The Mathematician: 20th May 2025

From τὰ φυσικά (ta physika) to physics – XLIV (thonyc.wordpress.com, 2025-05-14). Bonaventura Cavalieri, a key figure in mathematics, developed the method of indivisibles, leading to integral calculus, geometric principles, and the parabolic law of projectile motion amidst controversies with contemporaries over his ideas

Review: The Shape of a Life (blog.piaw.net, 2025-05-15). The autobiography of Shing-Tung Yau, ghost-written by Steven Nadis, chronicles his rapid ascent in mathematics, his contributions to Calabi-Yau manifolds, and the complexities of academic politics in Chinese communities

Euclid, Fermat, and the 65537 Reasons We Have Never Drawn Their Last Shape (liveatthewitchtrials.blogspot.com, 2025-05-17). Euclidean constructions using only a compass and straightedge link to number theory, with Fermat primes determining the constructibility of shapes like the 65537-gon, challenging to draw even mechanically

The NSA’s “Fifty Years of Mathematical Cryptanalysis (1937–1987)” (schneier.com, 2025-05-19). Glenn F. Stahly's declassified report, 'Fifty Years of Mathematical Cryptanalysis (1937-1987)', highlights the NSA's historical evolution in cryptanalysis, although heavily redacted, inviting readers to contribute insights from the document

Is the pope a mathematician? Yes, actually – and his training may help him grapple with the infinite (theconversation.com, 2025-05-15). Pope Leo XIV's mathematical background aids his understanding of concepts like infinity, bridging a gap between mathematics and theology, particularly through Georg Cantor's transfinite set theory, which reintroduces absolute infinities

I trained neural nets on large cardinal axioms (karagila.org, 2025-05-14). Asaf Karagila details his experience training neural nets on large cardinal axioms, highlighting recent developments like the Bagaria–Goldberg characterization and summarizing a course on related concepts, including ultraexacting cardinals

How Did Geometry Create Modern Physics? (quantamagazine.org, 2025-05-15). Yang-Hui He discusses the evolution of geometry from ancient land surveying to its pivotal role in modern physics, including its application in general relativity and string theory, alongside the potential influence of AI

New 'Superdiffusion' Proof Probes the Mysterious Math of Turbulence (quantamagazine.org, 2025-05-16). Mathematicians have proved the superdiffusion phenomenon in turbulent fluids, using homogenization techniques to demonstrate particle spread rates influenced by fluid eddies, potentially addressing a $1 million Millennium Prize Problem in turbulence

What does the end of mathematics look like? (awanderingmind.blog, 2025-05-19). Speculation on the future of mathematics in a capital-driven world, discussing Lean/mathlib proofs, AI models, commodification of thought, and implications for human creativity and education

A near 200 year old math problem has finally been cracked (neowin.net, 2025-05-13). UNSW mathematician Norman Wildberger has developed a new approach to solve high-degree polynomial equations, moving beyond traditional methods involving radicals by utilizing power series and hyper-Catalan numbers

A New Equation? (asymptotia.com, 2025-05-19). Clifford explores the potential of a new mathematical object related to the Gel'fand-Dikii equation, deriving a previously unknown equation while reflecting on its implications for understanding quantum mechanics and geometry

22/7 and the Approximation of Irrational Numbers (jdhwilkins.com, 2025-05-19). Explores irrational numbers' approximation using continued fractions, demonstrating how 22/7 and 355/113 provide close rational approximations for π and other irrational numbers through mathematical transformations

Linkage (11011110.github.io, 2025-05-15). The NSF faces budget cuts, a thought experiment on knot theory is proposed, complex number sequences solve algebra's oldest problems, and various mathematical and geometric topics including high-dimensional polytopes are explored

Some variants of the periodic tiling conjecture (terrytao.wordpress.com, 2025-05-13). Tao and Greenfeld explore periodic tiling conjectures, presenting three significant results with proofs involving integer-valued solutions, Fourier coefficients, and combinatorial structures, emphasizing algorithmic decidability and the intricacies of higher-dimensional spaces

What is proof to a non-mathematician? (storytotell.org, 2025-05-14). Exploring geometric proof, theorem provers like Coq, and the distinction between truth-value and understanding in mathematics, focusing on the learning process and challenges faced by non-mathematicians

Souvenirs from Tunnel Mountain (noncommutativeanalysis.wordpress.com, 2025-05-14). Orr Shalit discusses his participation at the BIRS workshop, presenting on spectral radius in operator spaces and highlights research talks on polynomial approximation and matrix convex sets relevant to quantum theory

Sylvester's womb of numbers (1850) (rigelkent.blogspot.com, 2025-05-17). James Sylvester explores mathematical matrices in 1850, using a biblical term 'matrix' to describe numeric arrays, explaining how determinants emerge from underlying numerical 'wombs'

