Math and the Beaches of Rio

Abstraction: History of Fields Medal and Stephen Smale's horseshoe map work in Rio

Key points:

• Stephen Smale discovered the horseshoe map on Copacabana beach (Rio) in 1960 while visiting IMPA (Instituto Nacional de Matemática Pura e Aplicada)
• The horseshoe map work contributed to his proof of the Poincaré conjecture in all dimensions ≥ 4, earning a Fields Medal
• The Fields Medal-Nobel comparison originated in 1966 when mathematicians defending Smale (subpoenaed by HUAC while in Moscow) inflated the award's prestige to the press
• Historian Michael Barany documented that John Charles Fields intended the prize to support promising young mathematicians, not create national rivalry; the age-40 limit codified over time to reduce candidates
• The phrase "math on the beaches of Rio" became mathematical lore after a Johnson-administration science advisor criticized publicly-funded mathematicians working in such settings

Connections: Stephen Smale · Fields Medal · Topology · Poincare Conjecture

Source: https://blogs.scientificamerican.com/roots-of-unity/math-and-the-beaches-of-rio/