Permanence and Impermanence of Mathematical Concepts

October 21st, 2023 at 2:30pm EST
Past Event

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... read more! »

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.

Tags

All Helix Center events are free and open to the public, including this one!

Roundtables are streamed live our website and the recording remains available after the event events.

This is a past event that happened on October 21st, 2023 at 2:30pm EST.

Participants

Michael Harris

Professor of Mathematics, Columbia University

Michael Harris is Professor of Mathematics at Columbia University; before that he held positions at Brandeis University and Université Paris-Diderot. He obtained his Ph.D. in 1977 from Harvard University, under the direction of Barry Mazur. He has organized or co-organized more than 20 conferences, workshops, and special programs in his field of number theory. He... read more! »

Barry Mazur

Gerhard Gade University Professor, Harvard University

Barry Mazur is a mathematician at Harvard University who has often taught courses in History of Science and Philosophy. His books include: Imagining Numbers (particularly the squareroot of minus fifteen) (Farrar Straus and Giroux); Prime Numbers and the Riemann Hypothesis, written with William Stein (Cambridge University Press) and he has edited with Apostolos Doxiadis the... read more! »

Nathalie Sinclair

Distinguished University Professor, Faculty of Education, Simon Fraser University

Nathalie Sinclair is Distinguished University Professor at Simon Fraser University, in the Faculty of Education. She is co-editor of Mathematics and the aesthetic: New approaches to an ancient affinity and What is a mathematical concept?. She has also led the development of two multi-touch apps for arithmetic learning, called TouchCounts and TouchTimes.

Alma Steingart

Assistant Professor, History, Columbia University

Alma Steingart researches the interplay between politics and mathematical rationalities. Steingart’s second book manuscript, Accountable Democracy: Mathematical Reasoning and Representative Democracy in America, 1920 to Now, examines how mathematical thought and computing technologies have impacted electoral politics in the United States in the twentieth century. Focusing on the census, apportionment, congressional redistricting, ranked voting, and election... read more! »

Jared Weinstein

Professor, Mathematics & Statistics, Boston University

Jared Weinstein is a professor in the department of Mathematics and Statistics at Boston University, where he has worked since 2011.  He studies number theory, which is ultimately the study of the whole numbers and their properties, but which links promiscuously with practically every other mathematical subject.  A New York native, he received his PhD... read more! »