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Results tagged with gm.general-mathematics
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user 3106
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
16
votes
Examples of theorems where numerical bounds on $\pi$ played a role
In the paper, Space vectors forming rational angles, by Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen, and Michael Rubinstein, the authors classify all sets of nonzero vectors in $\mathbb{R}^3$ s …
- 82.7k
5
votes
Accepted
Where can I access American Mathematical Monthly problems given an index?
Unfortunately, I don't think there's any particularly easy way to find a specific problem given its index number, but let me summarize some of the comments (and add some of my own) in a community wiki …
13
votes
Examples of ZBMath reviews that motivated you to read the paper
It has been emphasized in the comments that a zbMATH or MathSciNet review is not an endorsement, and that unlike a "review" that one might find in a newspaper or a magazine, its primary purpose is not …
14
votes
Why do infinite-dimensional vector spaces usually have additional structure?
We can get some insight into this question by considering matroid theory.
But first, I think the question is phrased in a somewhat misleading way: "Why is there not much interesting theory of infinite …
- 82.7k
8
votes
Oddities of evenness
Finding the shortest odd-length directed cycle in a directed graph is a straightforward algorithmic problem. On the other hand, finding the shortest even-length directed cycle in a directed graph is …
6
votes
Oddities of evenness
The biggest little polygon is a regular polygon if the number of sides is odd, but is an unexpectedly interesting shape when the number of sides is even (and at least 6).
7
votes
Oddities of evenness
The special orthogonal group $SO_n$ behaves quite differently depending on whether $n$ is even or odd. In the Cartan–Killing classification, the odd case is type $B$ and the even case is type $D$. The …
1
vote
Oddities of evenness
There are a lot of results that are more difficult, or at least different, in characteristic 2 compared to odd characteristic. See for example the math.SE question, What's so special about characteris …
32
votes
Are there any fields of academic mathematics whose epistemic status as math is controversial...
There are several possible dimensions to the question, "Is it math?"
Does it belong in the mathematics department? I think you mostly want to exclude this dimension, because of your comment about pur …
15
votes
Examples of bad notation and its consequences
Suppose that $A$ is an oracle; then it is standard to write $\mathsf{P}^A$ for the complexity class $\mathsf{P}$ relativized to $A$. As I have mentioned elsewhere on MO, this is incredibly confusing …
10
votes
Books containing new results
The question seems too broad to me; it's almost like asking for a comprehensive list of long papers. For example, Aschbacher and Smith's Classification of Quasithin Groups spans two books and over a …
4
votes
What are examples of problems we know how to solve for primes (or prime powers), but not for...
Problem 105b in Chapter 1 of Richard Stanley's Enumerative Combinatorics, Volume 1 (2nd edition) notes that if $n$ is odd, then the number of necklaces (up to cyclic rotation) with $n$ beads, each bea …
2
votes
What are examples of problems we know how to solve for primes (or prime powers), but not for...
The Alon–Tarsi conjecture says that if $n$ is even, then the number of even Latin squares is different from the number of odd Latin squares (where the parity of a Latin square can be defined as the pr …
6
votes
Classification results
There is no precise definition of a "classification theorem," so I don't think one can assert with mathematical certainty that a classification theorem of type 1 implies a classification theorem of ty …
- 82.7k
14
votes
Is rigour just a ritual that most mathematicians wish to get rid of if they could?
Another MO question about rigor got me thinking about this old question again. One valuable feature of rigor, which I don't think has been said explicitly in the other answers, is that rigor allows m …