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But how does bitcoin actually work?
What is Wordle?
Initial ideas
The most unexpected answer to a counting puzzle
Exponential growth and epidemics
The Bug
The hardest problem on the hardest test
But what is the Fourier Transform? A visual introduction.
This problem seems hard, then it doesn't, but it really is
Simulating an epidemic
Intro
How the best first guess is chosen
Introduction
Fake sphere proof
Information theory basics
Fake pi = 4 proof
Does this ruin the game?
Why do prime numbers make these spirals?
Fake proof that all triangles are isosceles
Group theory and why I love 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
How secure is 256 bit security?
Incorporating word frequencies
Solving Wordle using information theory
Why do colliding blocks compute pi?
Oh, wait, actually the best Wordle opener is not “crane”…
Final performance
Visualizing quaternions (4d numbers) with stereographic projection
Where do convolutions show up?
Roots of polynomials
The players
Who cares about topology? (Inscribed rectangle problem)
What does it feel like to invent math?
The pattern
But WHY is a sphere's surface area four times its shadow?
The essence of calculus
Featured guests
Add two random variables
Newton’s method
Why is pi here? And why is it squared? A geometric answer to the Basel problem
How to start
Bayes theorem, and making probability intuitive
The impossible chessboard puzzle
How to lie using visual proofs
Music And Measure Theory
Alice's initial thoughts
The Essence of Calculus, Chapter 1
Hamming codes, h■w to ov■rco■e n■ise.
Hamming codes part 2, the elegance of it all
Image processing
Moving averages
The fractal
Moving average analogy
The unexpectedly hard windmill question (2011 IMO, Q2)
The more general uncertainty principle, beyond quantum
Euler's formula with introductory group theory
Piecing together the cube
Some light quantum mechanics (with minutephysics)
Alice, Bob, and the average shadow of a cube
Surfaces with holes
Polynomial multiplication
The boundary property
A simple example
Puzzle statement and motivation
SoME1
Researchers thought this was a bug (Borwein integrals)
Why this puzzle is impossible
Measuring runtime
So why do colliding blocks compute pi?
Winners
A simplified Galton Board
Quaternions and 3d rotation, explained interactively
Closing thoughts
Concluding thoughts
The quick proof of Bayes' theorem
Bob's conclusion
Simpler example
Visualizing the Riemann hypothesis and analytic continuation
Visualizing the Riemann zeta function and analytic continuation
The general idea
The generating function
Q&A with Grant Sanderson (3blue1brown)
All possible pythagorean triples, visualized
The Mandelbrot set
Your challenge
Pi hiding in prime regularities
Dice simulations
The true distributions for sums
Rational functions
What they won't teach you in calculus
Mean, variance, and standard deviation
Fixed points and stability
Alice's conclusion
impossible
Fractals are typically not self-similar
Bayes theorem
Unpacking the Gaussian formula
Evaluation tricks
The statistician's friend
Which is better?
Bayes theorem, the geometry of changing beliefs
The more elegant formulation
Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2
But what is a convolution?
Roots of unity
How (and why) to raise e to the power of a matrix | DE6
Cycles
But what is a neural network? | Chapter 1, Deep learning
How colliding blocks act like a beam of light...to compute pi.
Lockdown math announcement
Trigonometry fundamentals | Ep. 2 Lockdown live math
Tattoos on Math
Hidden Mandelbrot
Essence of linear algebra preview
The rising tide
Group theory, abstraction, and the 196,883-dimensional monster
Newton's Fractal (which Newton knew nothing about)
Fatou sets and Julia sets
The mathematically optimal Wordle strategy
How pi was almost 6.283185...
Recap and final trick
How to send a self-correcting message (Hamming codes)
Takeaways
But what is a Fourier series? From heat flow to drawing with circles | DE4
The classic proof
Underlying assumptions
Homework
Sample means
A concrete example
Q&A with Grant (3blue1brown), windy walk edition
Tips to be a better problem solver [Last live lecture] | Ep. 10 Lockdown live math
The Brachistochrone, with Steven Strogatz
What's coming up next
Hamming codes and error correction
But what is the Central Limit Theorem?
The universal advice
Triangle of Power
Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra
Winding numbers and domain coloring
Gradient descent, how neural networks learn | Chapter 2, Deep learning
Olympiad level counting
Hilbert's Curve: Is infinite math useful?
