The Mathematician: 1st July 2025

Girls’ Angle Bulletin, Volume 18, Number 5 (girlsangle​.wordpress​.com). Interview with mathematician Amanda Tucker, middle schoolers' investigations on powers of 2 and 3, and Latin squares exploration featured in Girls' Angle Bulletin

Craig Kaplan named 2025 Fields Institute Fellow (uwaterloo​.ca). Craig Kaplan honored as 2025 Fields Institute Fellow for contributions to mathematics, computational geometry, and art; known for aperiodic monotile discovery

Travels, 10 (cameroncounts​.wordpress​.com). Peter Cameron reflects on his month in Aveiro, Portugal, reviewing an academic aggregation process for Maria Elisa Fernandes’ research on regular polytopes

Counting with Categories (johncarlosbaez​.wordpress​.com). Minicourse on combinatorics covering species, generating functions, and binary trees at the National Technical University of Athens

Double Maths First Thing: Issue 2A (aperiodical​.com). Colin Beveridge discusses combinatorial problems, Rubik's Cube competitions, and recent mathematical findings while promoting joy in mathematics across the cosmos

He was a spy and a scam artist who also invented the bar chart (mathewingram​.com). William Playfair, a spy and scam artist, invented the bar and pie charts and pioneered line charts while navigating a life of scandal and debt

Breakthrough on 125 Year-Old Physics Problem (backreaction​.blogspot​.com). Sabine Hossenfelder explores a significant advancement in solving a long-standing physics issue, highlighting mathematics, quantum gravity, and implications for particle physics

Quick Thinking (futilitycloset​.com). Richard Feynman's quick problem-solving skills tested by Paul Olum, involving a complex mathematic challenge related to the tangent function

Finding Peter Putnam (nautil​.us). Peter Putnam, a forgotten physicist and philosopher, made groundbreaking contributions to the understanding of consciousness yet remains largely unknown due to his unpublished work

Fashion tips for writing math. (mathwithbaddrawings​.com). Ben Orlin explores writing mathematics with style, emphasizing aesthetics over conventions, and tips on notation, derivatives, and variance manipulation

Learning is About Bridge-Building, Not Jumping (justinmath​.com). Importance of bridging foundational skills in cognitive science to enhance working memory and problem-solving capabilities in education

Recall First, Reason Second (justinmath​.com). Automaticity in learning emphasized through recall-first strategies; practice applying results from memory before reasoning or deriving them

Responsible modelling – Erica Thompson (andifugard​.info). Erica Thompson discusses responsible modelling ethics in mathematics for decision-making, focusing on AI applications and the limitations of mathematical models for real-world decisions

A Cubic Challenge (themathdoctors​.org). Explore methods to find a cubic function with specified maxima and minima using algebra, graphing software, and calculations without derivatives

Oxford Entrance Exam How Many Distinct Real Solutions (mindyourdecisions​.com). The Oxford Entrance Exam problem explores the equation with nested squares, revealing seven distinct real solutions through a step-by-step analysis

How Does Graph Theory Shape Our World? (quantamagazine​.org). Maria Chudnovsky discusses graph theory, her perfect graph problem solution, and its applications in everyday life, along with reflections on mathematical communication

Row and Columns (futilitycloset​.com). A mathematical problem from the Moscow Mathematical Olympiad demonstrating that the sum of the two largest numbers in rows equals that in columns

Inequality Union Finds: Baby Steps to Refinement E-graphs (philipzucker​.com). Exploration of refinement e-graphs and inequality union finds for better handling of rewrites and assertions in programming languages

QuiverTools: the writeup (pbelmans​.ncag​.info). QuiverTools v1.1 released for SageMath and Julia, enhancing quivers and moduli spaces with Riemann–Roch theorem insights and new algorithms

Conway's game of life in 3 dimensions (pbelmans​.ncag​.info). Exploration of Conway's Game of Life in 3D using D3.js, featuring preloaded patterns and encouraging further development in open-source projects

“Matrix Inverse Using Cayley-Hamilton with C#” in Visual Studio Magazine (jamesmccaffrey​.wordpress​.com). Cayley-Hamilton matrix inverse method demonstrated in C#; explores characteristics, implementation challenges, and limitations for machine learning algorithms

Scales as Multipermutations of 0 and 1 into Twelve Places (petecorey​.com). Generating arbitrarily defined musical scales using multipermutations of 0 and 1 to explore interval relationships and property testing in Elixir

Drawing with Circles: Vibe coding the Fourier Transformation (punyamishra​.com). Explores visualizing the Fourier Transformation through circles, showcasing its role in digital signals, sound processing, and creating intricate images through mathematical harmony

Triangle wave (jimkang​.com). Exploration of triangle wave equations using Desmos for visualization and understanding component synthesis in waveform creation

