Linked Questions
66 questions linked to/from Examples of common false beliefs in mathematics
238
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46
answers
90k
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Most interesting mathematics mistake?
Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove ...
107
votes
36
answers
21k
views
Interesting examples of vacuous / void entities
I included this footnote in a paper in which I mentioned that the number of partitions of the empty set is 1 (every member of any partition is a non-empty set, and of course every member of the empty ...
113
votes
25
answers
37k
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Examples of math hoaxes/interesting jokes published on April Fool's day?
What are examples of math hoaxes/interesting jokes published on April Fool's day?
For a start P=NP.
Added 2024-04-01 Anything new in 2024?
212
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14
answers
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Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?
To begin with, I am aware of these questions, which seems to be related:
How do I fix someone's published error?, Examples of common false beliefs in mathematics, When have we lost a body of ...
58
votes
43
answers
11k
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What are some mathematical sculptures?
Either intentionally or unintentionally.
Include location and sculptor, if known.
71
votes
28
answers
8k
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Results from abstract algebra which look wrong (but are true)
There are many statements in abstract algebra, often asked by beginners, which are just too good to be true. For example, if $N$ is a normal subgroup of a group $G$, is $G/N$ isomorphic to a subgroup ...
121
votes
4
answers
39k
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Is the analysis as taught in universities in fact the analysis of definable numbers?
Ten years ago, when I studied in university, I had no idea about definable numbers, but I came to this concept myself. My thoughts were as follows:
All numbers are divided into two classes: those ...
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49
votes
11
answers
7k
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In "splendid isolation"
While browsing the Net for some articles related to the history of the Whittaker-Shannon sampling theorem, so important to our digital world today, I came across this passage by H. D. Luke in The ...
127
votes
4
answers
32k
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Slick proof?: A vector space has the same dimension as its dual if and only if it is finite dimensional
A very important theorem in linear algebra that is rarely taught is:
A vector space has the same dimension as its dual if and only if it is finite dimensional.
I have seen a total of one proof of ...
53
votes
11
answers
6k
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What is an important mathematical question?
$\DeclareMathOperator\GL{GL}$Many times I have heard people say sentences like X is an important question/ X is a natural question. I find this very surprising because to me it's all a matter of taste....
48
votes
6
answers
12k
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Intuition for Integral Transforms
It is well known that the operations of differentiation and integration are reduced to multiplication and division after being transformed by an integral transform (like e.g. Fourier or Laplace ...
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59
votes
7
answers
4k
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How closed-form conjectures are made?
Recently I posted a conjecture at Math.SE:
$$\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx\stackrel{?}{=}\frac{\pi}{2}(\mu^2-\nu^2),$$
where $J_\mu(x)$ and $Y_\mu(x)$ ...
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75
votes
3
answers
11k
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Cohomology and fundamental classes
Let X be a real orientable compact differentiable manifold. Is the (co)homology of X generated by the fundamental classes of oriented subvarieties? And if not, what is known about the subgroup ...
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75
votes
4
answers
6k
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When is a singular point of a variety ($\mathcal{C}^\infty$-) smooth?
If $X$ is a nonsingular algebraic (or analytic) variety over $\mathbb C$ or $\mathbb R$ then it is certainly $C^\infty$ over the reals.
The converse is false for a silly reason : in the real or ...
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63
votes
7
answers
5k
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What well known results with countability assumptions can be naturally extended to uncountable settings?
In many of the common categories of spaces (or algebras) in mathematics, one often restricts attention to those spaces or algebras which are "countable" or "countably generated" in ...