Monday, December 28, 2015

Why mathematics is exceptional

“Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the “initiated few.” It belongs to all of us.” ― Edward Frenkel (Love and Math: The Heart of Hidden Reality - via goodreads.com)

Tuesday, December 22, 2015

Bridges - 2016 conference



Atentie pentru cei interesati: submission deadlines:
Regular Papers: 1 February 2016 
Workshop Papers: 1 March 2016 
Short Papers: 15 March 2016 
Acceptance Notifications: 30 March 2016 
Final Submissions: 30 April 2016
http://bridgesmathart.org/bridges-2016/

bridges - mathematics and art

The Bridges Archive: an online repository of every paper ever published in the annual Bridges Conference on art and mathematics.

Wednesday, December 9, 2015

The attractiveness of primes for experimental mathematics...

'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

All primes in terms of one: non-associative algebra and Google cloud computing

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

Love and Tensor Algebra - from "The Cyberiad" by Stanislaw Lem

"Come, let us hasten to a higher plane
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!"
SOURCE: http://www.aleph.se/Trans/Cultural/Art/tensor.html

Monday, September 7, 2015

The farthest known galaxy...

"the recently discovered EGS8p7 galaxy is a whopping 13.2 billion years old, making it both the farthest known galaxy to date and just 600 million years younger than the universe as we know it." (cf. The farthest known galaxy is 13.2 billion years old - http://www.engadget.com/2015/09/07/scientists-spot-farthest-ever-galaxy/ )

Sunday, August 30, 2015

Psychology - the 36 percent replication problem

"Despite this careful planning, less than half of the replication studies reproduced the original results. While 97 percent of the original studies produced results with a “statistically significant” p-value of 0.05 or less, only 36 percent of the replication studies did the same." (cf. "Psychology Is Starting To Deal With Its Replication Problem", Christie Aschwanden in FiveThirtyEight - August 27, 2015)

Thursday, July 23, 2015

a rigorous fantasy...

"Still more astonishing is that world of rigorous fantasy we call mathematics" -- Gregory Bateson

Saturday, July 18, 2015

Higher education crisis - a solution

A solution to higher education crisis in the US: general education done thoroughly at the secondary level, followed by 3 years (some programs may still need 4) of undergraduate studies in the chosen field. Student debt will decrease (as it should) and the quality/expertise of undergraduate education will increase (as well as the quality of secondary education).

Tuesday, June 30, 2015

Beautiful minds - 2015 ONU Summer Academic Honors Institute - Cryptography

Beautiful minds: gifted students participating in the 2015 ONU Summer Academic Honors Institute - Cryptography Camp

Friday, March 6, 2015

Mihai Raileanu - o amintire

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 1249 ≡ 1948441249 (mod 311920921441)...

Friday, January 30, 2015

Joint Dust Analysis Deflates Big Bang Signal - QUANTA Magazine

Joint Dust Analysis Deflates Big Bang Signal  - QUANTA Magazine
No definitive evidence for cosmic inflation is found, but support remains strong for the theory even as critics highlight its shortcomings as an explanation for how and why the universe began.

Saturday, January 10, 2015

A pure mathematician?...

“An impractical man--which he not only seems to be, but really is--will always be unreliable and unpredictable in his dealings with others. He will engage in actions that mean something else to him than to others, but he is at peace with himself about everything as long as he can make it all come together in a fine idea.”

Robert Musil, The Man Without Qualities Vol. 1: A Sort of Introduction and Pseudo Reality Prevails