Questions tagged [soft-question]
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
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Why is the theorem of the base mostly cited only for smooth proper varieties
This is a very soft question, and I'm not sure what I expect as an answer.
In SGA6, Expose XIII, Theoreme 5.1 it is proven that, if $X$ is a proper scheme over a field $k$, then $NS(X)$ is finitely ...
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Examples of proofs using induction or recursion on a big recursive ordinal
There are many proofs use induction or recursion on $\omega$, or on an arbitary (may be uncountable) ordinal. Are there some good examples of proofs which use a big but computable ordinal?
The ...
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In what area of study does one encounter this principle in timetabling?
A while ago I saw an image like the one below in a lecture, which was supposed to represent a rail network in a (square) city:
The circles represent trains that are moving either North/South or East/...
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Finding information about the basics of an advanced math topic
Yesterday I attended a seminar talk titled "Cluster presentation of reflection groups", and before it I tried to ask Google what is a "cluster presentation" --- but all one can find on this request is ...
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How to think of algebraic geometry in characteristic p?
How does a working mathematician usually think about algebraic geometry in characteristic $p$? For the sake of concreteness, and to make things more "geometric" (whatever that means), let's ...
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The "unification" of geometry via topos theory?
This question is somehow motivated by The unification of Mathematics via Topos Theory and Synthetic vs. classical differential geometry. Sorry if this is a naïve question.
There has been quite a lot ...
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Infinite-dimensional affine space in algebraic geometry and algebraic topology
In topology, there are of course many different infinite-dimensional topological vector spaces over $\mathbb R$ or $\mathbb C$. Luckily, in algebraic topology, one rarely needs to worry too much about ...
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Mirror site for the NIST Digital Library of Mathematical Functions (DLMF)
For research I use the NIST Digital Library of Mathematical Functions (https://dlmf.nist.gov/) quite often for looking up basic facts about special functions. At the moment, however, this gives
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Scholze's infinite to finite type ring theory reductions?
In following essay "The Perfectoid Concept: Test Case for an Absent Theory" by Michael Harris, there is the following sentence I found to be quite striking.
The most virtuosic pages in Scholze's ...
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Should every modern day mathematician care about category theory? [closed]
As far as I know, category theory is used mainly in topology. I have a dislike towards category theory, similar to my dislike of Bourbakism, and want to avoid it as much as I can. However, the head of ...
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Incidences of rigorous proofs used in legal proceedings
Motivation: Loius Pojman mentions in What Can We Know? (2001) of a certain Carneades (ca. 214-129 B.C>) who must have been a "remarkable dialectician"because " in 155BC he was sent on a diplomatic ...
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Best mathematics conference? [closed]
One conference per answer. Explain why it was great (mathematically or otherwise), and preferably post a link to the conference website or to abstracts/proceedings.
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Review papers in mathematics
Are there review papers, literature reviews in mathematics that describe the recent developments in various fields for a newcomer? Or is the prerequisite knowledge always provided in research ...
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Examples where adding complexity made a problem simpler
I can think of a few situations in math where a problem becomes easier or an object becomes simpler when some complexity is added. Examples:
$S^n$ is never contractible, but $S^{\infty}$ is.
The ...
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Making an intuition precise [closed]
In writing my senior thesis I met the following problem: Sometimes I have some intuition about some mathematical statement. Yet I find it extremely painful trying to put these intuition into precise ...
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Optical methods for number theory?
I found a paper: 'A New Method of Finding the Distribution of Prime Number', saying
We stack discs and annuluses with certain rules then turn on the light to illuminate. The projection of ...
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Do you use the Mathematics Subject Classification (MSC) when searching for literature?
I suppose most of you are familiar with the Mathematics Subject Classification (MSC). Particularly, when submitting an article for publication one has to
choose appropriate classification codes.
But ...
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Music: mathematical point of view (revised) [closed]
Mathematical analysis of music started when Pythagoras made his observations about consonant intervals and ratios of string lengths.
ADDED:
In the paper Mathematical Music Theory -- Status Quo 2000, ...
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Publication in proceedings
Why and how publishing a paper in proceedings?
What are the difference with a "classical" journal?
What's the list of the main proceedings in which one can publish?
Do proceedings papers (never, ...
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Math History Question about the exponential function
While tutoring a student recently, I have come across the situation of explain logarithms by first introducing functions of the form $$f(x)= a^x$$ where $a \ge 0,x\in \mathbb{R}$. My student then ...
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Philosophy of forcing and ctm
I asked a similar question on SE before and received an answer. Not completely convinced, I decided to ask it here with some modifications. Note: I understand how forcing works and how it proves ...
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A starting point for research in Graph Theory as a high schooler [closed]
I am a 10th grader and I'm very interested in mathematics. As of now, I'm into math contests and I take great pleasure in solving problems from contests such as the AIME/USAMO/IMO. These only require ...
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The name for an assumption made for the sake of contradiction
What is the name (or adjective) for an assumption made for the sake of contradiction?
To be clear, I'm in search of an expression in the form "a(n) $\underline{\quad \quad \quad \quad}$ ...
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What is soliton
I am new to this word.. This is not research level problem and it is soft question in nature. Just for curiosity, i am asking..
In literature, i am finding following words:(Wikipedia+ others).
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Why is this theorem (about $L(P(\omega_1))^V$ and $L(P(\omega_1))^{V[G]}$) nice?
I was recently told that the following (due to M. Viale) is a nice theorem:
Suppose there are arbitrarily large supercompacts, and $\mathrm{MM}$ holds in $V$. Let $G$ be generic for a proper ...
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What are some examples of journals that will accept undergraduate student research?
