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Infinity: History, Mathematics, Philosophy

at Brooklyn Institute for Social Research - Midtown

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$315
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Location:
Midtown, Manhattan
247 West 37th St 5th Fl
Btwn 7th & 8th Avenues
New York, New York 10018
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Description
Class Level: All levels
Age Requirements: 21 and older
Average Class Size: 12
Teacher: Suman Ganguli

Flexible Reschedule Policy: This provider has flexible, free rescheduling for any-in person workshop. Please see the cancellation policy for more details

What you'll learn in this history lesson:

This course is a historical approach to the mathematics of infinity, with a focus on conceptual and philosophical questions.  We will begin with the ancient Greeks’ discovery of irrational numbers and discussions of Zeno’s paradoxes, then jump forward to the development of the “infinitesimal” calculus in the late 17th century (by Newton and Leibniz), and finally examine how 19th century mathematicians (in particular Cauchy, Bolzano, Riemann and Weierstrass) examined the foundational concepts of calculus, leading to increasingly abstract notions of functions and sets.

Underlying all this, from Zeno to the calculus, is the concept of the continuum, i.e., the real numbers.  The mathematics of the continuum culminates with the work of Richard Dedekind and Georg Cantor in the 1870s and 1880s. Dedekind provides the first precise definition of the real numbers, while Cantor discovers the key distinction between countably and uncountably infinite sets.  We will go through Cantor’s famous “diagonalization” argument, which demonstrates that the continuum is uncountably infinite–meaning, in a precise sense, that the real numbers constitute a larger infinity than the integers (the “counting numbers”).

Time permitting, we’ll follow the story forward to the present: through the “foundational crisis” of mathematics in the early 20th century and the remarkable pair of results, proved in the mid-20th century by Kurt Gödel and Paul Cohen, which together show that Cantor’s continuum hypothesis, regarding the size of the continuum, is independent of the standard axioms of set theory. That is to say, the fundamental question of how many real numbers there are isn't settled by the currently accepted axioms of set theory.

As a guide to this intellectual history, we will read David Foster Wallace’s “Everything and More: A Compact History of Infinity,”in conjunction with readings on the history, mathematics and philosophy of infinity, including primary texts by Cantor, Dedekind, Hilbert and Gödel.

Note: 
  • There is no mathematical prerequisite for this course, just a willingness to grapple with the concepts.
There *is* no physical Brooklyn Institute. We hold our classes all over (thus far) Brooklyn and Manhattan, in alternative spaces ranging from the back rooms of bars to bookstores to spaces in cultural centers, including the Center for Jewish History, the Goethe-Institut, and the Barnard Center for Research on Women. We can (and do) turn any space into a classroom. You will be notified of the exact location when you register for a class.

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Refund Policy

Note: This provider has a temporary cancellation policy for COVID-19 related cancellations which is as follows:

We'll grant full course credit up to the start of the first class. After the first class we can offer 75% course credit; after the second 50%; and after the third 25%.

----

Original cancellation policy (non-COVID-19):


Upon request, we will refund the entire cost of a class up until 1 week before its start date. Students who withdraw after that point but before the first class are entitled to a 75% refund. After the first class: 50%. After the second: 25%. No refunds will be given after the third class.

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Reviews of Classes at Brooklyn Institute for Social Research (21)

(21 Reviews)
Infinity: History, Mathematics, Philosophy
Reviewed by Valerie V. on 11/10/2017
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School: Brooklyn Institute for Social Research

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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