Terence Tao explains 6 essential mathematical concepts [video]

I love the fact he mentioned the Reimann rearrangement theorem briefly in his examples about analysis. That is (in my opinion) one of the coolest and least intuitive consequences of infinities. Requires some intro to different types of convergence to fully appreciate.

https://en.wikipedia.org/wiki/Riemann_series_theorem

I've heard it said that true understanding is demonstrated when someone can explain difficult concepts well. Tao manages to convey complex ideas without making me feel like he is condescending to me. His depth of understanding is unmistakable.

My changes to his list would be s/Geometry/Topology/ and I might have found a place for logic and type theory. I am especially glad he brought to mind Dynamics since that is a field I know I need to pay more attention to.

Great video, we're lucky to have this kind of content so easily and widely available.

I respected Terence Tao but since listening to his "Mathematics in the age of AI" talk, I've become a fan. I have had nobody else explain so succinctly what is the purpose of Mathematical research, why it matters, and why it is so important to preserve the ways we do math. Even more importantly, I feel it resonates so well with every other field AI is taking over.

Related and a great read: "The Joy of X: A Guided Tour of Math, from One to Infinity" by Steven Strogatz:

https://www.goodreads.com/en/book/show/13356649-the-joy-of-x

Numbers

Algebra

Geometry

Probability

Analysis

Dynamics

I loved this talk, but these concepts are like an attempt at dimensional reduction of math research, science, the academics knowledge.

I would have loved to have his thoughts on the mathematical mind, the process, how to reason, infer vs deduct, abstract, prove..

I don’t really know, what are the primitives, essential concepts of math reasoning?

Saw him explain Fourier transforms once; it finally clicked. Probably another masterclass in clarity.

You can pre order his book Six Math Essentials at https://a.co/d/0e89Jcjf

His lectures are gold, always manage to unlock a new perspective. Wish he taught my undergrad courses!

this is great foundational content! I also enjoyed his earlier appearance on 3Blue1Brown

https://www.youtube.com/watch?v=YdOXS_9_P4U

Very good resource. However, I fail to understand how a monkey writing the Hamlet is akin to a brute-force problem, in Terence's own words. The thesis seems to be here that given enough time, a monkey will be able to reason as a human.

Edit: Probably refers to the evolutionary aspect of the problem. My criticism is that he compares the time for a monkey needed to learn the hamlet to merely "quadratic time". I disagree that such degree of non-linearity applies here. I think it is grossly simplified/underestimated.

I really enjoyed this video (watched it the other day). It makes me feel like it's possible for me to understand the math that I'm currently trying to understand.

wow, that's really nice

Apologies for the typo. I’ve asked mods to fix it.

Maybe he was joking -not sure but around the 5:45 mark he says "irrational" in irrational numbers comes from the Latin for insane or unreasonable. But just before that he defines the numbers as not being able to be expressed as a ratio (that's what we all learn). Just seems odd he'd juxta that. Or it's dry wit.

i blinked and read terrence howard. i was like good god

[dead]

At least spell his name correctly, my goodness...

Terence Tao.