The Mathematician 25-11-2025
history & mechanics of slide-rules, how infinity math links with computer science
🧩 Puzzles, Code & Projects
Fizz Buzz with Cosines (susam​.net). Explores Fizz Buzz using cosines, indicator functions, and a finite Fourier series in Python
Cosine FizzBuzz (re​.factorcode​.org). Cosine FizzBuzz in Factor demonstrates a finite Fourier series approach to FizzBuzz and shows code implementing it
Beach Spectres update – I’ve made a big tile! (aperiodical​.com). Update on Beach Spectres: Inkscape tiling, monotile cuts, 3D printed Spectre, schools activity, and a new beachspectres.com site
BrainTwister #100: Tricky angles (enigmaticcode​.wordpress​.com). Tricky angles in a square-triangle setup; calculations use tan, area relations, with Python code snippets in SymPy
Closest consecutive reciprocal sum to an integer (johndcook​.com). Explores how close sums of reciprocals of consecutive integers can come to integers, with Python and Mathematica analysis and 1908 proof by Kürschák
Solving H_n = 100 (johndcook​.com). Solving H_n = 100: exploring harmonic numbers, large-n approximations, and high-precision computations in Python/Mathematica with John D. Cook
🎼 Math & Culture
Is Matrix Multiplication Ugly? (mathenchant​.wordpress​.com). Matrix multiplication, transformations, and symmetry explored through critique of Hardy quote, with Propp's geometric view and links to AI, physics, and group theory
Ten Recent Questions for ChatGPT (gilkalai​.wordpress​.com). Ten questions for ChatGPT span combinatorics, topology, representation theory, and travel ideas, with AI-informed discussion and personal anecdotes
Beyond the Geometry of Music (golem​.ph​.utexas​.edu). Tymoczko's use of groupoids and symmetry in music theory, moving beyond orbifold geometry
đź“ś History & Biographies
The Hindu-Arabic Numerals: a Blessing for Modern Civilisation (thatsmaths​.com). Hindu-Arabic numerals, zero, decimal notation, Fibonacci, Al-Khwarizmi, numeration history and impact on commerce
The leading scientific instrument maker in seventeen-century London (thonyc​.wordpress​.com). Overview of Elias Allen, Charles Whitwell, Augustine Ryther, and their influence on 17th-century London instrument making and networks of mathematicians
Monday Morning Math: The first US PhD in mathematics (threesixty360​.wordpress​.com). Brief look at the first US PhDs in mathematics (1861–1862) at Yale and other universities, with Wright and Worrall and context on interdisciplinary titles
What’s your number? (arnoldzwicky​.org). Hungarian mathematician Paul Erdős, collaborative math network, Erdős numbers, and references to colleagues and calculators
How Slide Rules Work (amenzwa​.github​.io). Explores slide rules: history from ancient measurements to Gunter’s scales, Mannheim, Darmstadt and log-log duplex types, plus usage, accuracy, and notable models
🧠Logic & Foundations
Gödel, Mechanism, Paradox (umsu​.de). Explores Gödel, mechanism, and paradoxes via Knower and Belief variants, Löb’s theorem, and concerns about modeling mind as computable
A game strategy that depends on the Continuum Hypothesis? (thehighergeometer​.wordpress​.com). Game strategy with ordinals; Continuum Hypothesis dependence; uses well-ordering and AC in a two-player guessing game
Set theory with types (lawrencecpaulson​.github​.io). Typed set theory, higher-order logic, and de Bruijn’s ideas; Isabelle/HOL, AUTOMATH, PM; ZF embedding, type classes, and dependent products explained
Where “simulation” came from (decomposition​.al). Historical origins of simulation between programs, Milner’s 1970–71 work, and early hand-drawn verification diagrams
đź’» Algorithms & Complexity
Specifying digital systems using sequential functions (yodaiken​.com). Sequential functions for specifying digital systems, Moore machines, automata products, and real-time circuit behavior explained with modularity and temporal properties
Emmy, the Algebra System: Infix Notation (clojurecivitas​.github​.io). Emmy's YAMLScript infix notation for Clojure code, functional programming, derivatives, and higher-order abstractions explored in examples
A New Bridge Links the Strange Math of Infinity to Computer Science (quantamagazine​.org). Descriptive set theory meets computer science as Bernshteyn links infinite graphs coloring to Lebesgue-measurable algorithms
Factoring Carmichael Numbers (blog​.computationalcomplexity​.org). Explores Carmichael numbers, Fermat’s theorem, Miller-Rabin, and a hinted factoring approach with AI prompts and references
The Little Theorems (blog​.computationalcomplexity​.org). Little theorems in computational complexity, AI-assisted writing, and glimpses of P vs PP/#P connections, with references to Fortnow, Duede Tail Novelty, and historical publishing habits
🔬 Research Deep Dives
Student projects in complex function theory – The Prime Number Theorem and Riemann’s paper (noncommutativeanalysis​.wordpress​.com). Final student projects on complex function theory: Prime Number Theorem, Riemann’s paper, and related topics presented as videos and reports
Back to basics : Fréchet-Shohat CLT from cumulants (djalil​.chafai​.net). Fréchet-Shohat CLT from cumulants; self-normalized CLT; cumulants properties; determinantal processes; references
Sum-difference exponents for boundedly many slopes, and rational complexity (terrytao​.wordpress​.com). Terence Tao uploads arXiv paper on sum-difference constants, rational complexity, entropy, and projections in bounded slope settings
Climbing the cosmic distance ladder: another sample chapter (terrytao​.wordpress​.com). Terence Tao and Tanya Klowden unveil a second draft chapter on measuring distances across the Milky Way, with historical tech like Harvard computers and big data
Notes - NLA MT25, Power method (ollybritton​.com). Power method notes cover shifted inverse method, Rayleigh quotient iteration, eigenvalue convergence rates, and symmetry advantages
Notes - NLA MT25, Eigenvalue problems (ollybritton​.com). Overview of generalized eigenvalue problems, power method, QR algorithm, and related NLA MT25 topics in numerical linear algebra
đź“š Academic Research
Splitting vector bundles over real algebraic varieties (arxiv:math). Uses motivic homotopy and Chow–Witt theory to identify algebraic and topological obstructions to splitting rank‑one summands on smooth affine real varieties. Crucial for algebraic geometers studying real loci and vector‑bundle obstructions
Exceptions to the Erd\H os--Straus--Schinzel conjecture (arxiv:math). Establishes large lower bounds and explicit prime constructions for n where m/n fails to be three unit fractions, and gives density/exception bounds. Major analytic number‑theory progress on classical fraction representation problems
On an extension problem on the moment curve (arxiv:math). Proves extendability to cyclic‑polytope triangulations for complexes on the moment curve in dimensions ≤4 and builds nonextendable examples for ≥5. Impacts combinatorial topology and higher cluster category theory
On the isomorphism problem for ultraproducts of $\mathrm{C}^*$-algebras in continuous model theory (arxiv:math). Assuming ¬CH, constructs elementarily equivalent infinite C^*-algebras whose ultrapowers (by nonprincipal ultrafilters) are nonisomorphic, linking set theory with operator‑algebra model theory. Important for logicians and operator‑algebraists
Instanton dimensions of knot surgeries over arbitrary fields (arxiv:math). Provides a general dimension formula for framed instanton homology of p/q knot surgeries over any field and derives SU(2)‑representation consequences. Significant for low‑dimensional topology and gauge‑theoretic invariants
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