The most beautiful formula not enough people understand
3Blue1Brown
Feb 27, 2026
Grant Sanderson argues that higher-dimensional geometry is a counterintuitive but essential tool for modern computation. By visualizing the recursive relationship between spheres and their boundaries, he reveals that in high dimensions, these shapes paradoxically become almost entirely concentrated at their surface and essentially vanish in volume relative to the space they inhabit.
Key insight: In 100 dimensions, a unit ball is so vanishingly small—approximately 2.37 x 10^-40—that it is essentially nothing, demonstrating why our three-dimensional intuitions fail in high-dimensional data spaces like machine learning.
