Is Mathematics a Belief System or Just Complex Concepts?

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The discussion highlights a sense of confusion and frustration regarding complex mathematical concepts and terminology, particularly in the realm of pseudo-particles like phonons and spinons. The comparison of mathematics to scientology emphasizes the perceived exclusivity and difficulty of understanding advanced mathematical theories, suggesting that only a select few can grasp these ideas fully. There is a critique of the language used in these discussions, which feels fabricated to some, leading to skepticism about the validity of the concepts. Additionally, there is a mention of nonlinear partial differential equations (PDEs), countering the claim that 20th-century mathematicians neglected this area by referencing significant developments in inverse scattering and numerical methods. Overall, the conversation reflects a struggle to reconcile advanced mathematical theories with accessible understanding.
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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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