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.
2,236
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Simple definition of the Hausdorff measure using squared paper
I am giving a "non-technical" seminar in which I would like to give an elementary introduction to the Hausdorff dimension and measure.
For simplicity, I was hoping to give a more intuitive ...
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2
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Indexed tensor manipulation CAS
hello.
I am looking for tensor manipulation software that would allow me:
declare indices
declare results of contraction (or simplification rules)
allow algebraic simplifications and expansion
index ...
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5
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Origins of names of algebraic structures
Consider the names of basic algebraic structures: 'group', 'ring', 'space', 'field', 'Körper', even the name 'structure' itself - all of them time-honoured terms, deeply rooted in our history and ...
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The definition of homotopy in algebraic topology
In this post, let $I=[0,1]$.
Something about the definition of homotopy in algebraic topology (and in particular in the study of the fundamental group) always puzzled me. Most books on the ...
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Should one use "above" and "below" in mathematical writing?
I started thinking about this question because of this discussion:
http://sbseminar.wordpress.com/2010/08/10/negative-value-added-by-journals/
about how journals often change a paper (for the worse) ...
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3
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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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1
answer
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Summation of consecutive positive integers [closed]
So it occurred to me recently that 21 kinda stands out among among its nearby neighbors in that there are several sets of consecutive positive integers that can be summed to equal 21 -- namely 1+2+3+4+...
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Non-English language Mathematical podcasts/audio
Following on from this question, does anyone know of any good quality non-English language mathematical podcasts? I'm particularly interested in anything relating to the history of mathematics.
I'm ...
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1
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Mathematicians and writing [closed]
Do many mathematicians write a lot (including expository articles)? Or are there a fair majority of mathematicians that just write papers and don't bother with expository material? Which is better? Do ...
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123
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When and how is it appropriate for an undergraduate to email a professor out of the blue?
This may not be appropriate for MathOverflow, as I haven't seen precedent for this type of question. But the answer is certainly of interest to me, and (I think) would be of interest to many other ...
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1
answer
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Isomorphism by classification
Are there any examples other than using dimension for vector spaces where the easiest way to show that two objects are isomorphic is by using a classification theorem and showing that they must both ...
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How do professional mathematicians learn new things? [closed]
How do professional mathematicians learn new things? How do they expand their comfort zone? By talking to colleagues?
51
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9
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Is Galois theory necessary (in a basic graduate algebra course)?
By definition, a basic graduate algebra course in a U.S. (or similar) university with
a Ph.D. program in mathematics lasts part or all of an academic year and is taken
by first (sometimes second) ...
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1
answer
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How many people fully understand the proof of Fermat's Last Theorem?
What is a rough order of magnitude estimate? $$ $$ There is a thread on Meta about this question, http://mathoverflow.tqft.net/discussion/567/rapid-closing-of-questions/#Item_0
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2
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Mathematicians and string theory?
Hello,
I'm curious on whether say, a ph.d in mathematics with no experience in physics could pick up a book on String theory (say some intro for mathematicians) and learn it and then do research kinda ...
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0
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How connected are you? [closed]
I apologize if this question seems frivolous, but the motivation for it is quite serious.
When I encounter the endless topic of the 'relevance' of mathematics, I am rather
fond of referring to a ...
4
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3
answers
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"In the sequel" - outdated mathematical jargon or precise technical term? [closed]
Possible Duplicate: https://math.stackexchange.com/questions/907/correct-usage-of-the-phrase-in-the-sequel-history-alternatives
As a non-native speaker of English, I have been perplexed by the phrase ...
2
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1
answer
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What happens to the boundary conditions as a PDE is approximated by a lesser order PDE?
Consider a fourth order linear (biharmonic) PDE in two variables of the form
$\nabla^4u + c\nabla^2u-\lambda u = F(x,y)$; $(x,y) \in \Lambda$
To have uniqueness, we must specify two equations per ...
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6
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Reading materials for mathematical logic [closed]
Hi everyone, the summer break is coming and I am thinking of reading something about mathematical logic. Could anyone please give me some reading materials on this subject?
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4
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How much reading do you do before you attack a problem?
When going off on a tangent from your regular area, where, presumably, you have such mastery of all cutting-edge research from your routine reading that you hardly need to do any extra (if this is ...
233
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14
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Have any long-suspected irrational numbers turned out to be rational?
The history of proving numbers irrational is full of interesting stories, from the ancient proofs for $\sqrt{2}$, to Lambert's irrationality proof for $\pi$, to Roger Apéry's surprise demonstration ...
9
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3
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How to find/guess a polynomial sequence?
My question is motivated by the recent question and more recent
appearance of its author Bruce Westbury.
Most of you know that the best way to find a sequence of integers is looking for it on
The On-...
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43
answers
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What are some mathematical sculptures?
Either intentionally or unintentionally.
Include location and sculptor, if known.
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Examples of "folk theorems"
In Folk Functorial Figuring, Justin Curry gives a quote about Raoul Bott that has this line in it:
He talked about 'folk' theorems… theorems everyone knew, but were never written down.
What are some ...
9
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2
answers
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Advantageous properties of 4 letter alphabet (in DNA)?
As you know DNA is composed of strings of 4 letters. I am wondering if the number 4 here has
any significance? Any property of 4 that makes using 4 letters more advantageous over more
(or less) ...
