Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [soft-question]

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

For questions whose answers cannot be objectively evaluated as correct or incorrect, but which are still relevant to mathematics.se.

12079 questions
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Popular textbooks and current research.

I am sure that I will be finding out first hand as I am entering a PhD program, but I will ask my question anyway. Say, for instance, a student has worked through the majority of a textbook like Dummit and Foote. How far removed is the…
dagaco
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How do mathematicians read math books?

I will describe what I mean by the above with an example. Suppose you are a professor, about to teach a first Calculus course in a university. There are dozens, if not hundreds, of calculus books out there. How do you choose which one to use as a…
Gauss
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How to minimize the chance of making an error in algebraic calculations?

This is a question about solving problems under significant time constraints, for example under exam conditions. Even though this question might be seen as "subjective", it is seriously related to many people who study mathematics, so an answer will…
Ma Joad
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Why are higher/graduate level books discussing deep topics/results written if the author clearly doesn't want the reader to understand any of it?

Have you noticed how almost anyone writing a text in the above mentioned category starts their work with examples and proofs fleshing out the minute details (stuff that you can do without the author doing it for you), but as you progress further,…
J. Doe
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Euclidean geometry in higher math?

Often, we study a lot of euclidean geometry during high school. For example,Pascal's Theorem,Cross-ratio,Ceva's Theorem` and others. I am looking for instances of theorems encountered in Euclidean geometry which are actually special cases of deeper…
user70532
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Relationship between Galois Theory and Real Analysis

I know that Galois Theory can be used to answer the following question: Why is there no formula for the roots of a fifth (or higher) degree polynomial equation in terms of the coefficients of the polynomial, using only the usual algebraic…
tim j
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What is the reason for saying that mathematics does not constitute science even if use experimental approach so often in mathematics?

Modern Science is divided into three major branches: $1.$ Natural Sciences (Includes Physics, Chemistry and Biology) Which studies nature in its broadest sense. $2.$ Social Sciences (Includes Economics, Sociology and Biology) Which study…
Vidyanshu Mishra
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Are there problems that cannot be solved without a change of perspective?

Imagine we have a "home domain" - a set of rules, or a "stage" upon which a question is posed, and a "question" - a set of conditions posed in language that makes sense and has meaning in the home domain in which it is posed. Are there…
Nine Thousand
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Are there maths articles that only need basic Calculus knowledge to be read??

I am a high school teacher with previous experience of maths research. I would like to organize a club for my talented 11th/12th grade students where we would go through some interesting and accessible maths papers. I would like to find maths…
user315016
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Are positive numbers somehow more "fundamental" than negative numbers?

I know this seems like a dumb question, but hear me out. Whenever you multiply a number by itself, you get a positive number, and whenever you divide a number by itself, you also get a positive number. For some reason, the operations of…
Tdonut
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Making maths videos

I have wanted to make math videos, but was never sure how to go about it. (Please redirect to the correct forum if this is wrong). I noticed how the khan academy videos are made on a computer, I would like to do the same thing with a software like…
picakhu
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How to direct a friend's genuine curiosity in mathematics?

I recently met up with an old friend, and asked how high up he's gone with mathematics. I said "So, what, like algebra?" He said, "Yeah." I can see that he is genuinely interested in mathematics, but he's in a situation where he can't feasibly get a…
dr_bubble_pops
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Examples of when a "new way of thinking" led to a solution

I was reading William Thurston's On Proof and Progress in Mathematics in which he discusses the value of the different ways people think about the same mathematical structure. He claims that many mathematical solutions are the result of different…
XVD
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Tricks in research vs. contest math

I know that research math problems are unsolved and unseen, while contest math problems can be solved. All bolds are mine. How do 'tricks' in research math differ from those in contest math? Do the meanings of 'tricks' differ between the 3…
user53259
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What is the "Biggest Distinction in All of Mathematics"?

First let me point out that I realise this is a subjective question, and so it doesn't follow the general guidelines for "a good question on MSE". However, I have read through the guidelines for "what makes a subjective question good" and I believe…
Harambe
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