I am currently doing a research project with a professor and 3 other students in an area that is usually seen as a "recreational" math topic; that of change-ringing and its relation to group theory. ...
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A terminological question concerning orbifolds.
The notion of orbifold is quite well established by now. I would like to ask how one should call a point of an orbifold with non-trivial stabilizer? Should one call this a singular point? Of something ...
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Why isn't there more interest in "large powerset axioms"?
By a large powerset axiom, let us mean informally an axiom that says that for some cardinal numbers $\kappa$, we have that $2^\kappa$ is somehow "large" or "difficult to access from below." For ...
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Advice on choosing an area of specialization [closed]
I'm not sure if this is an appropriate question for MO, but I figured it couldn't hurt to ask. I'm a second year graduate student, currently gearing up to construct a committee and syllabus for my ...
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how to think of monodromy transformations
I've come across the notion of Monodromy transformations while reading some aspects of variations of Hodge structures in context of Classical Mirror symmetry. I am having difficulty in grasping the ...
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famous papers/results by non professional mathematicians [duplicate]
Possible Duplicate:
What recent discoveries have amateur mathematicians made?
Dear overflowers
Out of curiosity: do you know any famous papers and/or results by non professional mathematicians? (...
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Intuition Behind a Decimal Representation with Catalan Numbers
From $0 = 0.5 - 0.5 = 0.5 - \sqrt{0.25}$, we can adjust the subtrahend slightly to obtain
$$0.5 - \sqrt{0.249} = 0.001\ 001\ 002\ 005\ 014\ 042\ldots$$
where the decimal representation contains the ...
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Applications of Math: Theory vs. Practice
I have a problem: I learned about a lot of the applications of mathematics from academics. Neither they nor I have had much contact with the "real world" to go and see for ourselves how mathematics ...
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When are $\mathbb{R}^n$ and $\mathbb{R}^m$ essentially similar?
Here is a rather vague and subjective question: for which $n$ and $m$ are
$\mathbb{R}^n$ and $\mathbb{R}^m$ ``essentially similar''? The answer depends partly on what type of
mathematician is ...
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Did Joseph Doob prove that random sequences don't exist?
In the book "The Mathematical Experience" it says:
"An infinite [binary] sequence $x_1, x_2, \ldots$ is called random in the sense of von Mises if every infinite sequence $x_{n_1}, x_{n_2}, \ldots$...
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An ubiquitous pattern of questions
There is an ubiquitous pattern of questions concerning assumedly any kind of mathematical object or structure: groups, graphs, numbers, categories, and so on. It goes like this (informally):
Can a ...
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How often do you put your research into trash?
A soft question.
I am a PhD student, at early stages of my academic career; and have personally experienced the following many times. Sometimes you come up with a result, that you are not quite ...
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Hyperbolic PDE in mathematics
Hyperbolic PDE (like the wave equation) are roughly speaking, PDE that satisfy the “finite propagation speed of information” property. They are ubiquitous in mathematical physics (essentially, most ...
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How do small central extensions drop the dimension of a faithful representation?
Apologies in advance that this is a very soft question. I might be talking complete nonsense. But I hope I am talking about something that has even been studied...
I am interested in the phenomenon ...
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When would you read a paper claiming to have settled a long open problem like $P$ vs. $NP$? [closed]
From time to time, people announce papers claiming to have settled long open problems like $P$ vs. $NP$. There have been many attempts, reading them is time-consuming, and finding bugs in their ...
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Representations of finite groups over the "field with one element"
Have there been any attempts to extend the "F_un" analogy to the representation theory of finite groups?
If I might be allowed some speculation:
If combinatorics can be regarded as analagous ...
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Practical Benefits of HTT/univalent foundations for assisted proofs
I'm trying to understand what the claimed practical benefits of HTT/univalent foundations are for doing computer assisted proofs and while I've seen a lot of claims of benefits they all seem to be ...
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Hard maths on viXra? [closed]
A few years ago a nice paper surveyed the differences in quality between papers submitted to arXiv and those submitted to arXiv's rough cousin, viXra. However, that paper was about generic ...
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Classification of $p$-groups, what after it?
In finite group theory, $p$-groups or simple groups can be considered as building blocks of all the groups. What is known about these families of groups is that
The classification of simple groups ...
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Algebraic structure on homotopy groups of spheres
It is about a "conjecture" I heard (when I was student). There would exist an algebraic structure on the homotopy groups of spheres such that this algebraic structure would be the free algebraic ...
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Progress towards a computational interpretation of the univalence axiom?
I will preface this by saying that I am not an expert on type theory. I am just a curious outsider slowly making my way through the HoTT book when I (rarely) have some spare time.
I am just curious ...
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Lower bound on the irrationality measure of $\pi$
There seems to be a lot of work on the upper bound for the irrationality measure of $\pi$, but I could not find anything on a lower bound except the general $\mu(\pi)\geq2$. Looks like it is the best ...
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Motivation for the proof of Hilbert's Theorem 90
The proof of Hilbert's Theorem 90 about cyclic extensions goes like this: Let $\sigma$ be the generator of the Galois group of order $n$ and let $b$ have norm $1$, i.e. $b \sigma(b) \cdots \sigma^{n-1}...
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Are there some interesting propositions independent with ZF+V=L that do not increase consistency strength?
In some MO questions such as this and this, Hamkins gave some examples that is independent with ZF+V=L, however, all of them increase the consistency strength.
Are there some propositions P, which is ...
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What is the etymology of zero-sharp?
I have wondered for a while what gave rise to the notation $0^\sharp$. According to wikipedia this is due to Solovay in 1967, but (perhaps unsurprisingly) there's no discussion of why that notation ...
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