The Mathematician: 15th July 2025

Five Years of Blogging (ethanepperly​.com). Ethan N. Epperly reflects on five years of blogging, applied mathematics, and connections made within the research community, including influential figures and personal growth

Einstein’s Tutor, by Lee Phillips (skullsinthestars​.com). Explore Emmy Noether's impact on mathematics and physics, her pioneering work, and her struggles against societal barriers in 'Einstein's Tutor' by Lee Phillips

Grace shares how she mapped her way from fashion design to computer science (blog​.coursera​.org). Grace transitions from fashion design to computer science, overcoming math anxiety, inspired by Amalie Emmy Noether, while balancing family and breast cancer treatments

Learning by Writing . . . and Revising . . . (poetrywithmathematics​.blogspot​.com). Exploring the integration of poetry and mathematics through revision, with insights from Fanny Howe's quote on understanding one's condition by writing and revising

July 10, 1856: The birth of Nicola Tesla (astronomy​.com). Nikola Tesla, father of radio astronomy, was born July 10, 1856, known for his work with cosmic radio waves and wireless communication innovations

Salem Prize now accepting nominations for 2025 (terrytao​.wordpress​.com). Nominations for the 2025 Salem Prize are open until September 15, with preference for recent PhD graduates. Nominations require a CV and supporting materials

Arranging Letters in Words, Revisited (themathdoctors​.org). Combinatorial strategies for arranging letters, including vowel placement, permutations with duplicates, and specific letter positioning in words like 'MATHEMATICS' and 'GUMTREE'

Travels, 12 (cameroncounts​.wordpress​.com). Conference highlights in Évora, featuring theoretical and computational algebra discussions, historical venues, and personal reflections from Peter Cameron amid extreme temperatures

Double Maths First Thing: Issue 2C (aperiodical​.com). Colin Beveridge explores category theory, highlights mathematical themes in 'Friends,' and promotes inclusivity in mathematics through featured links and livestreams

How the continuum hypothesis might have been a fundamental axiom, Lanzhou China, July 2025 (jdh​.hamkins​.org). Originating from Lanzhou 2025, Hamkins explores the historical context which could position the continuum hypothesis as a fundamental axiom in mathematics

Lecture series on the philosophy of mathematics (jdh​.hamkins​.org). Lecture series on the Philosophy of Mathematics at Fudan University, featuring themes by Joel David Hamkins and Ruizhi Yang from 30 June to 25 July 2025

Lindenmeyer systems playground (blog​.exupero​.org). Lindenmeyer systems playground explores procedural generation using L-systems and includes state management commands like push/pop, improving random L-system generation

Programming Language Theory has a public relations problem (happyfellow​.bearblog​.dev). Exploration of Programming Language Theory's misunderstood perceptions and its challenges: theory versus applications, abstraction, and the complexity of language design

Using Lean like an External SMT Solver from Python (philipzucker​.com). Utilizing Lean as an External SMT Solver via Python, focusing on integrating verification tools and querying using the grind tactic

Truchet Tiles for the Commodore PET (masswerk​.at). Truchet tiles from 1704 implemented on Commodore PET, showcasing 30 patterns based on Sébastien Truchet's work, available for online emulation

Computer Scientists Figure Out How To Prove Lies (quantamagazine​.org). Research reveals vulnerabilities in the Fiat-Shamir transformation, jeopardizing the security of blockchains, cryptocurrencies, and proof systems reliant on hash functions

It is 1939 and you want to use public-key cryptography (shkspr​.mobi). Exploration of public-key cryptography feasibility in 1939: mathematical concepts, Enigma, asymmetric encryption, key management, and the challenges faced by early cryptographers

A probability puzzle involving random fractions (mathematicaloddsandends​.wordpress​.com). Analyzing a probability puzzle involving independent uniform draws, rounding fractions, and Monte Carlo simulations to find even integer probabilities

The Kepler Problem (Part 2) (johncarlosbaez​.wordpress​.com). Exploration of the Kepler problem, eccentricity vector, conservation laws, and connections to classical mechanics and celestial dynamics

Stable Distributions (bruceediger​.com). Exploring stable distributions, particularly Cauchy distributions, through programming, statistical analysis, and understanding probability density functions using R and Go

All the GUTs Worth Considering (dispatchesfromturtleisland​.blogspot​.com). Explores Grand Unified Theories in physics, detailing constraints, minimal models like SU(5), implications on particle existence, and the quest for unification beyond the Standard Model

Adding Up Feynman Diagrams to Make Predictions about Real Materials (caltech​.edu). Caltech scientists develop a method using diagrammatic Monte Carlo to accurately sum Feynman diagrams, solving the polaron problem in electron-phonon interactions

