Terence Tao explains 6 essential mathematical concepts [video] (youtube.com)
260 points by matthewsinclair a day ago
stillpointlab 4 hours ago
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.
thedreammachine 2 hours ago
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 2 hours ago
The Joy of X and I think now renamed to “The Joy of y” is a great podcast for general knowledge building!
esalman 5 hours ago
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.
iTokio 6 hours ago
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 5 hours ago
So… numbers, algebra, geometry, probability, analysis, dynamics are not the primitives or essentials ?
N7lo4nl34akaoSN 19 minutes ago
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 3 hours ago
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 4 hours ago
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 2 hours ago
Isn't every summarization a reduction?
binyu 4 hours ago
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 2 hours ago
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
laybak 6 hours ago
this is great foundational content! I also enjoyed his earlier appearance on 3Blue1Brown
bobajeff 5 hours ago
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.
matthewsinclair 7 hours ago
Apologies for the typo. I’ve asked mods to fix it.
matthewsinclair 7 hours ago
Looks like it’s been fixed. Thanks.
mc32 3 hours ago
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.
Agentus 6 hours ago
i blinked and read terrence howard. i was like good god
stuxnet79 5 hours ago
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]
pixelpoet 7 hours ago
At least spell his name correctly, my goodness...
Terence Tao.
dang 7 hours ago
Can't believe we missed that. Fixed now. Thanks!