What is required to write a mathematical theory?

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Discussion Overview

The discussion revolves around the requirements and processes involved in writing a mathematical theory or article. Participants explore the parallels between mathematical and scientific proof, the necessary background knowledge, and the challenges faced by aspiring mathematicians.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses a desire to write a mathematical theory but feels uninformed about the writing process and seeks guidance on how to prove a theory in mathematics.
  • Another participant draws a parallel between physicists and mathematicians, suggesting that both must present their work clearly to convince skeptics, referencing Karl Popper's ideas on validation and falsification.
  • A different participant emphasizes the need for extensive study in mathematics before attempting to write and publish articles, highlighting the importance of understanding mathematical language and proof techniques.
  • One participant recommends reading published mathematical papers as a way to learn about writing in the field, noting that access to math journals may vary by library type.
  • A younger participant questions whether they can write a mathematical article without formal college education, expressing doubts about their ability to do so.
  • Another participant challenges the feasibility of writing a mathematics article with only high school knowledge, comparing it to writing in a language without prior study.

Areas of Agreement / Disagreement

Participants express differing views on the prerequisites for writing a mathematical article, with some suggesting extensive study is necessary while others question the feasibility of writing without formal education. The discussion remains unresolved regarding the specific requirements and pathways to writing a mathematical theory.

Contextual Notes

Participants mention various assumptions about knowledge levels and the nature of mathematical writing, but these assumptions are not universally agreed upon. There are also references to the clarity of proofs and the importance of understanding mathematical concepts, which may depend on individual backgrounds.

Quarlep
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I want to write to theory about math but I don't have enough information about writing process.What can I do to write correct theory or article.
I use theory and article in same meanings.
Example a physicist makes experiments to proof his theory.Whats a mathematician do to proof his theory ?

Thanks
 
Mathematics news on Phys.org
The physicist that would prove a theory by experimental observation must design a very clear experiment. Similarly, the mathematician must write out his proof so clearly that the skeptical observer is instantly convinced.

Karl Popper, in his Logic of Scientific Discovery, suggests that surprise is a powerful argument, albeit for validation or falsification.
 
To write and publish a good article about math, you first have to study math for many years. You will have to learn how to talk and think like a mathematician, so that you can state definitions and prove theorems.
 
Doug Huffman said:
Logic of Scientific Discovery
Thanks for the book
 
As a first step, read mathematical papers as published in math journals. Some, but not all, public libraries will carry some math journals. University libraries typically carry a large number.
 
I am 17 years old and I want to write an article but I think it is not easy as I think.Can I write an artice without college knowladge ?
 
An article on what? You certainly are not likely to be able to write a mathematics article that would be of particular interest of professional mathematicians with only knowledge of high school mathematics!
 
Quarlep said:
I am 17 years old and I want to write an article but I think it is not easy as I think.Can I write an artice without college knowladge ?
Would you be able to write an article about the Vietnamese language, in Vietnamese, for educated Vietnamese people, without first studying Vietnamese? It would be much more difficult than that.
 
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