# Tagged Questions

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### Correction symbols used for mathematical texts [closed]

When proof reading and correcting a mathematical text, I sometimes see people use special notation symbols in the margin to indicate correction, deletion, replacement and so on. Is there any standard ...
678 views

### On the parity of $[x^n]$

I am trying to find a problem which appeared years ago in the American Mathematical Monthly. It went something like this: There was a Putnam Competition question which asked to show that there is a ...
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### Expert, Intuitive, Organizing Analogies

In learning a new area it is very helpful to have high-level intuitive analogies that keep track of the various parts of an important argument or strategy. Experts have a store of such things, and ...
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### Where can square roots come from when they are not distances?

In a recent survey "Supergeometry in Mathematics and Physics", Kapranov points out cases in which observable quantities of immediate interest are represented as bilinear combinations of more ...
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### A search for theorems which appear to have very few, if any hypotheses [closed]

I'm interested in theorems which appear to have very few, if any hypotheses. Essentially a search for unexpected regularity or pattern in a relatively unstructured situation. By "few hypotheses" I ...
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### Idempotent solutions to the implict function theorem other than the identity?

I am interested in the following problem. Assume that an (anti)symmetric function $g:\mathbb{R}^2 \to \mathbb{R}$ satisfies the implicit function theorem. That is, $g(x,y) = \pm g(y,x)$ and $g(x,y)=0$ ...
358 views

### A logarithmic cotangent inequality

I must be a terrible googling searcher but I cannot find a reference to the following inequality: $$\forall_{\phi\in(0;\frac \pi 4)}\ \ln(\cot(\phi)))\, <\, \cot(2\!\cdot\!\phi)$$ I have just ...
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### Sophisticated treatments of topics in school mathematics

Sophisticated mathematical concepts typically shed light on sophisticated mathematics. But in a few cases they also apply to elementary mathematics in an interesting way. I find such examples ...
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### Conic sections in high dimensions

Can every $n$-dimensional ellipsoid be obtained as a (spherical) conic section? This is false for generic quadrics but seems true for ellipsoid. Does anybody have any references?
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### How does a mathematician choose on which problem to work?

Main question: How does a mathematician choose on which problem to work? An example approach to framing one's answer: What is a mathematical problem - big or small - that you solved or are ...
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### The impact of large cardinals in mathematics [closed]

What are the main applications of large cardinals in ordinary mathematics, and what is the philosophy behind using them. In particular: Question 1. What is the philosophy behind accepting large ...
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### Constructing a function from preimages

This question was inspired by Can we build a continuous function from "fibers"/preimages defined over a topological base? Let $X,Y$ be sets and $L\subseteq \mathcal{P}(Y)$. Suppose $L$ has ...
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### geometry formula adjacent neighbour of a N dimensional cube [closed]

A question from a curious. How many adjacent N dimensional cube there is when they are regularly distributed on a "grid". By N dimensional cube I mean: a point is a OD cube a segment is a 1D cube ...
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### Negative impact of wrong or non-rigorous proofs

The recent talks of Voevodsky (for example, http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf), which describe subtle errors in proofs by him as well as others, as well ...
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### Proof or citation?

I'm writing an article. I suppose that I'll submit it to a more or less decent journal (in English). I have doubts about the following: I have a lemma (with quite a trivial proof). I don't want to ...
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### Conjectures on fractions where each digit appears once in numerator and denominator

This is a highly redacted version of a question that was asked before. Please see Criteria of considering relevance of the question to the domain of research topics for details. Some numerical ...
466 views

### Do you have examples of such “transitive” elements?

(I've asked the same question at the MSE, so far with no answers, so I thought I'd try it here as well. If there's some clash with any site rules, please let me know and I'll abide.) Let $A$ be a set ...
517 views

### Are there any organized websites for seminar/conference videos?

These days, there are many conference centers and universities recording seminars and conference talks and make them available on the web. Some examples: http://www.fields.utoronto.ca/video-archive ...
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### Have you solved problems in your sleep?

I have hit upon major (for me—relative to my trivial accomplishments) insights in my research in various sleep-deprived altered states of consciousness, e.g., long solo car-drives extending ...
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### Jacobi triple product for multidimensional lattices

The Jacobi triple product identity gives as a special case a product formula for the theta function of a 1-dimensional lattice. Is there a more general product formula for the theta function of an ...
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### Sources of Theorem drafts by the original author

When I look at first time to a theorem and I try to understand it or when I try to memorise a useful theorem I always have difficulties (I am not the only one. For example: I read a question: I always ...
565 views

### What is an example of a non-axiomatic mathematical system? [closed]

In this wikipedia article on the foundations of mathematics, it says: In practice, most mathematicians ... do not work from axiomatic systems Is this correct? If so, what is an example of this?
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### Structures that turn out to exhibit a symmetry even though their definition doesn't

Sometimes (often?) a structure depending on several parameters turns out to be symmetric w.r.t. interchanging two of the parameters, even though the definition gives a priori no clue of that symmetry. ...
130 views

### Talking about properties of “random” elements

I asked this in MSE but did not get a satisfying answer. I apologize in advance if this is not appropriate for MO. Suppose that we have some set X and we want to say that a "random" (or generic) ...
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### Accessible proofs of contemporary results in mathematics

Are there strong results in contemporary mathematical research (last 20 years) which have a proof which every mathematician (holding a PhD) can completely understand within a few days? -- If yes, ...
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### Equal signs with fancy marks

Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions. In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which ...
Lawvere's fixed point theorem states that in a cartesian closed category, if there is a morphism $A \to X^A$ which is point-surjective (meaning that $\hom(1,A) \to \hom(1,X^A)$ is surjective), then ...