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Wolfram High School
Summer Research Program

Formerly known as the Wolfram High School Summer Camp

Bentley University, Boston, MA June 25–July 13, 2024


Seán Flaherty

Wolfram High School Summer Camp

Class of 2014


I am a rising senior from Austin, Texas, who likes to discover the inner workings of the universe, ranging from classical mechanics to quantum physics. Whenever I learn any concept, it is never enough to just have the formula; I must prove it to myself on the deepest level. When inspiration hits me, I can blather on for hours, even days, about Stokes' theorem, Maxwell's equations, or Euler's formula. When I am not studying mathematics, my hobbies include playing the clarinet, watching anime, reading manga, playing Dota 2, and practicing the esoteric art of pen spinning.

Project: The Hairy Ball Theorem

The hairy ball theorem states that for a sphere, or any homeomorphic surface, there is no continuous, nonvanishing tangent vector field—in other words, you cannot comb a hairy ball flat without at least one part or cowlick. In this Demonstration, a manipulatable vector field allows one to "comb" a tangent vector field on a sphere or torus, showing the point with the local minimum vector norm on that surface. If the smallest vector norm is zero, the hairy surface has a vanishing point, or "part," and is considered to be "not combed." On a sphere, this minimum point will always be zero for a tangent vector field, indicating a part, while a hairy torus can, in fact, be combed flat.