Erich Reck

RIVERSIDE, Calif. — Erich Reck, associate professor of philosophy, has been awarded a $142,922 grant by the National Science Foundation to further his research on 19th century German mathematician Richard Dedekind.

Dedekind was one of a handful of mathematicians who helped transform mathematics from the study of numbers and quantity to the much more general study of relational structures. However, the significance of his contributions to the early development of set theory and abstract algebra has not been studied systematically, Reck said. Those theories connect to modern logic, which influenced the development of computer science, among others.

"The 19th century was an interesting period of fruitful collaboration between philosophers and mathematicians, the kind of collaboration that has gotten lost a little in recent years," he said. "It was a period of time when the traditional view of mathematics as numbers and quantity was replaced by a much more abstract way of thinking. Dedekind was a central figure in that shift."

Philosophers of science and mathematics do not set out to prove new theorems, Reck explained. Rather, they ask more general questions: How exactly should we think about new scientific ideas? What is their bigger significance? For example, the development of abstract mathematics produced a new vocabulary of mathematical symbols, which prompted philosophers to explore new ideas about language more generally.

Reck plans to write a monograph on Dedekind and his trailblazing contributions. "The main outcome of this project will be a case study in the history and philosophy of mathematics," he said. "However, several of the issues addressed in it — the relationship between methodological and metaphysical views in science, the notions of explanation and understanding, the intertwining of conceptual continuity and change — have significance beyond mathematics, for human knowledge as a whole."