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.
9
votes
Differences between $p$-groups and $q$-groups
If it exists, what is a value $k$ for which there are different numbers of (isomorphism classes of) groups of order $p^k$ and $q^k$?
You already observed that $k$ can't be $1$, $2$, or $3$. So such …
27
votes
Swimming against the tide in the past century: remarkable achievements that arose in contras...
In the first decades of the 20th century, $p$-adic analysis (or valuation theory more generally) was regarded by many as rather exotic. After Hensel's work there was a steady development by Strassmann …
23
votes
Modern results that are widely known, yet which at the time were ignored, not accepted or cr...
Does acceptance of conjectures before they became theorems count?
Example 1. The Artin reciprocity law. When Artin went around to other people describing what he was trying to show, nobody else belie …
6
votes
What well known results with countability assumptions can be naturally extended to uncountab...
Here are some examples from algebra where finiteness assumptions can be removed. In the first two, the statement of the more general result is unchanged, but the third result has to be expressed in a …
24
votes
How would you have answered Richard Feynman's challenge?
Here are two questions, and both are about math that was known long before Feynman passed away.
Explain to him what unique factorization into irreducibles means (including the ambiguity from multipli …
28
votes
Examples of improved notation that impacted research?
There is a notation that had an immediate and profound impact on research in algebraic topology, later algebraic geometry, and was eventually adopted by all areas of mathematics: the introduction of a …
16
votes
Noteworthy, but not so famous conjectures resolved recent years
In number theory, the Sato-Tate conjecture about elliptic curves over $
\mathbf Q$ was a problem from the 1960s and Serre's conjecture on modularity of odd 2-dimensional Galois representation was a co …
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 …
17
votes
Special rational numbers that appear as answers to natural questions
For a prime number $p$, the number of nonisomorphic groups of order $p^n$ is $p^{(2/27)n^3 + O(n^{8/3})}$. I was surprised when I first saw this formula with leading coefficient $2/27$ in the exponent …
6
votes
Graduate program applications that require questionnaires and other non-letter material
Ohio State
It asks letter writers to fill out a questionnaire about the applicant and also asks if the letter writer knows the applicant well enough to write a recommendation. Excuse me?
7
votes
Graduate program applications that require questionnaires and other non-letter material
Georgia Tech
It asks letter writers to fill out a questionnaire about the applicant, including asking how the applicant works as part of a team.
21
votes
Widely accepted mathematical results that were later shown to be wrong?
Any rational function field over a finite field has genus $0$ and class number $1$, where the class number of a function field over a finite field is the number of degree-zero elements of the divisor …
5
votes
Interesting applications (in pure mathematics) of first-year calculus
In number theory, here are four applications of techniques or results in first-year calculus.
(1) Finding equations of tangent lines by first-semester calculus methods lets us add points on elliptic …
13
votes
Counterexamples in algebra?
If $f$ and $g$ are relatively prime in ${\mathbf Q}[X]$ then the mapping ${\mathbf Q}[X]/(fg) \rightarrow {\mathbf Q}[X]/(f) \times {\mathbf Q}[X]/(g)$ given by $h \bmod fg \mapsto (h \bmod f, h \bmod …
28
votes
Examples of using physical intuition to solve math problems
Theorem: Every permutation in $S_n$ is a product of transpositions.
Proof: If I number cups from 1 to $n$ and set them down in a row on the table in a mixed-up order, even a child could put the cups …