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3Blue1Brown summaries
Every long episode from 3Blue1Brown, read in minutes: the key takeaways, the chapters, and a digest of the whole conversation. My name is Grant Sanderson. Videos here cover a variety of topics in math, or adjacent fields like physics and CS, all with an emphasis on visualizing the core ideas. The goal is to use animation to help elucidate and motivate otherwise tricky topics, and for difficult problems t…
This picture broke my brain
Explore the mathematical underpinnings of M.C. Escher's "Print Gallery," revealing how conformal maps and complex logarithms unlock its self-referential paradox.
The most beautiful formula not enough people understand
Explore the beautiful, counterintuitive math behind high-dimensional spheres, revealing the surprising behavior of volumes and the elegance of formulas like $V_n(R) = \frac{\pi^{n/2}}{\Gamma(n/2 + 1)} R^n$.
The Hairy Ball Theorem
The Hairy Ball Theorem states you can't comb hair on a sphere flat without a cowlick. This has surprising implications in fields like game development and physics.
Why Laplace transforms are so useful
Learn how Laplace transforms simplify the analysis of differential equations, providing valuable insights into system dynamics.
But what is a Laplace Transform?
The Laplace Transform is a powerful tool converting functions into exponential forms, revealing key insights into differential equations.
The Physics of Euler's Formula | Laplace Transform Prelude
This video explores the power of Euler's Formula and its connection to complex numbers, leading toward understanding the Laplace transform.
What was Euclid really doing? | Guest video by Ben Syversen
This video explores Euclid's Elements, revealing how ruler and compass constructions shaped Greek mathematics and philosophical debates, establishing a foundation for geometry.
Exploration & Epiphany | Guest video by Paul Dancstep
Exploring Sol LeWitt's art reveals a profound intersection of mathematics and creativity, showcasing how systematic thinking leads to innovative solutions.
Simulating and understanding phase change | Guest video by Vilas Winstein
This video explores phase transitions using a liquid vapor model simulation, explaining the Boltzmann equation and its implications on system behavior.
But how do AI images and videos actually work? | Guest video by Welch Labs
AI image/video generation uses diffusion models that reverse noise addition, guided by CLIP embeddings and classifier-free guidance for prompt adherence.
But what is quantum computing? (Grover's Algorithm)
Quantum computing offers quadratic speedups for search problems like Grover's Algorithm, by manipulating quantum states rather than classical bits, but it's not true parallel processing.