Enlightened - Badge - Mathematics Stack Exchange

Enlightened

First to answer and accepted with score of 10 or more. This badge can be awarded multiple times.

Awarded 24784 times.

Motivation for Lie Bracket

Awarded Oct 20 at 14:57

Vladimir Lysikov

5,3602 gold badges21 silver badges34 bronze badges

Why doesn't the graph of $x^2-\cos x$ look wiggly?

Awarded Oct 20 at 9:32

Robert Z

148k12 gold badges112 silver badges194 bronze badges

Can you not tell if two covectors are "perpendicular" without using a metric? Unlike parallelism?

Awarded Oct 20 at 7:13

Franklin Pezzuti Dyer

41.7k9 gold badges84 silver badges182 bronze badges

Derivative of the Determinant of the Jacobian Matrix

Awarded Oct 20 at 3:38

peek-a-boo

68.3k4 gold badges69 silver badges134 bronze badges

Closed form of the integral $\int_{0}^{i\infty} \frac{E_4(z)}{\sqrt{j(z)}}dz$

Awarded Oct 19 at 17:06

user1363745

1,2573 silver badges7 bronze badges

Inequality involving the integral of vector valued function

Awarded Oct 19 at 4:40

Martin Argerami

219k17 gold badges162 silver badges301 bronze badges

Prove that $x^6+5x^2+8$ is reducible over $\mathbb{Z}$

Awarded Oct 19 at 4:40

Qiaochu Yuan

477k55 gold badges1.1k silver badges1.5k bronze badges

When is $x^n - a$ irreducible over a field?

Awarded Oct 19 at 1:41

Bill Dubuque

285k42 gold badges343 silver badges1.1k bronze badges

Simplify $ \frac{ \sqrt[3]{16} - 1}{ \sqrt[3]{27} + \sqrt[3]{4} + \sqrt[3]{2}} $

Awarded Oct 18 at 10:38

nonuser

92.5k20 gold badges112 silver badges220 bronze badges

Calculate the series $\sum_{n,m,r>0}\frac{1}{mnr(n+m)(n+r)(m+r)}$

Awarded Oct 18 at 3:52

te4

4154 silver badges9 bronze badges

Logarithmic integral containing an infinite series

Awarded Oct 18 at 3:52

Sangchul Lee

186k17 gold badges302 silver badges500 bronze badges

Let $R$ be a ring. Define a circle composition $\circ$ in $R$ by $a \circ b =a+b-ab$, $a, b \in R$.

Awarded Oct 17 at 21:48

John Lee

17.2k2 gold badges33 silver badges55 bronze badges

Axiom of irrelevant choice?

Awarded Oct 17 at 19:08

Franklin Pezzuti Dyer

41.7k9 gold badges84 silver badges182 bronze badges

Approximate inverse of the double factorial

Awarded Oct 17 at 12:37

Gary

37.3k3 gold badges46 silver badges76 bronze badges

Construct axis if you have drawn $y=x^2$ plot

Awarded Oct 17 at 12:37

Blue

85.3k16 gold badges131 silver badges270 bronze badges

Can Tarski's circle squaring problem be solved with measurable sets and/or without the Axiom of Choice?

Awarded Oct 16 at 17:06

Andrés E. Caicedo

82.1k10 gold badges233 silver badges367 bronze badges

Why are there more prime factors of the form $4k-1$ than of the form $4k+1$?

Awarded Oct 16 at 15:50

2'5 9'2

57.5k8 gold badges90 silver badges164 bronze badges

What is a good argument for rejecting the axiom of choice?

Awarded Oct 16 at 11:51

Asaf Karagila♦

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Injectivity of Fourier transform between $L^1(\mathbb{R})$ and $C_0(\mathbb{R})$

Awarded Oct 15 at 17:25

Bebop

3,82219 silver badges20 bronze badges

Moving index in a summation - how does that work?

Awarded Oct 15 at 15:32

Luke

1,1028 silver badges18 bronze badges

Tangent Plane to a regular surface

Awarded Oct 15 at 3:00

Américo Tavares

39.3k14 gold badges111 silver badges254 bronze badges

Explain what is wrong with the following proof that $1 = 0$.

Awarded Oct 15 at 2:15

Karl

13.5k3 gold badges24 silver badges38 bronze badges

Concrete examples of group actions.

Awarded Oct 14 at 21:57

Mariano Suárez-Álvarez

140k14 gold badges261 silver badges396 bronze badges

The sum of two continuous periodic functions is periodic if and only if the ratio of their periods is rational?

Awarded Oct 14 at 18:00

Hagen von Eitzen

384k33 gold badges381 silver badges687 bronze badges

Proving an infinite number of primes of the form 6n+1

Awarded Oct 14 at 8:34

user44197

9,85819 silver badges20 bronze badges

"The number of ways to choose 3 letters from FORTY-ONE is 41." Is there an infinite number of statements like this?

Awarded Oct 13 at 13:02

mjqxxxx

43.9k3 gold badges65 silver badges118 bronze badges

Half exact functor which is neither right exact nor left exact

Awarded Oct 13 at 5:28

Eric Wofsey

344k28 gold badges487 silver badges705 bronze badges

Does the hyperbolic plane embed as a subgroup of its isometry group? As a submanifold?

Awarded Oct 13 at 3:03

mezzoctane

1,5076 silver badges16 bronze badges

How to know if $\epsilon$ satisfying $100 \ln 2 = 69 + \dfrac{\pi}{10} + \epsilon$ is transcendental?

