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?
Read Polya's "How to Solve It" :)
So… numbers, algebra, geometry, probability, analysis, dynamics are not the primitives or essentials ?
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
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.
It’s like principal component analysis, the main axis, I don’t mean reduction in a negative way.
Isn't every summarization a reduction?
these might not be 100% complete, but i think this does a reaaalllly good job at capturing the vast majority of mathematics.
i'm sure you could come up with another breakdown, but these also have the benefit of tracking roughly with history. numbers and geometry (euclid), then eventually algebra. probability was a fundamentally new way of looking at the world. analysis comes via newton/leibniz and then dynamics tries to tackle complex systems (kinda where newton left off, e.g., 3-body problem type stuff).
also: dimension reduction is not a bad thing. this is like a decomposition: we can decompose so much of what research mathematics is doing into 6 different basis elements. that's pretty darn neat.
(edit: liebnitz -> leibniz)
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