Embeddings, Projections, and Inverses (johndcook.com, 2025-05-14). Discusses embeddings, projections, inverses, and the Moore-Penrose pseudoinverse. Covers the embedding of 3D vectors into quaternions and their retrieval process, and examines adjoints and left/right inverses

Gradients are the new intervals (mattkeeter.com, 2025-05-14). Explores the use of Lipschitz continuity in implicit surface rasterization, introducing gradient-based techniques for efficient rendering and optimization, highlighting differences between traditional interval arithmetic and new approaches

The Mary Queen of Scots Channel Anamorphosis: A 3D Simulation (charlespetzold.com, 2025-05-17). Charles Petzold explores John Napier's logarithms and creates a 3D simulation of the 'Mary, Queen of Scots' anamorphosis painting using WebGL, showcasing the transformation from a face to a skull

The Longest Pi Article on the Internet: Literally Everything About π (abakcus.com, 2025-05-17). Explore the multifaceted nature of pi (π), from its historical approximations by the Babylonians and Archimedes to its modern implications in calculus, computer graphics, and the challenges of calculating its infinite digits

From Complete Separation To Maximum Likelihood Estimation in Logistic Regresion: A Note To Myself (kenkoonwong.com, 2025-05-17). Logistic regression can face issues with complete separation, leading to extreme standard errors. Understanding maximum likelihood estimation through calculus concepts like the chain and quotient rules is crucial for accurate modeling

Turing Machine 3 (deejaygraham.github.io, 2025-05-16). A generic Turing Machine implementation using Python, focusing on program and tape validation with practical examples of binary character manipulation and a visualization feature to illustrate tape head movement

Matrix Inverse Using Cayley-Hamilton With C# (jamesmccaffrey.wordpress.com, 2025-05-19). Utilize the Cayley-Hamilton theorem for the practical computation of matrix inverses in C#, including coefficient determination using the Faddeev-LeVerrier algorithm

Riff on an integration bee integral (johndcook.com, 2025-05-16). Explores an MIT Integration Bee integral, discussing size estimation, beta functions, and techniques for numerical evaluation involving gamma functions and logarithmic calculations

A shower thought turned into a beautiful Collatz visualization (abstractnonsense.com, 2025-05-20). This exploration visualizes the Collatz Conjecture using a modified function that tracks binary sequences to create fractional representations, highlighting self-similar patterns while encouraging engaging interactions through JavaScript implementations and browser-based plots

Open Problems in Computational geometry (topp.openproblem.net, 2025-05-17). The Open Problems Project records over 75 challenging issues in computational geometry, inviting updates especially for solved problems. Each is numbered and categorized for easier navigation, covering various technical areas

MPS-Prover: Advancing Stepwise Theorem Proving by Multi-Perspective Search and Data Curation (arxiv:cs, 2025-05-16). MPS-Prover enhances automated theorem proving by utilizing a multi-perspective tree search and a data curation strategy, achieving superior performance on benchmarks while generating shorter, diverse proofs compared to existing methods

AutoMathKG: The automated mathematical knowledge graph based on LLM and vector database (arxiv:cs, 2025-05-19). AutoMathKG is a multi-dimensional mathematical knowledge graph that utilizes LLMs and a vector database for automatic updates, knowledge integration, and entity enhancement, achieving superior performance in reachability queries and mathematical reasoning

Symbolic Sets for Proving Bounds on Rado Numbers (arxiv:math, 2025-05-17). Using SAT solvers, new Rado numbers for equations $ax + by = bz$ and $ax + ay = bz$ are computed, with symbolic sets manipulated through a custom tool integrating SymPy and Z3 for automated proof verification

Lower bounds for the reach and applications (arxiv:math, 2025-05-13). A method to compute lower bounds for the reach of submanifolds using smooth functions, with applications including homology groups of planar curves, comparison inequalities for distances, and bounds on eigenvalues and deformation types

Counting Totally real units and eigenvalue patterns in $\rm{SL}n(\mathbb Z)$ and $\rm{Sp}{2n}(\mathbb Z)$ along thin tubes (arxiv:math, 2025-05-19). Explores counting totally real units and eigenvalue patterns in SL(n,Z) and Sp(2n,Z) lattices, revealing shared directional entropy and conjugacy class bounds

On the critical length conjecture for spherical Bessel functions in CAGD (arxiv:cs, 2025-05-15). Carnicer, Mainar, and Peña's conjecture investigates critical length for spherical Bessel functions using Hankel determinants and special function derivatives

Realizations of homology classes and projection areas (arxiv:math, 2025-05-13). Studying projections of convex bodies and irreducible surfaces in four-dimensional spaces, focusing on tuples of areas governed by Plucker relations and resolving the algebraic Steenrod problem, leading to conjectures on homology classes and projection volumes

Galois groups of simple abelian varieties over finite fields and exceptional Tate classes (arxiv:math, 2025-05-14). New cases of the Tate conjecture for abelian varieties over finite fields are proven, using Galois group properties and combinations of Newton polygons, revealing maximal angle ranks for certain geometrically simple varieties