribonacci Numbers (re​.factorcode​.org). Explore tribonacci numbers, a three-argument variant of Fibonacci, implemented with memoization in Factor for improved performance with tets

Little ray of sunshine (quantumfrontiers​.com). Nicole Yunger Halpern reflects on Ray Laflamme's impact in quantum computing, mentorship experiences, and personal growth in academia

The Kepler Problem (Part 6) (johncarlosbaez​.wordpress​.com). Explores quantum and classical aspects of the Kepler problem, highlighting symmetries, conserved quantities, Duflo isomorphism, and the connection to conformal field theory

The Kepler Problem (Part 5) (johncarlosbaez​.wordpress​.com). Exploration of Kepler's problem, 3-sphere wavefunctions, hydrogen atom Hamiltonian, and quantum mechanics angular momentum representations

Lawvere's Work on Arms Control (golem​.ph​.utexas​.edu). Lawvere's classified work on arms control in the 1960s during his thesis addresses technical aspects relevant to security and defense

A mathematician’s coming-of-age story. (mathwithbaddrawings​.com). Exploration of mathematical philosophies from Platonism to pragmatism, discussing the nature of mathematical objects and how mathematicians evolve in their understanding

(-e^{i\pi}) to Watch: Another Roof (aperiodical​.com). Alex's YouTube channel 'Another Roof' explores higher-level mathematics through theory-building, reflecting his teaching experience and passion for academic pursuit

Double Maths First Thing: Issue 2E (aperiodical​.com). Colin Beveridge explores puzzle-solving in math, discusses Galois fields, map projections, and shares resources like crochet projects and topological data analysis

Why the Key to a Mathematical Life is Collaboration (quantamagazine​.org). Fan Chung emphasizes collaboration's role in mathematics through her work across graph theory, Ramsey theory, and connections to computer science and engineering

Math Poetry: The Square (denisegaskins​.com). Explore math poetry with Denise Gaskins, emphasizing writing as a tool for creative reasoning and deeper understanding of mathematical concepts

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (arxiv:cs). Transfinite fixed points in Alpay Algebra, ordinal game equilibria, dependent type theory, constructive logic, semantic convergence, self-referential systems, proof assistants

IsaMini: Redesigned Isabelle Proof Lanugage for Machine Learning (arxiv:cs). Neural Theorem Proving with MiniLang enhances Isabelle/HOL proof language, improving LLM success rates on PISA benchmark significantly

A Scientist Question: Research on the Impact of Super Structured Quadrilateral Meshes on Convergence and Accuracy of Finite Element Analysis (arxiv:math). Explores global arrangement structures of super structured quadrilateral meshes and their effects on finite element convergence and accuracy using geometric topology theories

Splitting phenomenon in the Sathe-Selberg theorem, mod-Poisson convergence with auxiliary randomisation and universality of the Gamma factor (arxiv:math). Exploration of mod-Poisson convergence and universal Gamma factor in random variables, including permutations, Gauss integers, and probabilistic number theory

The norms for symmetric and antisymmetric tensor products of the weighted shift operators (arxiv:math). Study of norms for symmetric and antisymmetric tensor products of weighted shift operators; solutions to previously posed problems regarding weight regularity conditions

On harmonic quasiregular mappings in Bergman spaces (arxiv:math). Proves Hardy-Littlewood theorem for quasiregular harmonic functions in Bergman spaces; univalent mappings characterized in harmonic contexts

Learning neuro-symbolic convergent term rewriting systems (arxiv:cs). Neuro-symbolic architecture for learning convergent term rewriting systems, showcasing Neural Rewriting System and FastNRS with improved generalization and efficiency over strong neural baselines

The hidden subgroup problem for infinite groups (arxiv:cs). Exploration of hidden subgroup problem for infinite groups, NP-hardness findings, and stretched exponential algorithms for abelian hidden shift problem

Normally hyperbolic limit tori near monodromic singularities in 3D polynomial vector fields (arxiv:math). Maximal number of normally hyperbolic limit tori in 3D polynomial vector fields near monodromic singularities, utilizing averaging theory for improved bounds

Guessing sequences of eigenvectors for LMPs defining spectrahedral relaxations of Eulerian rigidly convex sets (arxiv:cs). Explores stable multivariate Eulerian polynomials, spectrahedral relaxations, and improved bounds for extreme roots using numerical vector sequences for Eulerian convex sets

I've got a big favor to ask - keeping Blaze running isn't expensive, but it does all add up, so I'm asking readers like you to help, if you can.
That's why I'm launching a Patreon page!. Nothing flashy, just a way for folks who find value in these newsletters to chip in a little each month. In return, you'll get:

• Real say in how Blaze evolves — vote on new topics, features, topic curation ideas
• First dibs on merch (details still cooking)
• That warm fuzzy feeling knowing you're supporting something that saves you time and keeps you plugged into great tech writing

If you are getting value from blaze, checking this out would mean the world. And if you can't contribute, no worries—the newsletters keep coming either way, and you can follow along on patreon for free.
Thanks for reading and being part of this nerdy corner of the internet. All the best - Alastair.