Segerman received his Master of Mathematics (MS) at the University of Oxford (2001) and then his PhD at Stanford University (2007) for the dissertation "Incompressible Surfaces in Hyperbolic Punctured Torus Bundles are Strongly Detected" under Steven Paul Kerckhoff.[7]
Segerman's research lends itself to mathematics with a strong visual component.[6] This led directly to his involvement with 3D printing. In 2016 he wrote the book Visualizing Mathematics With 3D Printing.[8]Laura Taalman in a review said, "Segerman's book is an inside tour of mathematics with breathtaking 3D-printed scenery."[8]
3D printing
Triple gear by Saul Schleimer and Henry Segerman Figure eight knot complement by François Guéritaud, Saul Schleimer, and Henry Segerman
Mathematicians used to rely on wooden or plaster models to visualizing complex geometrical shapes. Nowadays, if they can be described mathematically, we can "print" them with 3D printers.[9] Segerman uses mathematical tools including quaternions,[10] Euclidean and non-Euclidean geometries and stereographic projection to create instructions for 3D printers.[4] Sometimes the goal is to produce a work of art.[11] Sometimes it is to shed light on four-dimensional geometry[12] or some other field such as mathematical group theory. Sometimes it is both.[10] One of his sculptures depicts a set of monkeys joined together to form a 4-dimensional hypercube.[13]
Segerman's techniques help us visualize a four dimensional world.[14] Just as the frame of a cube can cast a shadow on a flat wall, Segerman makes analogous shadows of four dimensional objects via a 3D printer.[15][12] Segerman has also explored kinetic artwork, designing mechanisms that move in unusual or seemingly paradoxical ways.[6]: 128
Combining his interests in mathematics and art he is one of 24 mathematicians and artists who make up the Mathemalchemy Team.[19]
In another foray into recreational mathematics Segerman founded Dice Lab with mathematical artist Robert Fathauer. Using computer search and help from fellow recreational mathematician Robert Bosch, they created a "numerically balanced" 120-sided die in the shape of a disdyakis triacontahedron. It is the "biggest, most complex fair die possible".[20] They concede that the die is "expensive and there’s no real use for it", but it's still theoretically interesting.[21]
Selected papers
Segerman does research in three-dimensional geometry and topology. Papers published in this area include:
2020 "Ray-marching Thurston geometries", arXiv:2010.15801 [math.GT, cs.GR, math.DS], [with Coulon, Matsumoto and Trettel], October 2020
