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Just consider that academic math refused for over 300 years to acknowledge the existence of complex numbers, leaving the problem to the engineers. No scientist

Just consider that academic math refused for over 300 years to acknowledge the existence of complex numbers, leaving the problem to the engineers. No scientist could afford this substitution of dogma for reality.

tgb 9y ago
Do you have a citation for that? Wikipedia's history of complex numbers makes no mention of this. What uses for complex numbers did engineers have prior to Gauss that weren't anticipated by mathematicians? https://en.m.wikipedia.org/wiki/Complex_number#History https://en.m.wikipedia.org/wiki/Complex_number#History
j2kun 9y ago
This is a straw man and does a huge disservice to the complicated history behind complex numbers. [1] In particular, mathematicians came up with it first (the Italians, Cardano et al., if you don't count the greeks who did something fuzzily approaching complex numbers), but it doesn't matter anyway because back then there were no clear lines between the sciences. Mathematicians were physicists, engineers, philosophers, astronomers, and whatever else. The "refuse to acknowledge the existence" line is also nonsense (ignoring for the moment that "existence" is not a useful term for an abstraction), because Euler made "i" widespread by including it in his famous textbook, the complex plane was invented as early as the 1600s, Gauss used it for some of his most impressive discoveries (and he lived at the same time as Fourier, who, let's be real, was also a mathematician), and their reservations were more along the lines of "guarding against its misuse, "which still occurs today in algebra classes all around the world, and having doubts about its "metaphysics." But I understand the desire to glorify engineers. It does often happen that practical concerns drive great mathematical discoveries. Just... be humble and do your research :) [1]: https://en.wikipedia.org/wiki/Complex_number#History https://en.wikipedia.org/wiki/Complex_number#History
protonfish 9y ago
I don't have a problem with the pure math crowd doing their own thing. They absolutely discover some amazing things using their techniques. What I have a problem with is that these people write the math textbooks. Why are we bamboozling our poor children with this impractical, esoteric, overcomplicated, pseudo-religious, gobbledygook? Primary and secondary school mathematics need to change focus to applied and computational math.
- Jtsummers 9y ago
  Since I haven't been in a K-12 math classroom in about 10 years (contemplated becoming a teacher and visited some friends' classes), what's the gobbledygook we're teaching kids these days? I don't recall any gobbledygook from my years in K-12 education (excepting an awful, awful long-term substitute teacher). Arithmetic and algebra (K-8, basically), geometry, trig, and calc were all practical and applied (the latter two in advanced science courses and work rather than daily life). I think more probability and statistics courses would be easily justified. Regarding computational thinking, math in the K-12 level is computational thinking more than it's based on proof construction. Computational thinking should be added as a subset of the math and science courses. I think it helped many of my college classmates who weren't in CS to understand computational thinking when we ran simulations using matlab of experiments, or in the reverse used it to process our results.

tgb 9y ago

Do you have a citation for that? Wikipedia's history of complex numbers makes no mention of this. What uses for complex numbers did engineers have prior to Gauss that weren't anticipated by mathematicians? https://en.m.wikipedia.org/wiki/Complex_number#History https://en.m.wikipedia.org/wiki/Complex_number#History

j2kun 9y ago

This is a straw man and does a huge disservice to the complicated history behind complex numbers. [1] In particular, mathematicians came up with it first (the Italians, Cardano et al., if you don't count the greeks who did something fuzzily approaching complex numbers), but it doesn't matter anyway because back then there were no clear lines between the sciences. Mathematicians were physicists, engineers, philosophers, astronomers, and whatever else. The "refuse to acknowledge the existence" line is also nonsense (ignoring for the moment that "existence" is not a useful term for an abstraction), because Euler made "i" widespread by including it in his famous textbook, the complex plane was invented as early as the 1600s, Gauss used it for some of his most impressive discoveries (and he lived at the same time as Fourier, who, let's be real, was also a mathematician), and their reservations were more along the lines of "guarding against its misuse, "which still occurs today in algebra classes all around the world, and having doubts about its "metaphysics." But I understand the desire to glorify engineers. It does often happen that practical concerns drive great mathematical discoveries. Just... be humble and do your research :) [1]: https://en.wikipedia.org/wiki/Complex_number#History https://en.wikipedia.org/wiki/Complex_number#History

protonfish 9y ago

I don't have a problem with the pure math crowd doing their own thing. They absolutely discover some amazing things using their techniques. What I have a problem with is that these people write the math textbooks. Why are we bamboozling our poor children with this impractical, esoteric, overcomplicated, pseudo-religious, gobbledygook? Primary and secondary school mathematics need to change focus to applied and computational math.

Jtsummers 9y ago
Since I haven't been in a K-12 math classroom in about 10 years (contemplated becoming a teacher and visited some friends' classes), what's the gobbledygook we're teaching kids these days? I don't recall any gobbledygook from my years in K-12 education (excepting an awful, awful long-term substitute teacher). Arithmetic and algebra (K-8, basically), geometry, trig, and calc were all practical and applied (the latter two in advanced science courses and work rather than daily life). I think more probability and statistics courses would be easily justified. Regarding computational thinking, math in the K-12 level is computational thinking more than it's based on proof construction. Computational thinking should be added as a subset of the math and science courses. I think it helped many of my college classmates who weren't in CS to understand computational thinking when we ran simulations using matlab of experiments, or in the reverse used it to process our results.