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.
A Flock of Functions: Lambda Calculus and Combinatory Logic in JavaScript | Gabriel Lebec @ DevTalks
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.
Subcategories
- category_theory (47)
- entropy (7)
- group_theory (4)
- history (5)
- information_theory (26)
- linear_algebra (25)
- logic (40)
- measure_theory (4)
- statistics (11)