Tagged Questions
34
votes
1answer
446 views
Unexpected approximations which have led to important mathematical discoveries
One often finds at MSE approximate numerology questions like
Prove $\log_{{1}/{4}} \frac{8}{7}> \log_{{1}/{5}} \frac{5}{4}$,
Prove $\left(\dfrac{2}{5}\right)^{{2}/{5}}<\ln{2}$,
Comparing ...
4
votes
0answers
80 views
The mathematical heritage of Lewis Carroll
Which mathematical results has Lewis Carroll, the author of Alice's Adventures in Wonderland, produced? Wikipedia is very vague with regard to this topic and gives us little more than a matrix ...
6
votes
0answers
68 views
Examples of falsified (or currently open) longstanding conjectures leading to large bodies of incorrect results.
In general, the way that modern mathematical research is conducted isn't the way that many would assume is the ideal method of research. That is, mathematics is not the linear progression of ...
5
votes
1answer
102 views
Differences in worlds with and without $\aleph_0<|S|<2^{\aleph_0}$
Paul Cohen told us that whether or not there is $S$ with \begin{equation}
\aleph_0<|S|<2^{\aleph_0}
\end{equation} cannot be decided within ZFC, and hence it is reasonable to work in two ...
78
votes
31answers
6k views
Can you provide me historical examples of pure mathematics becoming “useful”?
I'm trying to think/know about something but I don't know if my basis premise is plausible, here we go.
Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because ...
48
votes
10answers
8k views
Results that came out of nowhere.
Most big results in mathematics are built on years and years of groundwork by the author and other mathematicians, such as Wiles' proof of FLT or the classification of finite simple groups. ...
12
votes
7answers
679 views
Films about math: a question about math education and motivation for learning math
I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
7
votes
11answers
528 views
Good examples for mathemathical problems/statements that are easely solvable/provable in one theory and hard to solve/prove in another
Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria:
Given two (or more) mathematical points of view ...
29
votes
6answers
716 views
Original works of great mathematicians
In almost every mathematical text there is a line as This was first proved by Gauss or This formula first appeared in a work of Riemann, but for me it's more like My friend told me once that...
For ...
7
votes
8answers
805 views
What mathematical ideas/concepts became obsolete due to technological progress?
As technology evolved, some ideas and methods became obsolete. What mathematical ideas entered this state due to technology progress?
We could consider that doing some mathematical operations done by ...
5
votes
2answers
486 views
Mathematics celebrities that every mathematician should know? [closed]
As a mathematician, sometimes I meet across very embarrassing questions which were posted by who does not learn of mathematics, for example, my wife and so on. She or he always posted such questions: ...
22
votes
13answers
2k views
Research done by high-school students
I'm giving a talk soon to a group of high-school students about open problems in mathematics that high-school students could understand. To inspire them, I would like to give them examples of ...
6
votes
5answers
1k views
Why do we consider prime numbers important, and what are their applications other than number theory in pure math?
Why do we consider prime numbers important, and what are their applications other than number theory in pure math? I know that Number theory is devoted to studying prime numbers, but there must be ...
5
votes
5answers
394 views
What are some unexpected things math predicts?
Once I heard about a prophet that used math to foresaw with great accuracy many events of the humanity. Today I oddly realized the time between falling drops after washing cups fit the inverse square ...
8
votes
2answers
541 views
Who are some forgotten mathematicians? [closed]
In Thomas' Calculus, he presents ''Nicole Oresme's Theorem'':
$$
\sum_{n=1}^\infty {n\over 2^{n-1}}=4.
$$
My first reaction was "who is this person?''.
As it turns out, he was a Frenchman from the ...
1
vote
0answers
104 views
Origins of mathematical terms? [closed]
I'm interested in the development and naming of mathematical terms that we probably take for granted. Why is integral called the integral? Who first used pathological in the mathematical sense? Please ...
14
votes
5answers
775 views
Results that were widely believed to be false but were later shown to be true
What are some results which were widely believed to be false, but were later to be shown to be true, or vice-versa?
9
votes
10answers
502 views
Good (Auto)Biographies of von Neumann and other physicists/mathematicians
Which is the "best" biography of von Neumann available to the casual reader (math undergrad)? Also, other than the Ulam book, which other good biographies of physicists/mathematicians can be ...
20
votes
6answers
2k views
Good books on Math History
I'm trying to find good books on the history of mathematics, dating as far back as possible.
There was a similar question here Good books on Philosophy of Mathematics, but mostly pertaining to ...
19
votes
9answers
2k views
Good books on Philosophy of Mathematics
Where can I learn more about the implications, meta discussions, history and the foundations of mathematics?
Is Russell's Introduction to Mathematical Philosophy a good start?
2
votes
4answers
496 views
What is your favorite isomorphism? [closed]
By "isomorphism" I mean any structure-preserving map with a structure-preserving inverse.
(Please accept my advance apology if this question is out of bounds. I sense that it's borderline, but I'm ...
