21–30 of 92 posts
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.
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.
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.
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 disagre…
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?
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 disagre…
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?
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?
So… numbers, algebra, geometry, probability, analysis, dynamics are not the primitives or essentials ?
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
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 disagre…