learning math

An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.

A clip of Richard Feynman contrasting the Greek and Babylonian traditions of mathematical reasoning. It compares the axiomatic approach of mathematicians with how physicists use mathematics.

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.

Mathematician Colin Wright demonstrates juggling and explains the mathematics of juggling patterns, including notation that led to new throwing patterns. It is a public presentation at the Museum of Mathematics aimed at a general audience.

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.

3Blue1Brown's first chapter on deep learning explains what neurons and layers are and the math underlying a basic neural network, using handwritten digit recognition with visual animations.

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.

The first lecture of Caltech's CS 156 Machine Learning course by Yaser Abu-Mostafa, introducing the learning problem and supervised, unsupervised and reinforcement learning. It is one of 18 lectures in the Learning from Data course.

The first episode of Google's Machine Learning Recipes series. It introduces machine learning and builds a first supervised-learning classifier in about six lines of Python using scikit-learn.

A GDC 2018 talk by Valve's John McDonald on VACNet, a deep learning system that analyzes CS:GO gameplay to detect cheaters. It covers how the model is trained on human-reviewed Overwatch cases and how its output feeds human moderation.

3Blue1Brown's third deep learning chapter gives a visual, intuitive account of backpropagation and what happens to a neural network as it learns. A follow-up video covers the underlying calculus.

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.

Mark Rober and Jabril build an app that uses machine learning to decode baseball sign sequences. The video also explains neural networks in a simple, accessible way.

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.

Conrad Wolfram argues that the part of math taught in schools, hand calculation, is tedious and mostly irrelevant to real mathematics. He proposes teaching math through computer programming so students can tackle real problems.

Matt Parker's Royal Institution talk based on his book Humble Pi, covering everyday mathematical mistakes and spurious patterns that went wrong in engineering and software. It mixes stand-up comedy with stories of coincidence and error.

A ten-minute clip of Richard Feynman describing how mathematicians and physicists differ in their interests and customs. He argues physics rests on visualizing and applying math rather than pure abstraction.

Gregory Chaitin is interviewed on Closer To Truth about whether mathematics is invented or discovered. He gives a nuanced view that ties the question to the nature of reality.

A short Great Big Story piece about Hagoromo, a Japanese chalk brand so prized that mathematicians stockpiled it, with some reportedly dealing it on the side. It tells the quirky tale of a writing tool whose supply became scarce.

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 first lecture of David Silver's reinforcement learning course, introducing the field and its basic concepts. The course follows the Sutton and Barto textbook.

Martin Gorner's Devoxx talk introduces deep learning with TensorFlow, walking through neural networks for MNIST, how to choose an architecture and how to diagnose networks that fail to train.

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.

An amateur animation of Tom Lehrer's satirical song New Math, which pokes fun at 1960s math teaching and subtraction in base 8. The animation illustrates the old and new subtraction methods.

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.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

Matt Parker of Stand-up Maths demonstrates MENACE, Donald Michie's 1961 machine made of matchboxes that learns to play noughts and crosses through reinforcement. He builds and trains a physical version.

Mathematician Kevin Buzzard explains why he believes the Lean theorem prover will shape the future of mathematics, and describes digitizing his university curriculum in Lean with undergraduates, plus the cultural challenges.

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

The first lecture of Stanford's Natural Language Processing with Deep Learning course, taught by Chris Manning and Richard Socher. It introduces NLP and word vectors, including SVD, skip-gram, CBOW, negative sampling and word2vec.

Geoff Hinton's 2010 Google Tech Talk on deep belief networks, learning layers of representation one at a time from unlabeled data, and extending them with multiplicative interactions.

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.

A clip of Australian Prime Minister Malcolm Turnbull saying the laws of Australia prevail over the laws of mathematics, regarding encryption. The audio is quiet in the second half.

Geoffrey Hinton's Google Tech Talk linking machine learning to biology, explaining dropout as a form of model averaging and why sexual reproduction and stochastic spiking neurons may prevent overfitting.

3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.

Chris Lonsdale presents a TEDx talk on how adults can learn a language in about six months, centering on immersion, comprehensible input and a practical learning methodology.

3Blue1Brown explains space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations. It touches on mapping between dimensions and sensory ideas.

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.