Adonis Diaries

5 Greatest Mathematics Lectures Of All Time

Posted on: February 15, 2022

The lectures that will make you fall in love with math

Note: It would have been more interesting if an abridged version of the Video of each lecture have been published.

Sunny Labh

“The study of mathematics is the indispensable basis for all intellectual and spiritual progress.”

— F.M. Cornford (1874–1943)

Top [L-R] Terence Tao, John Nash, and David Hilbert. Bottom [L-R] John H. Conway, Alexander Grothendieck, and John Von Neumann. Copyright/courtesy: Respective Archives and owners

Mathematics is the language in which nature speaks. Prolific 20th-century physicist Paul Dirac once said, “God used beautiful mathematics in creating the universe”.

We use mathematics in our daily lives knowingly or unknowingly, in buying and selling stuff, in cooking, in measuring stuff, and so on. It is an integral part of our understanding of physical reality.

As useful as this tool is, it is also beautiful in its own way.

There are patterns and shapes everywhere, geometric structures that are measurable and associated with some of the complicated phenomena of the universe.

And if you love mathematics, then I’m sure you look out for math resources online.

There have been several brilliant mathematicians in the last 20th and the 21st century. Thousands of lectures that you can find online about multiple disciplines of mathematics.

There are few such lectures that are iconic in their own ways due to the brilliance in their presentation, simplicity, and wit.

In this article, I shall discuss 5 such amazing mathematics lectures that you must watch.

All the lectures mentioned in the article are freely watchable or readable online.

Prof. Terence Tao on The Erdős Discrepancy Problem

https://cdn.embedly.com/widgets/media.html?src=https%3A%2F%2Fwww.youtube.com%2Fembed%2FQauoO0j9Y9Y%3Ffeature%3Doembed&display_name=YouTube&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DQauoO0j9Y9Y&image=https%3A%2F%2Fi.ytimg.com%2Fvi%2FQauoO0j9Y9Y%2Fhqdefault.jpg&key=a19fcc184b9711e1b4764040d3dc5c07&type=text%2Fhtml&schema=youtube

Terence Tao is undoubtedly the most brilliant mathematician of our time. He has been a child prodigy and grew interested in numbers from quite an early age.

Prof Tao has published more than 300 research papers and has contributed some of the most important problems in mathematics including the 3-D Navier-Stokes problem which is also one of the Millennium Prize problems in mathematics, the Collatz Conjecture, which is considered to be one of the most ‘dangerous’ problems in mathematics, and many more.

Prof Tao has won several honorable awards including the 2006 Fields Medal, which is also considered the Nobel Prize of mathematics.

In this lecture, Tao is presenting a lecture on the Erdős Discrepancy Problem at the UCLA.

The lecture was uploaded in 2015 by Institute for Pure & Applied Mathematics (IPAM).

Paul Erdős teaching 10 years old Terence Tao at the University of Adelaide, 1985. Wikimedia Commons Image

Prof. Benoit Mandelbrot on Fractals

https://cdn.embedly.com/widgets/media.html?src=https%3A%2F%2Fwww.youtube.com%2Fembed%2Fock9Gk_aqw4%3Ffeature%3Doembed&display_name=YouTube&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dock9Gk_aqw4&image=https%3A%2F%2Fi.ytimg.com%2Fvi%2Fock9Gk_aqw4%2Fhqdefault.jpg&key=a19fcc184b9711e1b4764040d3dc5c07&type=text%2Fhtml&schema=youtube

Prof. Mandelbrot is also known as the father of fractal geometry, the field of mathematics that concerns with geometric structures having fractional dimensions.

Fractals is an important element for generating computer-generated graphics, animations, and games.

Mandelbrot worked at IBM for many years after moving from France and discovered Mandelbrot set while being there. Mandelbrot Set is regarded as one of the most important discoveries in the history of mathematics.

In this lecture titled Fractals in Science, Engineering and, Finance (Roughness and Beauty), Prof. Mandelbrot explains the importance of fractals in different sectors. The lecture was given at MIT in 2001 and is uploaded by MIT Video Productions for free to watch. Highly recommend it.