Structuring math explanations
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
What's so special about Euler's number e? | Chapter 5, Essence of calculus
Linear transformations and matrices | Chapter 3, Essence of linear algebra
Intro example
Linus the linelander
Vectors | Chapter 1, Essence of linear algebra
Final thoughts
The more general uncertainty principle, regarding Fourier transforms
Taylor series | Chapter 11, Essence of calculus
Speeding up with FFTs
A few of the best math explainers from this summer
The paradox of the derivative | Chapter 2, Essence of calculus
I'm still astounded this is true
Sponsorship and end
How They Fool Ya (live) | Math parody of Hallelujah
The medical test paradox, and redesigning Bayes' rule
e^(iπ) in 3.14 minutes, using dynamics | DE5
Reflecting back on the proof
Why π is in the normal distribution (beyond integral tricks)
Binary, Hanoi and Sierpinski, part 1
This pattern breaks, but for a good reason | Moser's circle problem
Generalizing as a formula
But what are Hamming codes? The origin of error correction
Math animation software
e to the pi i, a nontraditional take
What makes the natural log "natural"? | Ep. 7 Lockdown live math
Why do prime numbers make these spirals? | Dirichlet’s theorem, pi approximations, and more
Differential equations, a tourist's guide | DE1
Essence of calculus, chapter 1
Circle Division Solution
The medical test paradox (well "paradox")
Proof
Results
Motivation (macro)
Binomial distributions | Probabilities of probabilities, part 1
Limits, L'Hôpital's rule, and epsilon delta definitions | Chapter 7, Essence of calculus
Don't let it fool you!
Visualizing the chain rule and product rule | Chapter 4, Essence of calculus
Solution
What is an ellipse
Complex multiplication
Why slicing a cone gives an ellipse
Solving 2D equations using color, a story of winding numbers and composition
Change of basis | Chapter 13, Essence of linear algebra
A resposta mais inesperada para um problema de contagem
Matrix multiplication as composition | Chapter 4, Essence of linear algebra
The Newton art puzzle
A questão mais difícil da prova mais difícil
Choosing winners
Honorable mentions
Contact Tracing and Privacy Protection (via Nicky Case)
Thinking outside the 10-dimensional box
Derivative formulas through geometry | Chapter 3, Essence of calculus
But what is a GPT? Visual intro to Transformers | Deep learning, chapter 5
What makes the natural log "natural"? | Lockdown math ep. 7
The Wallis product for pi, proved geometrically
Who is the villain
Leonardo Euler
Lessons
A bonus problem
Have you seen more math videos in your feed recently? (SoME2 results)
A Curious Pattern Indeed
But what is a Neural Network? | Deep learning, chapter 1
The 3b1b podcast
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra
What is eccentricity
But what is a GPT? Visual intro to transformers | Chapter 5, Deep Learning
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
Discrete case, diagonal slices
Implicit differentiation, what's going on here? | Chapter 6, Essence of calculus
Ledgers and digital signatures
Pythagorean triples
The discrete formula
The determinant | Chapter 6, Essence of linear algebra
Olympiad level counting: How many subsets of {1,…,2000} have a sum divisible by 5?
The unreasonable effectiveness of complex numbers in discrete math
The absurd circle division pattern (updated) | Moser's circle problem
Euler's Formula and Graph Duality
Making probability intuitive
What is group theory
Euler and pi
The ledger is the currency
Intro quiz
Explanation
Which rating is better, mathematically speaking? | Probabilities of probabilities, part 1
Complex number fundamentals | Ep. 3 Lockdown live math
Beyond the Mandelbrot set, an intro to holomorphic dynamics
What is backpropagation really doing? | Chapter 3, Deep learning
Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra
Have you seen more maths in your feed recently? (SoME2 results)
Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus
Decentralization
Example with uniform distributions
Why do this
What does area have to do with slope? | Chapter 9, Essence of calculus
But what is a Fourier series? From heat flow to circle drawings | DE4
Does contact tracing necessarily sacrifice privacy? (via Nicky Case)
Recap on where we are
Cryptographic hash functions
Math
Central limit theorem
Continuous case, diagonal slices
Самый неожиданный ответ задачи о подсчёте
Imaginary interest rates | Ep. 5 Lockdown live math
Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebra
But what is a partial differential equation? | DE2
Binary, Hanoi, and Sierpinski, part 2
Issues with the Steve example
Conclusion
Rational points on the unit circle
Returning to the intro quiz
Group of symmetries
Motivation (micro)
Abstract vector spaces | Chapter 16, Essence of linear algebra
Então por que blocos colidindo computam Pi?
Zastanawiałeś się kiedyś jak właściwie działa Bitcoin (i inne kryptowaluty)?
Logarithm Fundamentals | Ep. 6 Lockdown live math
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