Six Math Essentials
teorth.github.io
teorth.github.io
Terence Tao explains 6 essential mathematical concepts: https://www.youtube.com/watch?v=OOMx2BHHWtE
1. numbers as the gateway to quantitative thinking
2. algebra as the gateway to abstraction
3. geometry as a way to calculate beyond what we can see
4. probability as a tool to navigate uncertainty with rigorous thinking
5. analysis as a means to tame the very large or the very small
6. dynamics as the mathematics of change
That's a historical artifcat, not an innate property. (Math was first invented in the Bronze Age for accounting and architecture.)
There's a theoretical parallel universe with a mathematics where numbers aren't first on the ladder but down there around number five. (Ironically computers are an example of that. Figuring out how to do numbers when all you have is finite sequences from an alphabet is advanced CS.)
That said, you can switch to the Kindle version and request a sample. The kindle samples usually have a ToC.
It's direct and well-written; a high-level overview of mathematics from numbers to analysis and dynamics. I think it's well organized, if brief at ~100pp.
This would be a great read for laypeople as well as a potential gap-filler for anyone in STEM.
> A big part of mathematical training is becoming acquainted with different concepts and recognizing how they’re cousins to each other.
> I encourage everyone to fool around with numbers—some enthusiasts discover important patterns that way, and some famous mathematicians, like the late John Conway, made a career of it.
> When we give word problems in school, we tend to cherry-pick perfect models that have one correct answer. Rather than teach a preordained procedure, we could encourage exploration by asking students to fix more realistic models where things are slightly noisy or slightly incorrect.
Perplexing how it's on the front page then given the background of the median HN user (presumably technical with some STEM background in general, some pure VC bros peppered in etc).
The Tao love conquers all, as it were.
Does Tao intend that as the 100,000 ft view of all mathematics, a way to categorize (almost) all of it, the roots of the mathematics tree? Are these the essentials or just some valuable ones.
For comparison, Gowers begins a much larger book with, "there is a crude division that undoubtedly works well as a first approximation, namely the division of mathematics into algebra, geometry, and analysis." [0]
There must be other schemes out there? What are the respected ones?
[0] Timothy Gowers, ed. The Princeton Companion to Mathematics. p.1 (2008)
TIL about Quanta Books, thanks OP — will be checking this out! :D
Is this a book for children?
[1] https://www.sciencefriday.com/articles/six-math-essentials-b...