Ancient axioms and modern ingenuity combine in math professor’s world

Every workday, without fail, Professor Michael ‘Miki’ Neumann, head of the Department of Mathematics, pedals around his home or the UConn campus on his silver Raleigh, contemplating complex mathematical problems.

Neumann operates in a world of linear algebra, matrix theory, and other high-end mathematics, developing algorithms that often expand the very science to which he has devoted much of his life.

Like an engineer building a bridge on bedrock, he relies on axioms accepted since the time of Archimedes.

With Neumann’s ingenuity, mathematical bridges built long ago are being extended to address modern problems.

Last year he was named one of the University’s Research Fellows.

One day recently, he explained to a visitor what numerical analysis – his primary research interest – is all about.

Drawing an ameba-like shape on the board, he said, “This is the kind of thing that numerical analysis deals with – approximating the area of any irregular shape. It is very difficult to find the area, but it has an area. You can see that.”

To find it, he said, “You develop an algorithm based in part on calculus. You divide the area into very, very thin strips and join their ends at the boundary to create a number of small trapezoids.

" We know how to find the area of a trapezoid, so our formula adds them all together and we end up with a very good approximation of the total area.”

His specialty has application in all sorts of chance problems, ranging from predicting the when the weather might change to understanding the long-term trends in migration of human populations to and from urban areas.

A perfect system
Neumann relates to mathematics not only as a tool for solving problems, but also as a world to enjoy for its own sake. In fact, he speaks of his science in much the same way one might speak of a magnificent painting or sculpture.

“Mathematics is a beautiful thing unto itself. It’s a complete system. It’s perfect,” he says.

He notes that writers ranging from Aristotle to Bertrand Russell have expressed similar sentiments, appreciating the symmetry of math and comparing it to music, art, and poetry.

If Neumann feels any frustration in his field, it probably derives from the fact that mathematics is often overlooked when people marvel at achievements as common as e-mail transmission or as uncommon as sending a rocket to the moon.

“One does not see that there’s a whole lot of mathematics in an e-mail, turning it into a pulse, decoding and encoding,” Neumann says.