Mathematics affects other industries
To the editor:
It doesn't surprise me that a column critical of theoretical mathematics should come from an engineer. The goal of an engineer is to design and build practical things. A scientist's goal is to expand human knowledge. However, scientific exploration often leads to useful practical applications. Mathematicians are not engineers, they are scientists.
The time between theory and application in mathematics can be very long indeed. A good example of this is number theory. Some of the most powerful work in number theory was done by Euclid around 500 B.C. Until this century, number theory was little more than a set of interesting number tricks.
Now number theory is responsible for protecting the privacy of your e-mail (cryptography), ensuring the accuracy of electronic data (data correction) and speeding up communications (data compression). If V. Lakshman had his way, Euclid would have spent his time working on "useful mathematics" and the Internet would still be a few thousand years off. The time between theory and practice in mathematics is getting shorter but, just like science, it may be years before practical applications are found.
So, what use is algebraic topology? Right now, I don't know. But that isn't the point. If history is any indication, a powerful practical application will eventually be found. Perhaps algebraic topology is the key to faster-than-light travel, or the end of disease and hunger.
Without continuing theoretical work in mathematics, the work being done in the engineering, medical and scientific communities would eventually stop.
Alan Ludwig
Mathematics senior
Math research leads to new knowledge
V. Lakshman's column left me cold. I do not share Lakshman's joy over the reduction of the University of Rochester mathematics department. I further disagree with his claim that "all rationale" is on the side of the Rochester regents who disbanded the graduate program.
Virtually every faculty handbook of virtually every major university declares the creation of new knowledge as its research aim (see 3.6.2 of the OU Faculty Handbook).
Abstract mathematical research leads to new knowledge. How society applies the knowledge gained through research is largely irrelevant. This condition has been a bedrock principle of universities since the inception of higher education. Certainly the accomplishments of mathematicians should not be evaluated by criteria dictated by a generation of engineering students who base their assessments on their possibly temporary lack of vision concerning how to use these accomplishments to the advantage of the market. I would rather not be associated with a university so enfeebled by market whims that researching mathematicians can not find support for their pursuit of knowledge for its own sake.
The University of Rochester is diminished by its decision, and the OU Board of Regents should never follow its imprudent example.
Michael Lee
Assistant professor of music history
Mathematics has scientific utility
To the editor:
V. Lakshman thinks he knows what is of ultimate benefit to society, and that mathematics contributes nothing to this, hence it should be banished to the liberal arts, which apparently benefit no one. Moreover, unlike history or English, mathematics should have no graduate program, as punishment for daring to call itself a science.
In fact, mathematics is both art and science, and to separate these aspects is as futile as separating the two halves of our brains. And what is
carelessly called "a benefit to society" is more likely a benefit to
shareholders. If Lakshman is convinced that telephone lines provide
"ultimate benefit," he can join the ants, who never stray from the
righteous path of practicality.
The scientific utility of mathematics is known to educated persons, but mathematics is also a growing chain of ideas that began before written history. In this sense, mathematical development is more valuable and enduring than telephones. Humans have always worked on mathematics, with or without practical application, because many brains find primordial satisfaction in it. So mathematics will continue to blossom, despite the angry ignorance exemplified by Lakshman.
At root, this anger is directed at the university, whose purpose, I
believe, is to cultivate our inheritance, of which mathematics is a
central branch. (Read the uncut version of this letter at http://www.math.uoknor.edu/~mreeder).
Mark Reeder
Associate professor of mathematics