Linked Questions

2 votes
2 answers
616 views

Easy to explain conjectures that are still unsolved [duplicate]

Mathematics has many open conjectures which are ridiculously hard to even understand. But this is not always the case. An example is: Collatz conjecture. I would like to see some more examples. So ...
181 votes
60 answers
42k views

Examples of eventual counterexamples

Define an "eventual counterexample" to be $P(a) = T $ for $a < n$ $P(n) = F$ $n$ is sufficiently large for $P(a) = T\ \ \forall a \in \mathbb{N}$ to be a 'reasonable' conjecture to ...
35 votes
62 answers
21k views

What's your favorite equation, formula, identity or inequality? [closed]

Certain formulas I really enjoy looking at like the Euler-Maclaurin formula or the Leibniz integral rule. What's your favorite equation, formula, identity or inequality?
67 votes
28 answers
12k views

Examples of seemingly elementary problems that are hard to solve?

I'm looking for a list of problems such that a) any undergraduate student who took multivariable calculus and linear algebra can understand the statements, (Edit: the definition of understanding here ...
90 votes
11 answers
13k views

What are possible applications of deep learning to research mathematics?

With no doubt everyone here has heard of deep learning, even if they don't know what it is or what it is good for. I myself am a former mathematician turned data scientist who is quite interested in ...
114 votes
4 answers
25k views

Is the series $\sum_n|\sin n|^n/n$ convergent?

Problem. Is the series $$\sum_{n=1}^\infty\frac{|\sin(n)|^n}n$$convergent? (The problem was posed on 22.06.2017 by Ph D students of H.Steinhaus Center of Wroclaw Polytechnica. The promised prize for ...
Lviv Scottish Book's user avatar
57 votes
14 answers
18k views

Open problems in Euclidean geometry?

What are some (research level) open problems in Euclidean geometry ? (Edit: I ask just out of curiosity, to understand how -and if- nowadays this is not a "dead" field yet) I should clarify a bit ...
166 votes
3 answers
38k views

Convergence of $\sum(n^3\sin^2n)^{-1}$

I saw a while ago in a book by Clifford Pickover, that whether the Flint Hills series $\displaystyle \sum_{n=1}^\infty\frac1{n^3\sin^2 n}$ converges is open. I would think that the question of its ...
Andrés E. Caicedo's user avatar
96 votes
7 answers
19k views

Can we cover the unit square by these rectangles?

The following question was a research exercise (i.e. an open problem) in R. Graham, D.E. Knuth, and O. Patashnik, "Concrete Mathematics", 1988, chapter 1. It is easy to show that $$\sum_{1 \...
Kaveh's user avatar
  • 5,362
93 votes
5 answers
9k views

Is there a dense subset of the real plane with all pairwise distances rational?

I heard the following two questions recently from Carl Mummert, who encouraged me to spread them around. Part of his motivation for the questions was to give the subject of computable model theory ...
Joel David Hamkins's user avatar
57 votes
8 answers
6k views

Two (probably) equal real numbers which are not proved to be equal?

Can someone give me a nice example of two computable real numbers which are believed but not proved to be equal? I never really understood the assertion that "the reals do not have decidable equality"...
59 votes
7 answers
7k views

Status of PL topology

I posted this question on math stackexchange but received no answers. Since I know there are more people knowledgeable in geometric and piecewise-linear (PL) topology here, I'm reposting the question. ...
43 votes
10 answers
4k views

List of long open, elementary problems which are computational in nature

I would like to ask a question of a similar vein to this question. Question: I'm asking for a list of long open problems which are computational in nature which a beginning graduate student can ...
63 votes
6 answers
5k views

Shortest closed curve to inspect a sphere

Let $S$ be a sphere in $\mathbb{R}^3$. Let $C$ be a closed curve in $\mathbb{R}^3$ disjoint from and exterior to $S$ which has the property that every point $x$ on $S$ is visible to some point $y$ of $...
Joseph O'Rourke's user avatar
43 votes
12 answers
2k views

Can a discrete set of the plane of uniform density intersect all large triangles?

Let S be a discrete subset of the Euclidean plane such that the number of points in a large disc is approximately equal to the area of the disc. Does the complement of S necessarily contain triangles ...
Roland Bacher's user avatar

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