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4
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"Slap your forehead" moments- Greatest Hits [closed]
We've all done it: we have a "proof" that is so pretty... but we know it's wrong. Either it proves something we know is false, or the proof doesn't use one of the hypotheses you know it needs to, or ...
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4
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Infinite games: are they well defined?
It is just my curiosity about this question where we have an infinite game and (according to the answers) winning strategies for both players. I am familiar with terminating games only, and I am ...
22
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2
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Why are they called isothermal coordinates?
On a Riemannian manifold, a coordinate system is called "isothermal" if the Riemannian metric in those coordinates is conformal to the Euclidean metric:
$$g_{ij} = e^{f} \delta_{ij}$$
My question is:...
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5
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Advantages of working with CW complexes/spaces over Kan complexes/simplicial sets?
Many topologists express a clear preference for working with CW complexes instead of simplicial sets.
One of the reasons is that the cellular chain complex of a CW complex is often easier to work ...
103
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19
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Can a mathematical definition be wrong?
This question originates from a bit of history. In the first paper on quantum Turing machines, the authors left a key uniformity condition out of their definition. Three mathematicians subsequently ...
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Suggestions for wiki farm with good latex support
I've decided to start a wiki to do collaborative mathematics. However I don't have access or control over a server. So I need a wiki farm. I've tried out pbworks and wikidot, but their latex support ...
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Problem suggestions for polymath for undergraduates research
I'm inspired by the polymath project. It might be great for few undergraduates to work together on a research topic.
What are some research problems with the following properties(Experimental ...
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6
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What are you using for symbolic computation?
What are the pluses and minuses of different software packages? Anything new worth checking out?
I'm especially interested in open source packages.
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1
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approximately linear functions
i suppose it's fairly well known that if a (continuous, real-valued) function $f$ on the real line satisfies
$f(x-y)=f(x)-f(y)+const$
then it is necessarily linear.
are there any general ...
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What subfields of mathematics better lend themselves to visualization?
In some of my classes (e.g. graph theory, mechanics), the professors encourage the students to visualize solutions to problems; I do well in these classes. In other classes (e.g. linear algebra), we ...
103
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eBook readers for mathematics
For a while I have been eying stand-alone eBook readers that use "electronic ink" displays, the most popular ones seem to be the Amazon Kindle readers.
My criteria are as follows: It should be able ...
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44
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Demystifying complex numbers
At the end of this month I start teaching complex analysis to
2nd year undergraduates, mostly from engineering but some from
science and maths. The main applications for them in future
studies are ...
55
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6
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What is the etymology of the term "perverse sheaf"?
Grothendieck famously objected to the term "perverse sheaf" in Récoltes et Semailles, writing "What an idea to give such a name to a mathematical thing! Or to any other thing or living ...
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What's the notation for a function restricted to a subset of the codomain?
Suppose I have a function f : A → B between two sets A and B. (The same question applies to group homomorphisms, continuous maps between topological spaces, etc. But for simpicity let's restrict ...
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Presenting a paper: Do's and Don'ts?
I was wondering what would be the best way to present your paper at a conference, if your paper is selected for "short communication", lasting for about 15 minutes?
Should you concentrate on the main ...
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Grothendieck's mathematical diagram
I was going through this article (Who Is Alexander
Grothendieck?)(Wayback Machine) which appeared in the Notices of the AMS, and in it, there's a picture(page 936) which shows a mathematical diagram ...
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Undiscovered for a long time before it is realised it is the same concept developed under different names.
Mathematics has been described as the giving of the same name to different things,
but sometimes different names are given to the same thing.
Can you give examples of concepts where researchers in ...
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1
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Drinfeld's 1988 letter to Schechtman: translation request
Inspired by an old question by Kevin Lin and the communal translation of an answer by Laurent Fargues, I am proposing a communal effort to translate from Russian to English Drinfeld's famous 1988 ...
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Work of ICM 2010 plenary speakers (and other humans) [closed]
The ICM is approaching. It would be nice for everybody who feels qualified to give a brief overview of the work of one of the plenary speakers. If anything, this would serve to make all of us a little ...
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What's wrong with the surreals?
Of all the constructions of the reals, the construction via the surreals seems the most elegant to me.
It seems to immediately capture the total ordering and precision of Dedekind cuts at a ...
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Why are proofs so valuable, although we do not know that our axiom system is consistent? [closed]
As a person who has been spending significant time to learn mathematics, I have to admit that I sometimes find the fact uncovered by Godel very upsetting: we never can know that our axiom system is ...
11
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1
answer
881
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What is happening to Martin Gardner's files?
Martin Gardner kept voluminous correspondence with amateur and professional mathematicians worldwide throughout his career. His files are a treasure trove of information about all areas of ...
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3
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Medium-Sized Calculations and Organization
This is not a math question as much as a process question. For the first time in my (very short) career, I find myself doing one of those messy calculations, where each 'line' of the calculation can ...
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63
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Counterexamples in algebra?
This is certainly related to "What are your favorite instructional counterexamples?", but I thought I would ask a more focused question. We've all seen Counterexamples in analysis and ...
2
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1
answer
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Probability of system failure in a distributed network
I am trying to build a mathematical model of the availability of a file in a distributed file-system. The system works like this: a node $x$ stores a file $f$ (encoed using erasure codes) at $rb$ ...
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