Gresham College | How to Prove 1=0, And Other Maths Illusions - Sarah Hart @GreshamCollege | Uploaded 4 months ago | Updated 5 hours ago
In this lecture I will show you some mathematical illusions: “proofs” that 1=0, that fractions don’t exist, and more. There are curious and important implications behind what’s going on.
These “proofs” reveal some very common logical slips that can go unnoticed when we are trying to prove more plausible statements. And the stakes are high. As I’ll show you, once you have “proved” one false claim, you can prove absolutely any statement at all.
Chapters
00:00 Introduction
02:35 1=0
04:12 The smallest positive number is 1
06:04 All triangles are isosceles
10:45 What is proof?
14:13 1p=£1
15:15 Real-world impacts of mathematical mistakes
19:15 Solving 1p = £1
20:14 More proofs that 1=0
22:42 Everything is true
24:58 0 is greater than 0
27:26 Explaining infinite series
40:04 Riemann series theorem and 1/2 = 1/3
48:00 Spotting the errors
53:52 Conclusion
55:55 Q&A session
This lecture was recorded by Sarah Hart on 14th May 2024 at Barnard's Inn Hall, London
Sarah is Gresham Professor of Geometry.
She is also Professor Emerita of Mathematics at Birkbeck, University of London.
The transcript of the lecture is available from the Gresham College website:
gresham.ac.uk/watch-now/maths-illusions
Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: gresham.ac.uk/support
Website: gresham.ac.uk
Twitter: twitter.com/greshamcollege
Facebook: facebook.com/greshamcollege
Instagram: instagram.com/greshamcollege
In this lecture I will show you some mathematical illusions: “proofs” that 1=0, that fractions don’t exist, and more. There are curious and important implications behind what’s going on.
These “proofs” reveal some very common logical slips that can go unnoticed when we are trying to prove more plausible statements. And the stakes are high. As I’ll show you, once you have “proved” one false claim, you can prove absolutely any statement at all.
Chapters
00:00 Introduction
02:35 1=0
04:12 The smallest positive number is 1
06:04 All triangles are isosceles
10:45 What is proof?
14:13 1p=£1
15:15 Real-world impacts of mathematical mistakes
19:15 Solving 1p = £1
20:14 More proofs that 1=0
22:42 Everything is true
24:58 0 is greater than 0
27:26 Explaining infinite series
40:04 Riemann series theorem and 1/2 = 1/3
48:00 Spotting the errors
53:52 Conclusion
55:55 Q&A session
This lecture was recorded by Sarah Hart on 14th May 2024 at Barnard's Inn Hall, London
Sarah is Gresham Professor of Geometry.
She is also Professor Emerita of Mathematics at Birkbeck, University of London.
The transcript of the lecture is available from the Gresham College website:
gresham.ac.uk/watch-now/maths-illusions
Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: gresham.ac.uk/support
Website: gresham.ac.uk
Twitter: twitter.com/greshamcollege
Facebook: facebook.com/greshamcollege
Instagram: instagram.com/greshamcollege
