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Press Release

Jonathan Potts

For immediate release:
May 27, 2003

Carnegie Mellon Professor Receives Prestigious Grant to Delve into Mathematics History

PITTSBURGH—To fund an ambitious research project that spans philosophy, mathematics and the history of science, The Andrew W. Mellon Foundation has awarded a New Directions Fellowship to Jeremy Avigad, an associate professor of philosophy at Carnegie Mellon University.

Avigad will spend a full year studying developments in mathematics during the 19th century, a period in which dramatic conceptual advances laid the foundations of modern mathematics. As they worked to develop a more rigorous foundation for calculus and unify the diverse branches of their subject, mathematicians introduced increasing levels of abstraction and employed a new boldness in dealing with the infinite. Many mathematicians also began to de-emphasize calculation in favor of more conceptual forms of understanding, a shift that was highly controversial at the time.

Specifically, Avigad will examine the work of two of the 19th century's most prominent mathematicians, Leopold Kronecker and Richard Dedekind. Many of the methodological and ideological tensions can be discerned in their divergent approaches to a branch of mathematics known as algebraic number theory. Kronecker was explicit in stating that the goal of mathematics is to develop powerful methods of calculation, while Dedekind was equally explicit in claiming that the goal is to develop an abstract conceptual framework that would render calculations largely unnecessary.

Avigad's research will be significant in light of recent debates in the philosophy of mathematics over the proper role of historical data in understanding the goals and methods of mathematics. "The challenge is to mine the historical events for philosophical insights, without denying the special character of mathematics as a rigorous and objective science," Avigad said.

The New Directions Fellowships are for faculty members in the humanities or humanistic social sciences who have not yet received tenure-or have recently done so-and who wish to acquire systematic training in topics outside of their own disciplines. Avigad, a trained philosopher and mathematician whose specialty is mathematical logic, will use the fellowship to study the history of math. The grant will enable him to take four courses in the University of Pittsburgh's History and Philosophy of Science Department during the 2003-04 academic year and to discuss his findings with historians of mathematics both in the United States and abroad.

"Because this kind of research combines a number of disciplinary perspectives, it tends to fall through the cracks," Avigad said. "I feel tremendously fortunate to have the support of both Carnegie Mellon and The Andrew W. Mellon Foundation. I wouldn't have been able to do this work otherwise."


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