Explore mathematical illusions and logical fallacies in this engaging lecture by Sarah Hart, Gresham Professor of Geometry. Discover seemingly valid "proofs" that lead to absurd conclusions like 1=0, the non-existence of fractions, and all triangles being isosceles. Examine the nature of mathematical proof and its real-world implications. Delve into infinite series, the Riemann series theorem, and learn to spot errors in deceptive mathematical arguments. Gain valuable insights into common logical pitfalls and their consequences in mathematics and beyond through this comprehensive exploration of mathematical paradoxes and reasoning.
How to Prove 1 = 0 and Other Mathematical Illusions
Overview
Syllabus
Introduction
1=0
The smallest positive number is 1
All triangles are isosceles
What is proof?
1p=£1
Real-world impacts of mathematical mistakes
Solving 1p = £1
More proofs that 1=0
Everything is true
0 is greater than 0
Explaining infinite series
Riemann series theorem and 1/2 = 1/3
Spotting the errors
Conclusion
Q&A session
Taught by
Gresham College
