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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Higher-dimensional analogues of the equivalence of compact Riemann surfaces and projective curves

I'm going to be studying this result for a dissertation this year, and I wondered what there were in the way of higher-dimensional analogues? Also, what are some standing research questions on this theme? I think the interplay of the different…
Latimer Leviosa
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How do you explain paradoxes to non-mathematicians?

For example, how do you explain why the perimeter of this staircase does not converge to $\sqrt2$? Or, why isn't $\sqrt{(-1)(-1)}=\sqrt{-1}\sqrt{-1}$? I would say, the reason is simply because they cannot be proved. But non-mathematicians don't find…
kasdip
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rearrangement of sequences

In Barry Simons book "Trace ideals and Their Applications" in "1.4 Rearrangement Inequalities and All That" he says: "Let $a_n$ be an infinite sequence of numbers with $a_n\rightarrow 0$ as $n\rightarrow\infty$. $a_n^*$ is the sequence defined by…
Peter Melech
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Mathematics Lecture

I am going to be presenting a 2hr math lecture to a few students and I am supposed to make the lecture so interesting that they are left utterly fascinated about the topic that I choose. The students have a good foundation of calculus, algebra and…
anonymous
  • 1,556
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Example of a theory that requires infinitely many axiom schemas

Before asking this question, I want to know if anyone has formalized what an axiom schema is. Assuming that there is a formalization, many theories we normally encounter have a finite number of axiom schemas, even if they are not finitely…
user107952
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Where are multisets used in mathematics?

Outside of factorization (integers into primes, polynomials into irreducibles) where else are multisets naturally useful in mathematics? [edit] Deleting. If anybody wants me to stop, please say so now.
wlad
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Building a training program... for mathematics

I want to ask for your advice building my one-year training program for mathematics. Objectives: Keep 'mathematically fit' Improve for the pleasure Get competent at high-level economics and mathematical/applied statistics.…
snoram
  • 614
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What does it mean when a field of mathematics has 'differential' in its name?

Topology and geometry, for example, have their 'differential counterparts' (as well as 'algebraic'). What is required of a mathematical discipline for there to exist such a subfield? For example, why isn't 'differential knot theory' a thing?
galois
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What are metric spaces examples of?

A metric space is a very strange kind of object. It is not simply a set with some operations that satisfy some operations, like a group. In the higher reaches of abstract algebra, an algebra is defined to be a class of sets and their associated…
user107952
  • 20,508
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Visualization of theorem relationships

A few minutes ago a thought for a website/program crossed my mind and now I somehow hope that such a thing already exists. I thought of: A set of theorems linked by arrows telling the viewer/reader eg. that (the "typical" proof) of Theorem A is…
Keba
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Suggestions to solve for $A$ in the equation $e^{-\frac{(A-B)^{2}}{D}}=C$

This seems almost silly to ask but I am stuck with it. I have the following equation \begin{equation}\tag{*} e^{-\frac{(A-B)^{2}}{D}}=C \end{equation} I know $A,B \in \mathbb{R}, 00 $. Everything is known except $A$. I computed $A$ in…
NAASI
  • 997
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Is it possible to provide a proof of some unsolved result using elementary methods? Is there no merit to this?

Is it possible to provide a proof of some unsolved result using elementary methods? I get the feeling it would be looked down upon and/or not taken seriously. Why is this? Is there no merit to proving some conjecture using elementary methods?
user5826
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The difference between mathematics and statistics?

I am learning how to construct proofs. I always wondered why stats is considered "different" to math? I know that it is an open-ended question.
Johnathan
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Starting mathematical education late

(Math)degreeless people who are self taught are doubtless viewed with at best suspicion, having countless holes in their mathematical knowledge, questionable methods, whose lack of academic qualifications understandably inspire little confidence in…
martin
  • 8,998
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Building up mathematics from nothing / becoming a math hobbyist

I just did this Google search and the first hit was along the lines of what I was looking for, which is a set of statements, each one building on the ones before it that start from nothing and go on to describe math. Another way to phrase my…
Aaron Anodide
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