The last known lecture of Prof. John Nash Jr.

https://cdn.embedly.com/widgets/media.html?src=https%3A%2F%2Fwww.youtube.com%2Fembed%2Fmi2cGEjQ1Ks%3Ffeature%3Doembed&display_name=YouTube&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dmi2cGEjQ1Ks&image=https%3A%2F%2Fi.ytimg.com%2Fvi%2Fmi2cGEjQ1Ks%2Fhqdefault.jpg&key=a19fcc184b9711e1b4764040d3dc5c07&type=text%2Fhtml&schema=youtube

This lecture is relatively short but is very special. John Nash shouldn’t be a new name if you are reading this story.

He was a prolific mathematician and game theorist who had several significant contributions to multiple areas of mathematics including differential equations, game theory, cryptography, economic sciences, and many more.

The genius of Prof. John Nash is well captured in the 1998 book A Beautiful Mind by Sylvia Nasar.

The above lecture is the last known lecture of the ingenious mathematician delivered at the University of Oslo on 20th May 2015. On 23rd May

Prof. Nash sadly passed away in an accident.

In this lecture, Prof. Nash talks about An Interesting Equation. I suggest you watch it and feel motivated. The video remains uploaded by The Abel Prize channel and I really feel inspired every time I watch it.

Prof. Nash once stated, as mentioned in the book Doing Psychiatry Wrong: A Critical and Prescriptive Look at a Faltering Profession (2013) by René J. Muller, that

People are always selling the idea that people with mental illness are suffering. I think madness can be an escape. If things are not so good, you maybe want to imagine something better. In madness, I thought I was the most important person in the world.

David Hilbert’s 1900 Sorbonne Speech

David Hilbert is one of the most intellectual mathematicians of the 20th century having significant contributions to the field of calculus of variation, number theory, geometry, and many more.

Hilbert gave a speech to the International Congress of Mathematicians in 1900 about unsolved problems in mathematics.

The Sorbonne lecture is considered to be one the most important lectures in history as it was influential to the development of 20th-century mathematics.

The lecture talked about 10 such problems and then later Hilbert published 23 of them in the same year which are now famously called Hilbert’s Problems.

Source: https://www.researchgate.net/publication/254908894_Hilbert’s_1990_ICM_Lecture_the_23_problems

Some of the Hilbert Problems have already been solved in the past few decades while some of them haven’t been solved yet.

A complete list of Hilbert’s Problems as presented in the 1900 lecture can be read online in HTML format here:

Mathematical Problems

Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances…

mathcs.clarku.edu

Prof. John H. Conway on the Game of Life

John Horton Conway is a popular name in the field of game theory.

He is widely known for creating the Game of LifeAlong with that, he’s had several contributions to the fields of number theory, group theory, and geometry.

Horton spent the first half of his academic career at the University of Cambridge and the rest of it at Princeton University.

Conway was a keynote speaker and lecturer at Princeton University and every lecture delivered by him is a treat in itself.

I learned a lot about game theory, cellular automation, symmetry, and logic by watching his lecture videos.

One of my favorites is the one where he talks about the Game of life and mathematical challenges associated with set theory.

https://cdn.embedly.com/widgets/media.html?src=https%3A%2F%2Fwww.youtube.com%2Fembed%2FcQUAwhhC8cU%3Ffeature%3Doembed&display_name=YouTube&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DcQUAwhhC8cU&image=https%3A%2F%2Fi.ytimg.com%2Fvi%2FcQUAwhhC8cU%2Fhqdefault.jpg&key=a19fcc184b9711e1b4764040d3dc5c07&type=text%2Fhtml&schema=youtube

Some Honorable Mentions

String Compactifications by mathematical physicist Edward Witten
Paul Cohen Lecture (the quality isn’t that great)
John Von Neumann Lectures
Alexander Grothendieck Lectures on Mathematics

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