Navigating Mathematics: A Journey of Beliefs and Experiences

In summary, the conversation discusses the confusion and skepticism surrounding certain mathematical concepts, specifically in the field of non-linear PDEs. The speaker questions the validity of these concepts and expresses difficulty in understanding them. They also mention that some mathematicians have focused on other branches of mathematics rather than non-linear PDEs.
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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?
 
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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.
 

1. What is "Navigating Mathematics" about?

"Navigating Mathematics: A Journey of Beliefs and Experiences" is a book that explores the beliefs and experiences that shape one's understanding and relationship with mathematics. It delves into the psychological and sociological factors that influence how we approach and learn mathematics.

2. Who is the target audience for this book?

The target audience for this book is anyone who has an interest in mathematics and wants to gain a deeper understanding of the subject beyond just the numbers and equations. It may be particularly useful for students, educators, and researchers in the fields of mathematics and education.

3. What makes this book different from other books about mathematics?

This book takes a unique approach by focusing on the beliefs and experiences that shape our understanding of mathematics, rather than just the technical aspects of the subject. It also incorporates personal stories and perspectives from individuals with diverse backgrounds and experiences with mathematics.

4. Can this book be helpful for someone who struggles with math?

Yes, this book can be helpful for someone who struggles with math as it offers a different perspective and understanding of the subject. It may also provide insights into why one may struggle with math and how to overcome those challenges.

5. Is this book based on scientific research?

Yes, this book is based on scientific research in the fields of mathematics education, psychology, and sociology. The author, Dr. Lilianne R. Mujica-Parodi, is a neuroscientist and educator who has conducted extensive research on the relationship between beliefs and experiences with mathematics and academic performance.

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