The Mathematician: 27th May 2025

LICHNEROWICZ CONFERENCE, IHP, 11-13 June 2025 (philippelefloch.org, 2025-05-21). The Lichnerowicz Conference at IHP from June 11-13, 2025, will feature discussions on mathematical general relativity and compressible fluids, with presentations by notable speakers including Xavier Bekaert and Laura Bernard

Topics I taught this year (aperiodical.com, 2025-05-23). Peter Rowlett reflects on teaching a redesigned mathematics degree course, covering proof, mathematical modelling, and supervising various dissertation topics including game theory and machine learning

Math/IQ challenge update: some thoughts (greyenlightenment.com, 2025-05-25). The math challenge led to original results, including new proofs and conjectured results using the 6th degree integral, integral ratio method, and series-shifting method, showcasing novel mathematical methods

Seminal ideas and controversies in Statistics [book review] (xianblog.wordpress.com, 2025-05-23). The review covers seminal statistical papers and controversies, including Bayesian analysis, hypothesis testing, and the replication crisis, highlighting contributions from Fisher, Yates, Efron, and others while acknowledging areas lacking emphasis

Professor Andrew Pitts elected as Fellow of the Royal Society (darwin.cam.ac.uk, 2025-05-20). Professor Andrew Pitts is elected as a Fellow of the Royal Society for his contributions to Theoretical Computer Science, utilizing category theory, mathematical logic, and type theory to enhance programming language semantics and theorem proving systems

Discrete Diffusion: Continuous-Time Markov Chains (inference.vc, 2025-05-22). Explore continuous-time Markov chains, their relation to discrete diffusion models, and the significance of waiting times in transitioning states, using geometric and exponential distributions for probabilistic modeling

Convolutions, Polynomials and Flipped Kernels (eli.thegreenplace.net, 2025-05-20). This post explores the connection between polynomials and convolution sums, featuring techniques for multiplying polynomials, properties of linear time-invariant systems, and the significance of the Fourier transform in convolution

Taylor Series Approximation To Newton Raphson Algorithm - A note for myself of the proof (kenkoonwong.com, 2025-05-25). The Newton-Raphson algorithm is derived from Taylor series approximation for logistic regression, demonstrating updates, parameter comparisons, and convergence using the Fisher Information matrix and Hessian optimization

Backward bifurcations and multistationarity (alanrendall.wordpress.com, 2025-05-20). Recent research reveals backward bifurcations in hepatitis C models, demonstrating unstable positive steady states under specific parameters, and introduces the concept of 'moving fold' bifurcations as a new analytical tool

For Algorithms, a Little Memory Outweighs a Lot of Time (quantamagazine.org, 2025-05-21). Ryan Williams' breakthrough proof highlights the computational advantage of a small memory over extensive time, suggesting a universal simulation method that transforms algorithms to utilize less space consistently

Estimating Logarithms (obrhubr.org, 2025-05-21). A method developed by John Napier in 1615 for estimating base 10 logarithms is explored, using Python implementation to illustrate the process of calculating logarithmic values with precision based on the number of digits

Math Art Part 2: Ethereal Structures (3D Continuous Cellular Automata) (marcusvolz.com, 2025-05-24). 3D continuous cellular automata based on Stephen Wolfram's 1D systems demonstrate unique ethereal structures, utilizing cell states in [0, 1] and previously studied thresholds by Richard Southwell for 3D printing applications

The Geometry of Intelligence: Why I Think Math Might Hold the Key to Understanding Minds and Machines (novaspivack.com, 2025-05-26). Nova Spivack proposes a geometric framework for understanding intelligence, leveraging concepts like natural gradients and information manifolds to bridge gaps in AI, neuroscience, and consciousness research

The triumphs of lattice gauge theory (condensedconcepts.blogspot.com, 2025-05-20). Lattice gauge theory, developed by Ken Wilson, utilizes discrete spacetime for numerical simulations, enabling accurate calculations of particle properties, revealing quark confinement and significant insights into QCD and quantum spin liquids

Dungeons, Dragons, and Numbers (johndcook.com, 2025-05-24). Explores the D&D alignment matrix with humor, linking mathematical concepts like the golden ratio, π, Feigenbaum's constant, and Rayo's number to chaotic and orderly alignments

That fractal that's been up on my wall for 12 years (chriskw.xyz, 2025-05-22). Chris K. W. explores a self-created fractal, dubbed 'the wallflower,' analyzing its generation methods using drag and drop techniques and L-Systems, while uncovering mathematical relationships and cardinality properties

Brute E-Graphs Modulo Theories 2: Extraction, Proofs, and Context (philipzucker.com, 2025-05-26). Exploration of extraction and proof production in E-Graphs, emphasizing simplification methods like the 'extract and simplify' technique and its implementation in e-graph structures within a Swept-based framework

Computing Hessian Matrix Via Automatic Differentiation (leimao.github.io, 2025-05-22). Learn how to compute the Hessian matrix using automatic differentiation tools like PyTorch and TensorFlow, focusing on mathematical principles, the Jacobian matrix, and the relationship between gradients and higher-order derivatives

Computing the Coefficients of the Characteristic Polynomial of a Matrix Using Polynomial Expansion with C# (jamesmccaffrey.wordpress.com, 2025-05-22). This post describes computing the coefficients of a matrix's characteristic polynomial using polynomial expansion in C#, emphasizing the QR technique for eigenvalue computation and comparing it with the Faddeev-LeVerrier method

Finding hard 24 puzzles with planner programming (buttondown.com, 2025-05-20). Utilizing planner programming with Picat, the article explores generating and solving valid 24 puzzles using arithmetic operations while implementing constraints for finding challenging configurations

