Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with big-list
Search options answers only
not deleted
user 3272
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
260
votes
Accepted
Consequences of the Riemann hypothesis
I gave a talk on this topic a few months ago, so I assembled a list then which could be appreciated by a general mathematical audience. I'll reproduce it here. (Edit: I have added a few more examples …
227
votes
Widely accepted mathematical results that were later shown to be wrong?
Mathematicians used to hold plenty of false, but intuitively reasonable, ideas in analysis that were backed up with proofs of one kind or another (understood in the context of those times). Coming to …
79
votes
Where is number theory used in the rest of mathematics?
Here are a few examples. In some, number theory provided an essential motivation. In the others, it plays a more direct role.
1) Are there nonisometric Riemannian manifolds that are isospectral (eig …
65
votes
What's the "best" proof of quadratic reciprocity?
The question asked for the nicest proof for a first undergraduate course. Has anyone who offered a proposal used their favorite choice in a course? (Obviously the suggestions referring to $K$-theor …
- 50.6k
63
votes
Accepted
Interesting results in algebraic geometry accessible to 3rd year undergraduates
If you want to teach something intriguing, you should do something that introduces a new geometric idea while also involving algebra in an essential way. I recommend that you give an introduction to t …
- 50.6k
56
votes
Why do we care about $L^p$ spaces besides $p = 1$, $p = 2$, and $p = \infty$?
Tim, I've got two words for you: interpolation theorems (e.g., Riesz-Thorin and Marcinkiewicz interpolation theorems). Such theorems let you pass from information about some operators on $L^1$ and $L …
53
votes
Do you read the masters?
In algebraic number theory, the existence of a Frobenius element
at any prime $p$ in a Galois extension $K/{\mathbf Q}$ is crucial. That is, for any
prime ideal $\mathfrak p$ lying over $p$ in $K$ th …
48
votes
Collecting proofs that finite multiplicative subgroups of fields are cyclic
I once collected six [edit: now seven [edit: now eight [edit:now nine [edit: now ten]]]] proofs of this theorem, for the field $\mathbf Z/(p)$, and they can be found here. While $\mathbf Z/(p)$ is not …
43
votes
Why are modular forms interesting?
This answer addresses one striking example for the second question: how modular forms relate to other mathematical topics.
Values of zeta-functions can arise as the constant terms of nice modular for …
37
votes
Early two-author math papers
The Brill--Noether paper appeared in 1874: "Ueber die algebraischen Functionen und ihre Anwendung in der Geometrie". Math. Annalen 7, 269–316.
35
votes
Mathematical conjectures on which applications depend
The Miller-Rabin primality test works very well in practice as a probabilistic algorithm for finding "practical" (not provable) primes in cryptography, but the algorithm would become an efficient poly …
35
votes
Fields of mathematics that were dormant for a long time until someone revitalized them
Modular forms were actively studied by number theorists Hecke and Siegel in the 1930s, but it was not widely appreciated. Around the same time Hardy, in a series of lectures on Ramanujan's work deliv …
35
votes
Applications of the Chinese remainder theorem
Here are some applications I don't see listed among the other answers.
Everyone knows $5^2$ ends in 5 and $6^2$ ends in 6. Your task: find multi-digit numbers whose squares end in themselves (e.g., $ …
33
votes
Examples of common false beliefs in mathematics
After learning that the Witt vectors of a finite field of size $p^n$ is the ring of integers of the unramified extension of ${\mathbf Q}_p$ of degree $n$, I think lots of people then think that the Wi …
32
votes
What are the worst notations, in your opinion?
Writing a finite field of size $q$ as $\mathrm{GF}(q)$ instead of as $\mathbf{F}_q$ always rubbed me the wrong way. I know where it comes from (Galois Field), and I think it is still widely used in c …