An animated introduction to the Fourier Transform.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/fourier-thanks…

Euler's formula about e to the i pi, explained with velocities to positions.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: htt…

sources and references, in temporal order:

Nature paper on the decline in disruptive science:
https://pubmed.ncbi.nlm.nih.gov/36599999/

Gordon Shepherd's book on the revolutionary 1950s "Creating Modern Neuroscience":
https://www.amazon.com/Creating-Modern…

The ability of the phenomenon of criticality to explain the sudden emergence of new properties in complex systems has fascinated scientists in recent decades. When systems are balanced at their “critical point,” small changes in individual units can trigger…