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A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

G.H.Hardy

Mathematics is the art of giving the same name to different things.

Henri Poincaré

Basis MathJax Tutorial

Visualization of $\Bbb{RP^2}$

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Top Questions
45 votes

What is the geometrical difference between continuity and uniform continuity?

real-analysis continuity uniform-continuity asked Apr 24, 2015 at 7:38
math.stackexchange.com

44 votes

How can I prove $\pi=e^{3/2}\prod_{n=2}^{\infty}e\left(1-\frac{1}{n^2}\right)^{n^2}$?

real-analysis exponential-function closed-form pi infinite-product asked Jul 2, 2015 at 8:30
math.stackexchange.com

42 votes

What are the theorems in mathematics which can be proved using completely different ideas?

reference-request proof-strategy big-list alternative-proof asked Nov 7, 2014 at 1:34
math.stackexchange.com

16 votes

Understanding the definition of stacks

higher-category-theory sheaf-theory stacks definitions differentiable-stacks asked Mar 21, 2020 at 20:03
mathoverflow.net

13 votes

Functional Equation $f(x+y)-f(x-y)=2f'(x)f'(y)$

functions recreational-mathematics functional-equations asked Aug 11, 2018 at 18:56
math.stackexchange.com

12 votes

How to understand adjoint functors?

ct.category-theory limits-and-colimits adjoint-functors universal-property kan-extension asked Jul 8, 2020 at 11:48
mathoverflow.net

11 votes

Fréchet L-Spaces

real-analysis general-topology reference-request convergence math-history asked Feb 18, 2016 at 10:20
math.stackexchange.com

10 votes

Number of solutions of $x_1+2x_2+\cdots+kx_k=n$?

combinatorics number-theory diophantine-equations generating-functions linear-diophantine-eqns asked Dec 11, 2016 at 2:12
math.stackexchange.com

9 votes

Automorphisms of punctured plane

complex-analysis geometry complex-numbers conformal-geometry mobius-transformation asked Aug 17, 2017 at 18:42
math.stackexchange.com

9 votes

Value of $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n!}}$?

number-theory special-functions analytic-number-theory gamma-function hypergeometric-function asked Apr 21, 2020 at 19:18
math.stackexchange.com

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Top Answers
13
Determine Minimum Value.
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13
Prime number between $n$ and $n!+1$
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12
What is $\frac{x^{10} + x^8 + x^2 + 1}{x^{10} + x^6 + x^4 + 1}$ given $x^2 + x - 1 = 0$?
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11
Find the value of : $\lim_{x \to \infty}( \sqrt{4x^2+5x} - \sqrt{4x^2+x})$
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11
Find five positive integers whose reciprocals sum to $1$
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11
What are the theorems in mathematics which can be proved using completely different ideas?
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9
How do I show that every group of order 90 is not simple?
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9
Find coefficient in quartic given product of roots
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8
Can you, given any semigroup, define an identity element to make it a monoid
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8
Examples of Axiom of Choice used in introductory-level undergradute math
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8
Trick with 3-digit numbers, always get 1089
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8
Show that for any a ∈ ℤ, 42 | $(a^7 − a).$
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7
Importance and Intuition of Polynomial Rings
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7
Integral $\int\left(\frac{1}{x^4+x^2+1}\right)dx$
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7
Which of the numbers $1, 2^{1/2}, 3^{1/3}, 4^{1/4}, 5^{1/5}, 6^{1/6} , 7^{1/7}$ is largest, and how to find out without calculator?
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7
Show that only one prime can be expressed as $n^3-1$ for some positive integer $n$
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7
Do there exist functions $f$ such that $f(f(x))=x^2-x+1$ for every $x$?
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7
How to compute this kind of limit?
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7
Surprising identities / equations
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7
Value of $\cos^2\alpha-\sin^2\alpha$
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6
Show that $\left|\dfrac{z-a}{1-\bar a z}\right|=r$ represents a circle
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6
Cauchy Sequence that Does Not Converge
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6
Solutions for $a^2+b^2+c^2=d^2$
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6
Solve $(n+1)f(n+1)=(n+2)f(n)+1$
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6
Is there any proof for this formula $\lim_{n \to \infty} \prod_{k=1}^n \left (1+\frac {kx}{n^2} \right) =e^{x/2}$?
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6
Help Evaluating $\lim_{x\to+\infty}\frac{\sqrt{x}}{\sqrt{x+\sqrt{x+\sqrt{x}}}}$
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6
What is the non-trivial, general solution of these equal ratios?
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5
Use the principle of mathematical induction to prove that $n \lt (\frac{3}{2})^n$ for all integers $n \ge 1$.
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5
Find the limit of $\lim_{ x\to 14} \frac{x^2-14x}{x^2-196}$
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5
Find the least number which when divided by 2, 3, 4, 5, 6 leaves a remainder of 1 but it is divided by 7 completely.
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