Internet, if used properly, is an ore of useful information. You literally do not need to attend any physical classes in order to learn anything, be it quantum mechanics or neurobiology. The internet has so many online free resources that we can get our hands on that we can’t even imagine. The idea is to be able to filter that information and those resources so that they can benefit us in the best way possible.

Previously, I had written a story about the five greatest mathematics lectures that you watch free online where I included lectures from some prominent mathematicians like Terrence Tao. If you haven’t read that story already, you can read it here:

There are many other brilliant mathematics lectures that can be great resources not just for aspiring mathematicians or mathematics majors but for anyone who is interested in mathematics. Math is the language that our universe speaks in. It is the best tool we have so far which, despite being so abstract, does the best job of describing the physical realities of the universe. With that being said, let’s make a list. These lectures have been extracted on the basis of their topic, the prominent expertise of the lecturer, and the clarity and wit with which the lectures are delivered.

Dynamics and Moduli space of curves by Maryam Mirzakhani

Maryam Mirzakhani, for those of you who don’t know, was the first female fields medalist. Fields medal, as I’ve mentioned earlier as well, is the highest honor given to any mathematician every four years. The brilliant Iranian mathematician had her expertise in the formation of structures on surfaces, hyperbolic surfaces to be more precise. Here, in this lecture, she explains her works on dynamics and moduli space of hyperbolic surfaces, the same work that won her the Fields Medal. Unfortunately, Mirzhakhani passed away in 2017 due to breast cancer leaving a great mathematical legacy behind.

Categorification of Fourier Theory by Jacob Lurie

Prof. Jacob Lurie is an American mathematician and also a gold medalist and a perfect scorer in International Mathematical Olympiad (so was Maryam Mirazhani) who specializes in algebraic geometry and infinite categories. He is also a McArthur Fellowship winner and a professor of mathematics at the Institute For Advanced Study. In this lecture, Professor Lurie explains the categorification of Fourier Theory in a very simple and elegant manner that even someone from a non-mathematical background can understand.

P vs NP Problem by Hackerdashery

This is not particularly a lecture by a professor but I want to include this video in the list due to its simplicity in explaining one of the most complicated mathematical and computational problems of all time: The P vs NP Problem. The problem is also on the list of 7 Millennium Prize Problems in Mathematics formed by Clay Mathematics Institute. This is arguably the only video on YouTube that can explain this problem in the easiest manner possible. So here it is,

The mathematical work of Vladimir Voevodsky by Dan Grayson

Vladimir Voevodsky is considered to be one of the most brilliant mathematicians in the field of algebraic topology who is best known for developing homotopy theory. Vladimir Voevosdk won the 2002 Fields Medal for his works on the development of motivic cohomology. Unfortunately, Professor Voevodsdk dies in 2017 due to an aneurysm. In this lecture, Prof. Dan Grayson explains Voevosdk’s works and legacy.

What do we mean by “equal” by Pierre Deligne

Pierre Deligne is a Belgian mathematician and 1978 Fields Medalist best known for his works on Weil Conjectures. The 2008 Wolf Prize winner is brilliant in his field working in several contemporary mathematical disciplines. His doctoral advisor was Alexander Grothendieck who is considered to be the Zeus of modern algebraic geometry. You can find plenty of lectures by Prof. Deligne online but this one, in particular, is one of my favorites. Here the prolific professor explains what it means to be “equal” in mathematics,

These are the lectures that I really enjoyed watching and I think they are worth investing time for. Some of the aforementioned lectures are for people who have significant knowledge about the fundamentals of mathematics and some are even for people who aren’t trained in mathematics. But these lectures are absolute gold in terms of understanding the concept, the concepts that are helpful in shaping our understanding of the cosmos.

“The Only Way To Learn Mathematics Is To Do Mathematics .”

— Paul Halmos

If you want me to make a series on the lectures associated with several disciplines of physics, or any other disciplines, do let me know in the responses.

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