Awarded Oct 12 at 22:09

K B Dave

10.1k1 gold badge23 silver badges36 bronze badges

Combinatorial or probabilistic proof of $\sum_{k=0}^n C_{2k}C_{2n-2k}=2^{2n}C_n$

Awarded Oct 12 at 21:17

Sayan Dutta

11.1k3 gold badges20 silver badges54 bronze badges

Is there such a mathematical notion as 'antideterminant'?

Awarded Oct 12 at 11:03

Noah Schweber

265k22 gold badges398 silver badges683 bronze badges

Epimorphisms on category of (finite) bounded distributive lattices = surjective?

Awarded Oct 12 at 1:01

Arturo Magidin

420k60 gold badges868 silver badges1.2k bronze badges

How do I solve this ominous integral?

Awarded Oct 11 at 21:13

Jorge Layja

Colimits in that category of short exact sequences of abelian groups

Awarded Oct 11 at 21:13

Martin Brandenburg

184k20 gold badges339 silver badges598 bronze badges

How common are non-solvable numbers?

Awarded Oct 11 at 10:11

Dietrich Burde

143k8 gold badges100 silver badges182 bronze badges

Professor insists $-0$ does not exist, am I crazy?

Awarded Oct 10 at 22:53

Rob Arthan

52.2k4 gold badges55 silver badges107 bronze badges

'Amount' of nowhere-differentiable functions in $C([0,1])$?

Awarded Oct 10 at 17:34

Reveillark

13.8k1 gold badge22 silver badges41 bronze badges

First homology group of a double torus (genus 2 surface) – intuition

Awarded Oct 9 at 5:38

user555203

3,45711 silver badges14 bronze badges

Strange symmetry regarding sum $\sum_{n=0}^\infty\frac{n^ne^{-bn}}{\Gamma(n+1)}$ and integral $\int_{0}^\infty\frac{x^xe^{-bx}}{\Gamma(x+1)}dx$

Awarded Oct 8 at 20:05

g.kov

13.9k1 gold badge15 silver badges40 bronze badges

How can the inner product space also be a vector space?

Awarded Oct 8 at 17:01

TY Mathers

20.8k2 gold badges36 silver badges85 bronze badges

Does every connected $r$-regular bipartite graph contain a Hamiltonian cycle?

Awarded Oct 8 at 17:01

Perry Elliott-Iverson

4,58218 silver badges21 bronze badges

Does the forgetful functor from $\mathbf{TopGrp}$ to $\mathbf{Top}$ admit a left adjoint?

Awarded Oct 8 at 10:46

Adam Bartoš

9,4531 gold badge21 silver badges36 bronze badges

Explicit description of a left adjoint to the forgetful functor from Unif to Top

Awarded Oct 8 at 10:46

Alex Kruckman

88.8k5 gold badges105 silver badges172 bronze badges

Prove $\sum_{\alpha<\omega_2}|\alpha|^{\aleph_0}=\aleph_2\cdot\aleph_1^{\aleph_0}$

Awarded Oct 7 at 19:41

Brian M. Scott

635k57 gold badges830 silver badges1.4k bronze badges

General form of elements of $SU(2)$

Awarded Oct 7 at 18:36

Angina Seng

162k28 gold badges116 silver badges220 bronze badges

defining smooth functions on smooth manifolds

Awarded Oct 7 at 17:23

Daniel Fischer

212k19 gold badges310 silver badges440 bronze badges

Proving the triangle inequality for the $l_2$ norm $\|x\|_2 = \sqrt{x_1^2+x_2^2+\ldots+x_n^2}$

Awarded Oct 7 at 13:46

Pedro♦

126k19 gold badges242 silver badges407 bronze badges

How is homology "weaker than" homotopy?

Awarded Oct 6 at 20:57

Ben Steffan

10.7k5 gold badges20 silver badges58 bronze badges

Solovay's Model and Choice

Awarded Oct 6 at 20:08

Asaf Karagila♦

408k48 gold badges651 silver badges1.1k bronze badges

Finding the determinant of a matrix defined by row indices

Awarded Oct 6 at 14:52

Afntu

4,2852 gold badges24 silver badges37 bronze badges

Example of a complete metric space which is not compact

Awarded Oct 6 at 14:52

Sal

2,24115 silver badges19 bronze badges

Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)

Awarded Oct 6 at 14:52

Zev Chonoles

133k23 gold badges352 silver badges572 bronze badges

Interesting antihomomorphisms of matrices?

Awarded Oct 6 at 0:04

Vladimir Lysikov

5,3602 gold badges21 silver badges34 bronze badges

The smallest odd perfect number must exceed $10^{300}$.

Awarded Oct 5 at 15:22

Ethan Bolker

107k7 gold badges129 silver badges228 bronze badges

Pythagorean Triples : Is every positive integer $\gt$ $2$ part of at least one Pythagorean triple?

Awarded Oct 5 at 4:37

MooS

32.5k1 gold badge33 silver badges55 bronze badges

Weil divisors fail over singular varieties

Awarded Oct 5 at 1:42

Roland

13.4k1 gold badge40 silver badges41 bronze badges

How to convert this extremely large group in GAP into a permutation group.

Awarded Oct 5 at 0:23

Max Horn

2,58619 silver badges35 bronze badges

Negative solution to $x^2=2^x$

Awarded Oct 4 at 7:13

Peter

87.1k17 gold badges89 silver badges241 bronze badges

Prove that this is a metric

Awarded Oct 4 at 5:32

Omran Kouba

29.2k1 gold badge57 silver badges102 bronze badges

Can you say $f$ that is continuous at point $a$ is differentiable at point $a$ provided that $\lim_{h→0}(f(a+2h) - f(a+h))/h$ exists?

Awarded Oct 4 at 2:09

Dermot Craddock

5,03413 silver badges32 bronze badges

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