Is Mathematics a Belief System or Just Complex Concepts?

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SUMMARY

The discussion centers on the perception of mathematics as either a belief system or a collection of complex concepts. An applied mathematician expresses frustration with the terminology used in advanced mathematics, particularly regarding pseudo-particles like phonons, magnetons, polarons, and spinons. The conversation highlights the challenges faced by learners in justifying their understanding of mathematics to outsiders, drawing parallels to belief systems such as Scientology. Additionally, it addresses misconceptions about the focus of 20th-century mathematicians, specifically regarding nonlinear partial differential equations (PDEs) and the existence of inverse scattering techniques.

PREREQUISITES
  • Understanding of pseudo-particles in physics, including phonons and spinons.
  • Familiarity with nonlinear partial differential equations (PDEs).
  • Knowledge of inverse scattering techniques in mathematical physics.
  • Basic comprehension of the philosophical implications of mathematics as a discipline.
NEXT STEPS
  • Research the role of pseudo-particles in quantum mechanics.
  • Explore nonlinear partial differential equations and their applications.
  • Study inverse scattering methods and their significance in mathematical physics.
  • Investigate the philosophical perspectives on mathematics as a belief system.
USEFUL FOR

Applied mathematicians, physicists, educators, and anyone interested in the philosophical implications of mathematics and its complex terminologies.

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http://school.diffiety.org/page23/page17/page27/page27.html.

I'm an applied mathematician, but I can't make heads or tails of what they're saying. Perhaps I should walk across the road and ask the Puries. I'm reminded of a quote in The Mathematical Experience where the authors (justifiably) compared mathematics to scientology: both 'fields' put the learners through various programs -- the ones who emerge are believers. The ones who don't are flunked. There's little way to justify to an outsider the reality of your program -- especially when there are only half-a-dozen who can understand what you're saying.
 
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I don't like the words they use there. They sound really made-up. Although I don't know, maybe they are real. I know I almost broke down crying when I start reading about all the pseudo-particles such as phonons, magnetons, polarons, spinons, etc. At some point I just started going "No, no, this has got to be utter BS."

So maybe it's real and I just don't get it?
 


WarPhalange said:
I don't like the words they use there. They sound really made-up. Although I don't know, maybe they are real. I know I almost broke down crying when I start reading about all the pseudo-particles such as phonons, magnetons, polarons, spinons, etc. At some point I just started going "No, no, this has got to be utter BS."

So maybe it's real and I just don't get it?

I dunno...some of the stuff is true. Some of it puts me on edge. For example,

Regardless to this, 20th century mathematicians busied themselves with studies in all branches but non linear PDEs

Depending on what you mean by "nonlinear", this is not true. Inverse scattering, for example, applied to the nonlinear Schroedinger or the KdV. Or numerics (which was clearly there before 2000) is another easy counterexample.
 

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