learning math

The first lecture of N J Wildberger's History of Mathematics course, starting with Pythagoras' theorem and following Stillwell's text. It emphasizes the flow of ideas over proofs.

Thomas Garrity discusses mathematical maturity, a concept mathematicians use for professional development, and how it can inform teaching, mentoring and careers. It was given at the IAS/PCMI Park City Mathematics Institute.

Andrew Ng presents unsupervised feature learning and deep learning, showing how algorithms can learn representations from unlabeled data instead of hand-designed features. He gives examples in vision and audio, including visualizations of features learned by successive layers.

Max Tegmark's MIT CBMM talk on why deep learning works so well. He argues that the laws of physics and the symmetries in physical data make it compressible into small neural networks, tying physics to network structure.

The first lecture of MIT 6.042J Mathematics for Computer Science, taught by Tom Leighton, introducing mathematical proofs. It covers propositions, implication and basic proof methods.

Ali Rahimi accepts the NIPS 2017 Test of Time Award and argues that machine learning has become alchemy, with practice running ahead of understanding.

The introductory lecture of Richard Hamming's capstone course, The Art of Doing Science and Engineering: Learning to Learn. It focuses on style of thinking and on educating rather than training, using technical material only as illustration.

The final lecture of Richard Hamming's Learning to Learn course, from 1995, based on his well-known talk 'You and Your Research'. It covers how to do important work and build a career.

Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.

3Blue1Brown's second neural network chapter explains cost functions and gradient descent, showing how a network learns by minimizing error during training.

Andrej Bauer's IAS talk introduces constructive mathematics and what it feels like to do mathematics without excluded middle. It is framed as a tour for classical mathematicians.

Chamath Palihapitiya talks with Jason Calacanis about how he bought into the mythology of Silicon Valley, which he calls a Ponzi scheme, and about rebuilding Social Capital. He urges founders to grow slowly and build what matters.

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

Tom Scott-style absurdist research by tom7 for SIGBOVIK 2021, using machine learning to discover letterforms that are 'uppercaser' than uppercase A and lowercaser than lowercase. It is a comedic, technically inventive deep dive with fonts and a paper.

3Blue1Brown's visual walkthrough of the attention mechanism inside transformers, covering self-attention, multiple heads and cross-attention. It is chapter 6 of his deep learning series.

Ali Rahimi's NIPS 2017 Test-of-Time award talk, in which he argues that modern machine learning has become alchemy, working without being rigorously understood. He calls for more rigor and understanding in the field.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

Yosh trains a reinforcement learning agent to drive Trackmania until he can no longer beat it. The video explains how the training works and the design choices involved.

Part 2 of Richard Feynman's Messenger Lectures at Cornell, The Character of Physical Law, on the relation of mathematics to physics. He explains why understanding nature requires mathematics.

A Veritasium video on how a feud between Russian mathematicians led to Markov chains and the modern prediction algorithms built on them. It covers the history and the math behind them.

Chamath Palihapitiya's Stanford GSB View From The Top talk on money as an instrument of change. HN mostly knows it for his remarks on social media's dopamine-driven feedback loops and regrets about Facebook.

A TED interview in which Chris Anderson talks with Jim Simons about his life: code-breaking, math, founding Renaissance Technologies, and his philanthropy in math education and origins-of-life research.

Chris Lattner and Brennan Saeta present Swift for TensorFlow at the TensorFlow Dev Summit 2019, covering language-integrated automatic differentiation and tooling for machine learning in Swift.

An original recording of a Verizon customer service call in which the rep fails to understand the difference between cents and dollars, known as Verizon Math.

The first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.

3Blue1Brown's visual explanation of how transformers and GPT-style language models work, tracing data through tokens, embeddings and attention.

Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

Stand-up Maths explains why the perimeter of an ellipse has no simple closed-form equation, showing the infinite series and presenting approximation formulas.

Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.

Inigo Quilez live-codes a cartoon character painting entirely from math, using signed distance fields in a Shadertoy shader. He explains each step of building the image from formulas.

Inigo Quilez live-paints a mountain landscape using only math in a shader, building up from a basic polynomial noise surface through fractal terrain, lighting and atmosphere. The code runs in real time on Shadertoy so viewers can edit it as they follow along.

The first lesson of MangoJelly's FreeCAD 0.20 beginner course, covering setup, preferences and navigation. The series teaches fundamentals through complete workflows such as sketching, Part Design and STL export.

Inigo Quilez live-codes a painting using only mathematics in a shader, building it up step by step. The linked Shadertoy source shows the result.

Kathy Sierra's Fluent 2015 keynote on the one metaskill for developers: the ability to come up to speed quickly and stay there. She covers how people learn, cognitive resources versus willpower, and building skill.

A 3Blue1Brown live lockdown math episode asking what Euler's formula e^(pi i) is actually saying. It builds intuition through exponentials, rotation and vectors landing on the unit circle.

Joseph Henrich's Talks at Google presentation of his book. He argues that human success comes from collective brains and cultural learning across generations rather than individual intelligence.

Gerald Jay Sussman speaks at Dan Friedman's 60th birthday celebration about how programming helps formulate and clarify ideas. He argues that ambiguous mathematical notation hinders understanding.

Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.

James Mickens's humorous USENIX Security keynote argues that improving security and trusting opaque technology like machine learning is far harder than the industry admits.