Friday, December 11, 2015
Wednesday, December 9, 2015
'Although the prime numbers are rigidly determined, they somehow feel like experimental data'Timothy Gowers. Mathematics: A Very Short Introduction (Oxford Univ. Press, 2002) p.118; as cited in "surprising connections between number theory and physics"
Monday, November 30, 2015
Under addition, the positive integers 1, 1+1, 1+1+1,.... form a cyclic (semigroup) structure generated by 1. We will explore a way of representing prime numbers in terms of the single generator g = 2, under a non-associative, non-commutative binary operation "o" on the set A of all primes, defined by setting x o y:=P(2x+y) where P is the greatest prime factor function. For example, 3 = 2 o 2, 5 = 2 o (2 o (2 o (2 o 2)))), etc. In a joint work with Paul A. Vicol from Simon Fraser University, we managed to verify that all primes up to 7259167 can be expressed as non-associative products involving the symbols 2, o, and parentheses ),(. This computational evidence points towards a cyclicity conjecture for the (magma) structure (A, o). Moreover, we searched for other similar non-associative algebraic structures on A (prime magmas) that might be cyclic, established a set of fairly restrictive necessary conditions for cyclicity, formulated a more general cyclicity conjecture for special prime magmas, and found computational evidence (after days of running Julia programs on a GCE platform) for the cyclicity of the structures in a representative set. (October 24, 2014 - MAA Ohio Fall Meeting)
Saturday, November 28, 2015
"Come, let us hasten to a higher planeSOURCE: http://www.aleph.se/Trans/Cultural/Art/tensor.html
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n
Commingled in an endless Markov chain!
Come, every frustrum longs to be a cone
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.
In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.
I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in our bound partition never part.
For what did Cauchy know, or Christoffel,
Or Fourier, or any Bools or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?
Cancel me not - for what then shall remain?
Abscissas some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.
Ellipse of bliss, converge, O lips divine!
the product o four scalars is defines!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.
I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a^2 cos 2 phi!"
Sunday, October 4, 2015
Sunday, September 27, 2015
Blog comment, collab help man attack old maths problem
Phys.Org - September 26, 2015 by Nancy Owano
The Erdos Discrepancy Problem - Terrence Tao - http://arxiv.org/abs/1509.05363
Sunday, July 26, 2015
Monday, March 23, 2015
Friday, March 6, 2015
De fapt una dintre multele amintiri ce nu se pot sterge. M-a introdus in lumea congruentelor si a lucrului cu 'numere mari'. In stilul problemelor ce le primeam la inceput de clasa a IX-a, sa se afle toate numerele naturale N astfel incat 1249N ≡ 1948441249 (mod 311920921441)...