Algebra Etc.
@AlgebraFact
Followers
193K
Following
202
Media
2K
Statuses
15K
Tweets about algebra, number theory, and miscellaneous math by @JohnDCook.
Joined January 2010
Eduard Kummer (1810–1893) was one of the important algebraists of the nineteenth century. But he was dreadful at arithmetic. Often in class he resorted to enlisting his students to help him with simple problems. Once he had to calculate 7x9. “Seven times nine,” he began. “Seven
13
34
265
Every group of order 4 is isomorphic to either Z_4 or Z_2 + Z_2.
3
6
70
Aries is transforming logistics with modern tracking and unmatched client experience. Get a Quote or Book Now.
0
12
131
Bertrand's postulate: For all x > 1, there is a prime p such that x < p < 2x.
2
6
30
Noosphere has launched in the US App Store, available on iOS. We are an innovative new platform connecting you directly with the world's best journalists and content creators. No middle man. Download and subscribe in the link in the bio.
1
4
8
An n x n matrix A is non-singular iff determinant(A) is not 0.
0
3
31
Proof by Poem: The RSA Encryption Algorithm Daniel G. Treat, NDA Mathematics Magazine, Vol. 75, No. 4 (Oct., 2002), p. 255
6
10
90
'Lo and behold, the convolution has become a product in the generating function world. Life is full of surprises.'
amazon.com
0
0
12
Li(x) = integral from 2 to x of 1/log(t). Number of primes less than x is approximately Li(x).
2
3
27
An n x n matrix A is diagonalizable iff A has n linearly independent eigenvectors.
0
7
29
Christmas Is Here Stuff Those Stocking With ICESPIKE!!! The Best Stocking Stuffer Ever!!!
0
4
9
The Cholesky factorization of an SPD matrix A is G G^T where G is lower triangular and has positive diagonal entries.
2
1
16
More explanation here: https://t.co/JOhXykNBpN
johndcook.com
A proof that there are infinitely many primes, based on a product of sines.
1
1
8
Suppose there are only finitely many primes and let P be their product. Then we have the following contradiction:
8
17
156
New post: What is a Pedersen commitment? https://t.co/haSceWSwRO
johndcook.com
What are Pedersen commitments? How are they used? Why do they not require a trusted setup? What do they have to do with homomorphic encryption?
0
0
5
Checkmate, Nicomachus
Nicomachus Theorem 1³ + 2³ + 3³ + ... + n³ = (1 + 2 + 3 + ... + n)² The sum of the first n cubes always equals the square of the sum of the first n integers. For n = 3: (1 + 2 + 3)² = 6² = 36 = 1 + 8 + 27
9
55
650
A mother cat and her three kittens...How cute? The feline mom's name is Stripe, and her three chatons were born on 4-15-25, just this last April! Stripe is one of many rescued cats we take care of at my "Guy's All-Night Diner Feline Shelter!" The kittens turned out to be two
0
2
16
In a commutative ring with identity, every maximal ideal is prime.
2
4
37