It's an interesting approach. They do like the classic sources.
I've at least skimmed more than half of those titles, long after college.
It's amusing that they have students read Pikkety's "Capital" before Marx's "Capital".
You don't want to learn geometry from Euclid. You read Euclid after you already know geometry, to see how he built it up. Similarly, you don't want to learn calculus from Newton. Or physics from Aristotle. What you're seeing there is people trying to figure something out before the tools for the job were developed.
There are great papers in engineering, where a theoretical advance changed the world. They're not well known. These should be as well known as the "Great Books".
* Maxwell's paper "On Governors". In a few pages, he invents feedback control theory. People were building steam engine governors but didn't understand stability and lag. It's a milestone in that it's one of the first times abstract math met practical engineering and the result worked.
* Shannon's discovery that telephone toll switches could be reduced from needing O(N^2) relays to O(N log N) was one. Suddenly, combinatorics went from a useless abstraction to a huge financial win for AT&T.
* "Rational Psychrometric Formulae", by Willis Carrier. Least click-bait title ever.
Basis of air conditioning. It's how you make an air conditioner and control both temperature and humidity at the cold end, rather than getting cold, humid air out.
* Von Neumann's Report on the EDVAC. That's better known. It's how to make a CPU. He got all the basic architecture right, except for index registers.
Methods I would use to teach math from scratch to day would be:
- get in a boat at night and do celestial navigation to get to a camp site (geometry)
- prove the earth is round using the moon. (geometry, proofs)
- count cards in blackjack and poker (combinatorics, probability, game theory)
- decode an ancient manuscript by constructing a grammar from frequency analysis (probability, statistics)
- decode a real american civil war cryptogram. (Vigenere, number theory)
- make a radio out of found stuff and transmit a message in various encodings by, finally with binary (from ohms law to information theory)
- reproduce Turing's Bomba from first principles in code to crack Enigma (number theory, computation)
- bet on a stock market return (brownian motion, randomness, shannon portfolio / information theory)
- structure an an election strategy for your candidate across multiple polls (conditional and independent probability, use dice and weightings for each poll result)
- work on a motorcycle / pocket-bike engine and optimize it win a drag race against someone elses engine configuration (differential calculus, sprocket sizes, power curves)
- synthesize a drum sound using an oscilloscope then sequence a loop and drone composition from oscillators and an ADSR filter (integrals, fourier analysis, feedback, deterministic chaos, complexity classes)
- configure or code a basic neural network to identify a signal or encoding. (complexity classes, godel's incompleteness)
- determine whether a piece of music is related to another (graphs, cosine similarity, pythagorian distance, homomorphisms)
That's off the top of my head, but each of these are 1-day to 2-week projects that give you a working competence in the area, imo. You could run a month long kids/teens camp on them.
You don't want to learn geometry from Euclid. You read Euclid after you already know geometry, to see how he built it up. Similarly, you don't want to learn calculus from Newton. Or physics from Aristotle. What you're seeing there is people trying to figure something out before the tools for the job were developed.
There are great papers in engineering, where a theoretical advance changed the world. They're not well known. These should be as well known as the "Great Books".
* Maxwell's paper "On Governors". In a few pages, he invents feedback control theory. People were building steam engine governors but didn't understand stability and lag. It's a milestone in that it's one of the first times abstract math met practical engineering and the result worked.
* Shannon's discovery that telephone toll switches could be reduced from needing O(N^2) relays to O(N log N) was one. Suddenly, combinatorics went from a useless abstraction to a huge financial win for AT&T.
* "Rational Psychrometric Formulae", by Willis Carrier. Least click-bait title ever. Basis of air conditioning. It's how you make an air conditioner and control both temperature and humidity at the cold end, rather than getting cold, humid air out.
* Von Neumann's Report on the EDVAC. That's better known. It's how to make a CPU. He got all the basic architecture right, except for index registers.