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Jeff then

Jeff now

Jeff Achter '92

First day of class, fall '88, Math 35. Tom looks exactly like a math professor ought to; I guess I'm in college now. He promises to broaden — redefine, actually — our horizons, and makes a fair stab at doing so on the spot.

Second day of class, fall '88, Math 35. Tom takes attendance by being attentive; naming those here, wondering after those not. Note to self: slack-free zone.

Thus, the journey begins. It had never occurred to me to work hard at exploring math. Tom showed us all both how and why. We developed tools — sometimes formulas, sometimes pieces of software — to aid this discovery. We gave him programs like Vector and VeNoM. He gave us all — the Vector group (Cassidy Curtis, Curtis Hendrickson, Greg Siegle and Matthew Stone) and team fnord (Scott Draves and Nick Thompson) the motivation to start these projects, the guidance to complete them, and the curiosity to use them to explore. Lifelong friendships arose in those groups, too; for that, as much as for anything else, I'm grateful to Tom.

Last year, I found myself teaching a course on surfaces and knots to a room full of Columbia students who thought they desperately hated mathematics. Fortified with the Book of Tom, I proceeded. Chapter one, paragraph one, I'd long ago committed to memory; learn who your students are, as fast as possible. (This turned out to never be nearly as fast as I'd seen it done by Tom.)

A few weeks later, sketching out various compact surfaces, I drew a stitching diagram for a Klein bottle and a two-dimensional shadow of a three-dimensional representation of it. In the very worst of mathematical traditions I muttered something about how the apparent intersection was an artifact of using a lowly three dimensions, and tried to continue. But my students would have none of it, and for that I'm grateful. Flipping back through the Book, I showed the class how if you pull this part into green, and push that part down into blue, it really doesn't intersect at all.

Most of all, I shared with my students the call and response I'd learned in math 35:

"What is the nature of [...]?"

"It depends."

"On what does it depend?"

My thanks to Tom for a life's worth of questions.

Jeff received his Ph.D. in Mathematics from the University of Pennsylvania, after which he taught at Columbia University, with recent courses in Surfaces and Knots, and Number Theory (see his web home page for more information). He is now a member of the Biology Department of Colorado State University.

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Created: 11 Oct 2003
Last modified: Nov 3, 2003 7:26:50 AM
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