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Results tagged with soft-question
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user 3272
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.
7
votes
Do empirical studies have a place in contemporary mathematics research?
The Birch and Swinnerton-Dyer conjecture was formulated on the basis of substantial computer calculations. They looked at the growth of products $\prod_{p \leq x} N_p(E)/p$ for large $x$ and various …
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 …
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 …
9
votes
Golden ratio in contemporary mathematics
In every real quadratic field $K$, the unit group of its ring of integers $\mathcal O_K$ is known to have the form $\pm u^\mathbf Z$ for a unique number $u > 1$, which is called the fundamental unit o …
31
votes
Is pure mathematics useful outside of mathematics itself?
Why do you want current work in pure math to "immediately benefit the population at large in a direct and obvious way"? Applications of pure math might take decades or centuries. As much as you may wi …
10
votes
What is the point of reading classics over modern treatments?
A question very similar to yours was asked quite a few years ago on MO here. Take a look at the answers there.
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 …
9
votes
Applications of functional analysis beyond analysis(towards algebra, geometry, number theory...
In number theory there are $p$-adic Banach spaces and $p$-adic Banach algebras (e.g., the Tate algebras), and more generally there is the whole subject of $p$-adic functional analysis. Applications of …
10
votes
Accepted
"Epicycles" (Ptolemy style) in math theory?
Euler found values of the Riemann zeta-function by artful manipulations of divergent series, e.g., interpreting a function that's $(-1)^{n/2}$ at even $n > 0$ and $0$ at odd $n > 0$ as $\cos(\pi n/2)$ …
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 …