A New Pyramid-Like Shape Always Lands the Same Side Up (quantamagazine​.org). Newly constructed tetrahedron shape balances on one face, confirming John's Conway's conjecture, engineered using carbon fiber and tungsten, with applications in spacecraft design

The Herschel enneahedron on Numberphile (aperiodical​.com). Christian Lawson-Perfect discusses the Herschel enneahedron, die fairness, symmetry, kite shapes, and offers a 3D interactive visualization

A maximally inefficient Monte Carlo estimate of pi (possiblywrong​.wordpress​.com). Monte Carlo methods estimate pi through coin flipping strategies, dart throwing simulations, and Buffon's noodle, exploring efficiency and computational cost

Why learn about the golden-section search (wordsandbuttons​.online). Explore the golden-section search and bisection search algorithms, comparing their computational efficiency and convergence characteristics in numerical optimization

Calculus Phobic’s Introduction to Differentiable Programming (andersource​.dev). Introduction to differentiable programming using JAX, focusing on optimization techniques, gradient descent, and automatic differentiation principles for solving computational problems

Optimal Addition Sequences for Integer Multiplication (jonot​.me). Exploration of optimal addition sequences for integer multiplication on limited CPUs, utilizing dynamic programming techniques for efficient computation

Constant-Time Breakthrough Raises the Hash-Table Speed Limit (emsi​.me). New hash table design achieves constant average access time and logarithmic worst-case time, revolutionizing data structure efficiency in high-load computing

New Proof Dramatically Compresses Space Needed for Computation (cosmicmeta​.io). Ryan Williams' proof revolutionizes algorithm memory efficiency, compressing space needed for computation and redefining the time-space trade-off in computer science

BusyBeaver(6) is really quite large (scottaaronson​.blog). Busy Beaver(6) exceeds previously known bounds, now at least 2 pentated to 5, showcasing Turing machine complexities and implications on set theory

The Distribution of Prime Numbers: A Geometrical Perspective (blog​.computationalcomplexity​.org). Exploration of prime number distribution using random walks and Jacob's Ladder visualization to uncover patterns and questions in number theory

Legendre and Ethereum (johndcook​.com). Legendre PRF and its potential use in Ethereum 2.0's proof of custody through pseudorandom number generation and zero knowledge proofs

Patching functions together (johndcook​.com). Exploration of patching functions, continuity, and smoothness; C¹, C² classifications, natural cubic splines, and implications for physical applications

Two high school students have a new proof of the Pythagorean Theorem / Pythag theorem older than thought (blog​.computationalcomplexity​.org). Two high school students prove the Pythagorean Theorem using elementary methods, with evidence of its use predating Pythagoras by a millennium

Convergence of Random Events (clojurecivitas​.github​.io). Exploring Central Limit Theorem's role in understanding converging random events, including coin flips, the Monty Hall problem, and average calculations in programming

Diophantine Equations over $\mathbb Z$: Universal Bounds and Parallel Formalization (arxiv:math). Explores bounds on Diophantine equations, universal pairs for integer unknowns, and integrates formal verification with the Isabelle proof assistant

LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving (arxiv:cs). LeanConjecturer automates university-level mathematical conjecture generation using LLMs, enhancing theorem proving with novel conjectures and verifying non-trivial topology theorems

Universal Gluing and Contextual Choice: Categorical Logic and the Foundations of Analytic Approximation (arxiv:math). Universal Gluing and Contextual Choice Principle enables local construction, analytic approximation, and stability in computational mathematics and constructive analysis through categorical logic

Trace Formulas in Noncommutative Geometry (arxiv:math). Asymptotic expansions of trace formulas in noncommutative geometry using multiple operator integration; Dixmier trace formula for density of states on manifolds

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research (arxiv:math). Study of collaboration network structures reveals popular topics form modular 'schools of thought,' while niche topics exhibit hierarchical core-periphery structures in mathematical research

General Mathematical Proof of Occam's Razor; Upgrading Theoretical Physicists' Methodology (arxiv:math). Mathematical proof of modernized Occam's razor utilizing Kolmogorov complexity; proposing efficient methodology for theoretical physics research through information assessment

Generalized Multiple Operator Integrals for Operators with Finite Dimensions (arxiv:math). Development of Generalized Multiple Operator Integrals (GMOIs) for non-Hermitian matrices, extending traditional operator theory and facilitating new applications in functional calculus and matrix derivatives

Iteration Steps of 3x+1 Problem (arxiv:math). Explores the 3x+1 problem, defining relationships among total, odd, and even iteration steps using the weak residue conjecture and logarithmic expressions

Some Mathematical Problems Behind Lattice-Based Cryptography (arxiv:math). Explores mathematical foundations of lattice-based cryptography, addressing SVP, CVP, and their complexities amid post-quantum cryptography standards by NIST

On the distribution of shapes of pure quartic number fields (arxiv:math). Investigates shapes of pure quartic number fields, revealing a distribution governed by continuous and discrete measures linked to residue classes and torus orbits

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