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

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.

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

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

• bobthe3

  today at 2:01 AM

  The Joy of X and I think now renamed to “The Joy of y” is a great podcast for general knowledge building!

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.

• SMEbooop

  yesterday at 10:49 PM

  [flagged]

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?

• Isamu

  yesterday at 10:18 PM

  So… numbers, algebra, geometry, probability, analysis, dynamics are not the primitives or essentials ?

  • N7lo4nl34akaoSN

    today at 3:17 AM

    I think OP wants reasoning primitives and techniques found in logic and finite math. Maybe even the theory of computation and the idea that proofs are programs (Curry-Howard).

  • MrbroJangles

    today at 12:21 AM

    Imo it's not numbers at all but linked to our awareness of physical relationships

    Making it about numbers is like making it about cans when it's more about grasping adding one can to a bag of cans, adding 100 cans (multiplication), or the inverse with subtraction and division

    Which is why I never liked numbers before algebra which then chucks numbers in the bin more or less.

    Numbers are just syntax meant to represent $anything; 1.5 can be half a pill and a whole pill or T or A; numbers are euphemism.

    That they can be infinitely big and yadda yadda isn't that meaningful in and of itself and that little bigness is all due to additive qualities of physical space

    Geometry is addition or subtraction of shape

    It's all built on 4 operations we see in daily life all the time

• binyu

  today at 12:04 AM

  Why do you feel this is a reduction? If anything, it is an attempt to summarize the various areas of math and how they relate to each other.

  • alansaber

    today at 1:56 AM

    Isn't every summarization a reduction?

• SMEbooop

  today at 12:16 AM

  [dead]

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.

• hmokiguess

  today at 1:32 AM

  Could you be conflating writing hamlet with understanding how to write hamlet? as in, what it takes to end up with the same raw output though devoid of intent and meaning

• yesterday at 11:57 PM

• today at 12:16 AM

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.

• matthewsinclair

  yesterday at 8:44 PM

  Looks like it’s been fixed. Thanks.

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

• stuxnet79

  yesterday at 10:17 PM

  For those not in the know, Terrence Howard's dreams of a career in Astrophysics were eviscerated after Neil Degrasse Tyson reviewed his "Theory of Everything" paper [1]

  [1] https://www.youtube.com/watch?v=1uLi1I3G2N4

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

Terence Tao.

• dang

  yesterday at 8:43 PM

  Can't believe we missed that. Fixed now. Thanks!

• 129476

  yesterday at 8:25 PM

  [flagged]

  • femiagbabiaka

    yesterday at 8:39 PM

    It was expected that people without established credibility would be looked down on for using AI, but it's been weird to see people with all the credibility in the world lose it for embracing AI.

    • yesterday at 8:45 PM

    • orf

      yesterday at 8:46 PM

      What credibility has he lost?

      • femiagbabiaka

        yesterday at 9:17 PM

        To sensible people? None. But the amount of criticism of his work that boils down to "he uses AI" is undeniable.

        • orf

          yesterday at 9:20 PM

          Can you share some of the criticism? I’ve not seen any from anyone real.

    • pfdietz

      yesterday at 9:03 PM

      It's weird to believe he's lost credibility.

    • nutjob2

      yesterday at 9:03 PM

      Tao gives or takes credibility from AI, not the other way around.

      • oliculipolicula

        today at 2:36 AM

        Is Tao the rising angel? Or AI the falling ape?

        --Another Terry, Perhaps

        AI-avatar-of-Tao wielded by an internet rando lies to or gets fooled by Tao, not the other way around

        --Me, attempting to take your Untouchable* joke all the way to a (sociopathic, one-party) joke

        *https://archive.ph/2023.11.28-152809/https://www.astralcodex...