#190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries

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Jun 13, 2021

Jordan Ellenberg, a mathematician from the University of Wisconsin and author of 'Shape,' explores the fascinating world of geometry and its connection to human experience. He discusses the interplay between creativity and mathematics, emphasizing the beauty of chaos and high-dimensional shapes. Ellenberg shares insights on the relevance of symmetry, the importance of visualization in understanding complex ideas, and the enigma of prime numbers. The conversation touches on artificial intelligence's relationship with mathematics and the philosophical implications of higher dimensions.

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INSIGHT

Math and Language

Mathematical thinking feels similar to language production, and it's difficult to imagine math without linguistic expression.
Visualizing shapes and manipulating them is akin to manipulating linguistic elements, suggesting a connection between language and math as processes.

ANECDOTE

Stereo Speaker Epiphany

Jordan Ellenberg's early math epiphany involved a stereo speaker's 6x8 hole array, revealing the commutative property of multiplication.
This visual experience highlighted the link between algebra (6x8=8x6) and geometry (same holes, different arrangements).

INSIGHT

Symmetry's Scope

Symmetry in math goes beyond mirror images and includes transformations like stretching or shrinking.
This broader view of symmetry helps analyze objects and spaces, addressing the fundamental question of when two mathematical entities are considered 'the same'.

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