The World of Blind Mathematicians, Volume 49, Number 10

1246 NOTICES OF THE AMS VOLUME 49, NUMBER 10 A visitor to the Paris apartment of the blind geometer Bernard Morin finds much to see. On the wall in the hallway is a poster showing a computergenerated picture, created by Morin’s student François Apéry, of Boy’s surface, an immersion of the projective plane in three dimensions. The surface plays a role in Morin’s most famous work, his visualization of how to turn a sphere inside out. Although he cannot see the poster, Morin is happy to point out details in the picture that the visitor must not miss. Back in the living room, Morin grabs a chair, stands on it, and feels for a box on top of a set of shelves. He takes hold of the box and climbs off the chair safely—much to the relief of the visitor. Inside the box are clay models that Morin made in the 1960s and 1970s to depict shapes that occur in intermediate stages of his sphere eversion. The models were used to help a sighted colleague draw pictures on the blackboard. One, which fits in the palm of Morin’s hand, is a model of Boy’s surface. This model is not merely precise; its sturdy, elegant proportions make it a work of art. It is startling to consider that such a precise, symmetrical model was made by touch alone. The purpose is to communicate to the sighted what Bernard Morin sees so clearly in his mind’s eye. A sighted mathematician generally works by sitting around scribbling on paper: According to one legend, the maid of a famous mathematician, when asked what her employer did all day, reported that he wrote on pieces of paper, crumpled them up, and threw them into the wastebasket. So how do blind mathematicians work? They cannot rely on backof-the-envelope calculations, half-baked thoughts scribbled on restaurant napkins, or hand-waving arguments in which “this” attaches “there” and “that” intersects “here”. Still, in many ways, blind mathematicians work in much the same way as sighted mathematicians do. When asked how he juggles complicated formulas in his head without being able to resort to paper and pencil, Lawrence W. Baggett, a blind mathematician at the University of Colorado, remarked modestly, “Well, it’s hard to do for anybody.” On the other hand, there seem to be differences in how blind mathematicians perceive their subject. Morin recalled that, when a sighted colleague proofread Morin’s thesis, the colleague had to do a long calculation involving determinants to check on a sign. The colleague asked Morin how he had computed the sign. Morin said he replied: “I don’t know—by feeling the weight of the thing, by pondering it.”