No Tension for Tensors? (hackaday​.com). FloatHeadPhysics explains tensors, showing their relation to vectors and operations in physics, illustrating concepts through engaging examples like satellites and hydroelectric dams

The Magic Theorem (aperiodical​.com). The Magic Theorem explores John Conway's classification of symmetrical patterns, detailing orbifold theory and its expansive implications across various geometric contexts

Big Daddy of Infinite Integrals (numberphile​.com). Tom Crawford delves into the Gaussian Integral, exploring its significance and applications in mathematics, alongside educational outreach through Numberphile

A new look at twin reduction (cameroncounts​.wordpress​.com). Peter Cameron explores twin reduction in graphs, introducing sibling partitions and their unique properties in relation to cographs and automorphism groups

A Continental Divide for Newton’s Method (johndcook​.com). Newton's method reveals a continental divide in quadratic roots, determining convergence based on initial points on either side of the divide

The Graceful Pi-Way (futilitycloset​.com). Exploration of a graceful graph labeling related to π, involving regions connected by roads in the U.S. and notable findings by Knuth and Rokicki

Uh-Oh (futilitycloset​.com). Explores a mathematical paradox involving area conversion, researched by Oskar Schlömilch and Lewis Carroll amidst historical insights and geometric analysis

BB(5)=47,176,870: BB(6) is … astronomically larger (thehighergeometer​.wordpress​.com). Recent advancements reveal BB(6) surpasses BB(5) by astronomical margins using Turing machines, igniting debates about the size of busy beaver numbers

Superimposed codes, take two (blog​.sesse​.net). Steinar H. Gunderson explores superimposed codes using brute-force techniques, bitsets, and symmetry for efficient enumeration, highlighting solutions up to 12-bit numbers

The Krull dimension of the semiring of natural numbers is equal to 2 (freedommathdance​.blogspot​.com). Exploration of the Krull dimension of the semiring of natural numbers, prime ideals, and their properties in number theory and commutative algebra

A stupid “real-life” application of quadratic reciprocity (blog​.evanchen​.cc). Using quadratic reciprocity humorously to divide students based on names by exploiting prime properties and number theory

One less than twice its reverse (earth​.hoyd​.net). Exploring the number 73: its unique property, patterns in numerics, and connections to prime numbers and Python scripts

Sum 10 consecutive numbers trick (mindyourdecisions​.com). Mathematical trick for summing 10 consecutive numbers using the 5th number and appending 5; applicable to two- and three-digit starting numbers

CriticLean: Critic-Guided Reinforcement Learning for Mathematical Formalization (arxiv:cs). CriticLean framework enhances mathematical formalization through CriticLeanGPT and CriticLeanBench, addressing semantic fidelity and introducing FineLeanCorpus dataset

KELPS: A Framework for Verified Multi-Language Autoformalization via Semantic-Syntactic Alignment (arxiv:cs). KELPS framework translates informal mathematics into verified theorems in Lean, Coq, and Isabelle, achieving 88.9% accuracy using Knowledge Equations

Leanabell-Prover-V2: Verifier-integrated Reasoning for Formal Theorem Proving via Reinforcement Learning (arxiv:cs). Leanabell-Prover-V2 enhances formal theorem proving in Lean 4 through reinforcement learning and verifier feedback, achieving improved performance over previous models

Comparing Dialectical Systems: Contradiction and Counterexample in Belief Change (Extended Version) (arxiv:cs). Dialectical systems facilitate belief change in automated agents, highlighting the significance of contradiction and counterexample in knowledge refinement and consistency

Large value estimates for Dirichlet polynomials, and the density of zeros of Dirichlet's $L$-functions (arxiv:math). Improved bounds on Dirichlet polynomials and zero densities of L-functions, with implications for prime progressions and Goldbach numbers

Lattice paths and the Geode (arxiv:math). Exploration of properties of formal power series 'G' (the Geode) and 'H' in relation to lattice paths and combinatorial interpretations

On the rigidity of manifolds with respect to Gagliardo-Nirenberg inequalities (arxiv:math). Study of Gagliardo-Nirenberg constants, Ricci tensor eigenvalues, and Yamabe-type constants revealing flatness of specific open subsets in manifolds

Integer Factorization: Another perspective (arxiv:cs). Explores integer factorization via Lebesgue space, matrix decomposition, and bivariate polynomials using innovative methods like Grobner basis and Coppersmith's method

Bisections of mass assignments by parallel hyperplanes (arxiv:math). Bisection of mass assignments in Euclidean vector bundles using a novel lifting method; results extend Soberón and Takahashi's conjecture on parallel hyperplanes

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