Permanence and Impermanence of Mathematical Concepts

What do you think of when you think of the number five? Do you think of symbol like 5, a pattern like ⁙ , or the fifth item on a list? Today, the concept of number is fixed and eternal, unlinked to anything in the universe. But history shows that mathematics is anything but fixed. In some oral societies, there may well have been no “five”, only five rocks or five chickens. To ancient Greeks like Euclid, number was closely linked geometry, the magnitude of a line segment five units long. Only in the late 19th century did mathematicians attempt to formalize a notion of number, resembling our intuitions today: five is what five rocks and five chickens have in common.
Impermanence of mathematical concepts is the rule rather than the exception. The progress of mathematics is punctuated by revolutions, in ways similar to the evolution of art and science Fundamental notions can change even in the space of a single generation, and disarray and controversy may follow. Given that something so basic as the number 5 is subject to such instability, how can we still claim that mathematics is about absolute truth? We will discuss various revolutions in mathematical concepts, from non-Euclidean geometry to imaginary numbers to some more intuition-defying contemporary developments.
Participants:
Michael Harris
Professor of Mathematics, Columbia University
Barry Mazur
Gerhard Gade University Professor, Harvard University
Nathalie Sinclair
Distinguished University Professor, Faculty of Education, Simon Fraser University
Alma Steingart
Assistant Professor, History, Columbia University
Jared Weinstein
Professor, Mathematics & Statistics, Boston University
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