Doing Math With Lean (unnamed.website, 2025-05-26). Explores the proof of the identity \sum_n=2^\infty \sum_p=2^\infty \frac1n^p = 1 using Lean, detailing challenges with double summation convergence and proof length

Collatz conjecture visualizations (rakuforprediction.wordpress.com, 2025-05-25). Explore various visualizations of the Collatz conjecture using Raku, showcasing technical tools like Graph, JavaScript::D3, and Math::NumberTheory to analyze sequences and patterns of hailstone numbers

Kepler kind of beat Newton to gravity I think? (blog.jordan.matelsky.com, 2025-05-24). Kepler's 'Somnium' presents early concepts of gravity, including mutual attraction, universality across scales, and an inverse-square law, predating Newton's principles, though lacking his mathematical rigor

Is mathematics useful? (cameroncounts.wordpress.com, 2025-05-22). G. H. Hardy and Kenneth Falconer present contrasting views on mathematics' usefulness, highlighting applications like multifractals in satellite imagery and medical diagnostics, while discussing theoretical versus practical mathematics

Mario Biagioli (1955–2025) (thonyc.wordpress.com, 2025-05-23). Mario Biagioli, a prominent historian of science, passed away in 2025. Notable works include 'Galileo Courtier' and 'Galileo’s Instruments of Credit', emphasizing the complexities of Galileo's achievements and his relationship with the Church

Some are Mathematicians, some are Carpenters' Wives, Some are Popes. (blog.computationalcomplexity.org, 2025-05-25). Exploring the qualifications of mathematicians, with references to Pope Leo XIV’s mathematics background, distinctions between applied and theoretical math, and considerations on what constitutes being a mathematician

A Formal Proof of Complexity Bounds on Diophantine Equations (arxiv:cs, 2025-05-22). A universal construction of Diophantine equations with bounded complexity is formalized in Isabelle/HOL, extending multivariate polynomial theory and establishing undecidable complexity bounds characterized by variables and degree

HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement (arxiv:cs, 2025-05-21). HybridProver integrates tactic-based generation and whole-proof synthesis to enhance automated theorem proving in Isabelle, achieving a 59.4% success rate on miniF2F, surpassing the previous state-of-the-art of 56.1%

An iterative approach toward hypergeometric accelerations (arxiv:math, 2025-05-20). Extends Wilf's acceleration method using Chu's $\Omega$-sum iteration patterns to prove accelerated Ramanujan-type formulas for universal constants

Multiple q-zeta values and traces (arxiv:math, 2025-05-20). Generalizes Bloch and Okounkov's result relating traces in representation theory to multiple q-zeta values, demonstrating that certain traces yield formal power series whose coefficients are quasi-modular forms and multiple q-zeta values

Alpay Algebra: A Universal Structural Foundation (arxiv:math, 2025-05-21). Alpay Algebra offers a category-theoretic framework, integrating classical and modern algebraic structures with concepts like transfinite evolution functors and internal universal properties, applicable in AI models and functional programming

MM-Agent: LLM as Agents for Real-world Mathematical Modeling Problem (arxiv:cs, 2025-05-20). MM-Agent uses Large Language Models for real-world mathematical modeling, improving solution accuracy by 11.88% over humans on the MM-Bench benchmark and assisting teams to achieve finalist status in MCM/ICM 2025

Kostka Numbers Constrain Particle Exchange Statistics beyond Fermions and Bosons (arxiv:math, 2025-05-23). Kostka numbers establish microstate uniqueness theorem, showing incompatibility between statistical-mechanics counting and quantum-mechanical exchange symmetry for indistinguishable particles, ruling out intermediate statistics based on higher-dimensional representations

Distinguishing sets of elliptic curve coefficients (davidlowryduda.com, 2025-05-23). Investigating how many elliptic curve coefficients are needed to uniquely identify an isogeny class using machine learning, point count analysis, and statistical heuristics

There is no Diffie-Hellman but Elliptic Curve Diffie-Hellman (keymaterial.net, 2025-05-24). Explores the choice of using elliptic curves over groups like the Monster Group for Diffie-Hellman key exchange, highlighting technical complexities of group homomorphisms, injectivity, surjectivity, and category theory

Derangements: How Often is Everything Wrong? (themathdoctors.org, 2025-05-23). Explore derangements in combinatorics, focusing on the probability of incorrect placements using the Inclusion-Exclusion Principle, exemplified through matching letters and envelopes to calculate expected outcomes

Deciding Equality for Trigonometric Expressions (pavpanchekha.com, 2025-05-21). Explores simplifying trigonometric expressions using the Weirstrass (Legendre) substitution, demonstrating techniques for deciding equality in expressions involving multiple variables and rational functions derived from trigonometric identities

The Schauder fixed point theorem and Leray-Schauder theory, part 2 (alanrendall.wordpress.com, 2025-05-21). The proof of the Schauder fixed point theorem is outlined using linear parameter dependence, emphasizing compact mappings in Banach spaces and their implications for fixed points, including contradictions arising from norm inequalities

Graduate Student Solves Classic Problem About the Limits of Addition (quantamagazine.org, 2025-05-22). Benjamin Bedert's proof of the Erdős conjecture reveals that any integer set contains a substantial sum-free subset, utilizing techniques from Fourier analysis and properties of arithmetic progressions to address a decades-old mathematical mystery

My favorite paper: H = W (johndcook.com, 2025-05-24). The paper 'H = W' proved the equivalence of Sobolev spaces H and W, impacting modern differential equations and generalized derivatives within functional analysis. Key concepts include Sobolev spaces, generalized solutions, and distributions