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Infinity: History, Mathematics, Philosophy
Brooklyn Institute for Social Research @ 247 West 37th St, New York, NY
How can we, as finite beings, grasp the concept of infinity? Yet humans have been contemplating infinity for millennia, whether inspired by nature, philosophy, spirituality—or mathematics. This course is a historical and conceptual approach to the latter realm, the mathematics of infinity. Our topics will include the ancient Greeks’ discovery of irrational numbers and Zeno’s paradoxes; Aristotle’s distinction between “actual infinity”...
Imaginary Numbers: Theory, Mathematics, and Possibility
Brooklyn Institute for Social Research @ 68 Jay St, Brooklyn, NY
The very idea of imaginary numbers appears at first glance preposterous, like something out of science fiction or the wildest philosophy. A real or ordinary number multiplied by an “imaginary unit” somehow mathematically produces a “complex” number that has both theoretical and practical applications. Rene Descartes, who coined the “imaginary” terminology, deemed them preposterous. And yet, imaginary numbers are indispensable—not...
Calculus: History and Concept
Brooklyn Institute for Social Research
“Calculus,” wrote the mathematician John Von Nuemann, “was the first achievement of modern mathematics … it is difficult to overestimate its importance.” What does it mean to say calculus initiated modern mathematics? Beyond mathematics, what influence has calculus had on the wider world? Most importantly, what is calculus—and why does it still stand as the culmination of our mathematics curriculum? In this course, we’ll examine the...
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Gödel’s Incompleteness Theorems: History, Proofs
Brooklyn Institute for Social Research @ Online Classroom
Gödel’s Incompleteness Theorems: History, Proofs, Implications In 1931, a 25-year-old Kurt Gödel published a paper in mathematical logic titled “On Formally Undecidable Propositions of Principia Mathematica and Related Systems.” This paper contained the proofs of two remarkable “incompleteness theorems,” which state: For any consistent axiomatic formal system that can express facts about basic arithmetic, 1. there are true statements...
Numbers: History, Mathematics, Philosophy
Brooklyn Institute for Social Research @ Online Classroom
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.
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