Bookmarks

these compression algorithms could halve our image file sizes (but we don't use them) #SoMEpi

An educational deep-dive into the source coding theorem, entropy, arithmetic coding, and asymmetric numeral systems, illustrating how these information-theoretic ideas can dramatically reduce image file sizes.

The First Real Application of Category Theory #SoME3

Introduces an early, concrete application of category theory via algebraic topology, illustrating how categorical constructs map to homotopy concepts within topological spaces.

Stephen Wolfram - Where the Computational Paradigm Leads (in Physics, Tech, AI, Biology, Math, ...)

Stephen Wolfram’s keynote explores the broad “computational paradigm” as a unifying lens across physics, technology, AI, biology and mathematics—an ideas-driven talk without focused technical implementation details.

Unsolved Problems in Calculus

Survey-style overview of several famous open mathematical conjectures related to calculus and analysis, outlining what is known and why they remain unsolved.

Kan Academy: Introduction to Limits

An example-driven primer on categorical limits, building from sets and vector spaces to equalisers, fibre products, cones, and universal properties, aimed at newcomers to abstract category theory.

A Brief Overview of Sheaf Theory - Part 1

The first lecture in a sheaf-theory series, defining presheaf stalks, sheafification, and exactness concepts such as kernels and images within a categorical framework.

A Swift Introduction to Geometric Algebra

Provides a rapid, physics-motivated introduction to geometric algebra, covering multivectors, grades, geometric products, and rotors as an extension of linear-algebraic concepts.

What Is an Interactive Theorem Prover? | Kevin Buzzard

Live demonstration of the Lean interactive theorem prover, showing how formal logic rules are encoded, manipulated, and verified, and discussing its role in mathematical research and future software tooling.

Halting Problem & Quantum Entanglement 2020 Breakthrough result [MIP*=RE]

Clear technical explanation of the groundbreaking MIP*=RE complexity-theory result—valuable foundational content for theoretical computer scientists.

What is a TENSOR? (Really this time!)

Provides an in-depth mathematical explanation of tensors, suitable for learners of linear algebra and theoretical physics.

A Crash Course in Category Theory - Bartosz Milewski

Bartosz Milewski provides an intensive introduction to category theory with programming examples, fitting both educational and theoretical criteria.

Category Theory, The essence of interface-based design - Erik Meijer

Conference-style talk by Erik Meijer connecting category theory to interface-based design and Java 8 lambdas; valuable for programmers interested in theoretical underpinnings.

"Categories for the Working Hacker" by Philip Wadler

Philip Wadler’s lecture introduces category theory concepts for programmers, bridging mathematics and software development.

Type Theory for the Working Rustacean - Dan Pittman

Technical presentation linking Rust’s type system with type theory and proof techniques, valuable for language theorists and systems programmers.

Category Theory for the Working Hacker by Philip Wadler

Conference talk by Philip Wadler connecting category theory to programming; foundational material for programmers interested in type theory.

Category Theory by Tom LaGatta

Applied Category Theory

Proofs in mathematics

THE THREE MATH BOOKS THAT CHANGED MY LIFE

Algebra - It's not what you think it is!

All of Multivariable Calculus in One Formula

This Will Make You Better at Mathematics FOREVER

set theory fundamentals

Euler's proof: there are an infinite number of primes!

The shocking connection between complex numbers and geometry.

What is algebraic geometry?

Category theory (2022-23): Lecture 1

A Look at Some Higher Level Math Classes | Getting a Math Minor

Algebraic Topology 19: Category Theory

Limits of Logic: The Gödel Legacy

The Greatest Mathematician Who Ever Lived

This is why you're learning differential equations

Algebraic topology: Fundamental group

What is...homotopy?

Into the Realm Categorical

The soundness and completeness of logic

Fractals are typically not self-similar

When Proof By Induction Fails

When CAN'T Math Be Generalized? | The Limits of Analytic Continuation

Let's code math | Lean4 | Theorem prover

What is category theory?

"Propositions as Types" by Philip Wadler

Formalizing a proof in Lean using Claude and o4

A Concrete Introduction to Tensor Products

The Key Equation Behind Probability

Day 3 - Interview to Terence Tao - Umberto Bottazzini

What is...homotopy of spheres?

Terence Tao - Machine-Assisted Proofs (February 19, 2025)

Ravi Vakil: Algebraic geometry and the ongoing unification of mathematics

What's the big deal with the Yoneda Lemma?

Galois Theory Explained Simply

How to self study pure math - a step-by-step guide

But what is the Central Limit Theorem?

3Blue1Brown visually proves and contextualizes the Central Limit Theorem and its importance in probability and data analysis.

Entropy is not what you think!

Clarifies entropy as a measure of information—not disorder—linking thermodynamic and Shannon definitions via microstate counting.

Mystery of Entropy FINALLY Solved After 50 Years? (STEPHEN WOLFRAM)

Stephen Wolfram discusses his computational approach to the second law of thermodynamics, entropy growth, and implications for AI governance.

"Self-regularizing Property of Nonparametric Maximum Likelihood Estimator" —Yury Polyanskiy (MIT)

Seminar proves the self-regularizing sparsity of nonparametric MLEs for mixture models, yielding logarithmic bounds on component count.

Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183

Wide-ranging conversation with Po-Shen Loh about competitive mathematics, combinatorics, and effective strategies for learning and teaching math.

The unreasonable effectiveness of linear algebra.

Explores why linear algebra underpins diverse scientific computations, illustrating its unifying power across optimization and physics.

Bayes theorem, the geometry of changing beliefs

Visual geometric interpretation of Bayes’ theorem, illustrating belief updates and prior-posterior relationships in probabilistic inference.

Why can't you multiply vectors?

Talk uses geometric algebra to show why no unique general vector-vector product exists in 3-D, highlighting dot, cross, and outer products.

The Test That Terence Tao Aced at Age 7

The World's Best Mathematician (*) - Numberphile

A Sensible Introduction to Category Theory

What is Group Theory? — Group Theory Ep. 1

Algebraic Topology 1: Homotopy Equivalence

Goedel-Prover-V2

Best Algebraic Geometry text book? (other than Hartshorne)

Matrices and graphs

A Group and Its Center, Intuitively

Russell’s Paradox and Possible Solutions

Algebraic Databases

Categorical Databases

Logical Complexity of Proofs

Proofs and Types

Richard Hamming - Wikipedia

TuringConf

context

Proof Explorer

Minimal Boolean Formulas

Hausdorff dimension - Wikipedia

The_Manga_Guide_to_Linear_Algebra

LADW_2017-09-04

Ludwig Wittgenstein: The Duty of Genius

Information

Bremermann's limit

Bekenstein bound

Linear Algebra Review and Reference

Linear Algebra

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