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Numbers: History, Mathematics, Philosophy

Uncover the profound roots and enigmatic nature of numbers as you explore their historical, mathematical, and philosophical dimensions. Join us in a captivating exploration of the concept of number, examining its evolution, cultural significance, and the fundamental questions it poses about the nature of reality.

  • All levels
  • 21 and older
  • $335
  • Online Classroom
  • 12 hours over 4 sessions

Start Dates (0)

  • $335
  • 12 hours over 4 sessions
  • Class will not meet Wednesday, April 24th.
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Class Description


What you'll learn in this history lesson:

Numbers are so common, so seemingly intrinsic to human life, that it’s baffling to recall that, for millennia, many humans did not use them at all. How, then, did the use of numbers come to be? Were they, in some sense, discovered? Are they qualities of the natural world or truths outside of time and space? Or, are numbers human creations—concepts devised to help us analyze, organize, and manipulate the world. If numbers “work,” are they therefore, in some sense, “real”?

In this course, we will examine the concept of number from various points of view: mathematical, historical, cultural, philosophical. We will consider the history and evolution of numbers and numeric systems: the prehistoric origins of the “natural numbers” (i.e., the positive integers) in the fundamental human activity of counting; the development of tally systems and numerals as symbolic/syntactic representations of numbers; and the use of different base systems, such as the “sexagesimal” (base 60) system used by the ancient Sumerians and Babylonians, the decimal (base 10) place-value representation of numbers that we use today, and the binary (base 2) system fundamental to modern computation. Students will look at the foundations of arithmetic, algorithms, and the branch of mathematics called “number theory.”  And we’ll consider the expansion of the concept of number beyond the natural numbers: to negative numbers, rational numbers, irrational numbers, complex (or “imaginary”) numbers, and infinite numbers. As we proceed, we’ll constantly pose and repose the central question: what, really, are numbers?

Readings will include selections from Arithmetic by Paul Lockhart; Numbers and the Making of Us: Counting and the Course of Human Cultures by Caleb Everett; The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene; The Universal History of Numbers by Georges Ifrah; Number Words and Number Symbols: A Cultural History of Numbers by Karl Menninger; and The Foundations of Arithmetic by Gottlob Frege.

Remote Learning

This course is available for "remote" learning and will be available to anyone with access to an internet device with a microphone (this includes most models of computers, tablets). Classes will take place with a "Live" instructor at the date/times listed below.

Upon registration, the instructor will send along additional information about how to log-on and participate in the class.

Refund Policy

  • Upon request, we will refund less 5% cancellation fee of a course up until 6 business days before its start date.
  • Students who withdraw after that point but before the first class are entitled to 75% refund or full course credit.
  • After the first class: 50% refund or 75% course credit.
  • No refunds or credits will be given after the second class.

In any event where a customer wants to cancel their enrollment and is eligible for a full refund, a 5% processing fee will be deducted from the refund amount.

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Brooklyn Institute for Social Research

The Brooklyn Institute for Social Research was established in 2011 in Boerum Hill, Brooklyn. Its mission is to extend liberal arts education and research far beyond the borders of the traditional university, supporting community education needs and opening up new possibilities for scholarship in the...

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Brooklyn Institute for Social Research

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