Amazing Resonance Experiment

The Heisenberg and Witt algebras

Here - a nice introduction by Akhil Mathew @ Climbing Mount Burbaki

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"

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)

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

The OEIS Movie. Experimental Mathematics

Experimental mathematics channel - You Tube

Erdős' discrepancy problem - recently solved

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

The Singular Mind of Terry Tao

The Singular Mind of Terry Tao 
A prodigy grows up to become one of the greatest mathematicians in the world. 
New York Times
By GARETH COOK, July 24, 2015

Vox: Emmy Noether revolutionized mathematics - and still faced sexism all her life

http://www.vox.com/2015/3/23/8274777/emmy-noether

OEIS - The Movie!

N. J. A. Sloane Article

Beauty in Math and Art Activate Same Brain Area

Beauty in Math and Art Activate Same Brain Area 
Elegant equations evoke the same activity in mathematicians' brains as gorgeous art or music 
Scientific American, Aug 14, 2014 
By Seth Newman

Maryam Mirzakhani - first woman to be awarded the Fields Medal - ICM 2014 Seoul

Maryam Mirzakhani - Iranian mathematician, full Professor of Mathematics at Stanford, first woman to be awarded the Fields Medal, at The International Congress of Mathematicians 2014 (Seoul, August 13-21)

"for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces" - see presentation and video @  http://www.icm2014.org/en/awards/prizes/f4

Eu si... Antonin Scalia

Pe o scara personal/academica, momentul cel mai interesant al anului care a trecut a survenit atunci cind am fost comparat (la o conferinta, deci in public) cu... Antonin Scalia (!). Intentia nu a fost magulitoare, iar motivul fiind inistenta mea pe cercetarea intreprinsa de profesori, (nici vorba de "publish or perish" la un 4 years college, insa macar "publish involving undergraduates" - pentru un 4 years college ar fi minunat). Insistenta mea a trezit reactii mixte: unii s-au bucurat ("it's about time!"), altii au subliniat ceva in genul "teaching is paramount" (so?... does this exclude engaging students in research?), altii au fost relativ ostili, negind orice rol special acordat publicatiilor cu sau fara studenti co-autori. In sfirsit, ma bucur ca macar aceasta atitudine i-a pus pe ginduri pe unii.

Cosmic inflation: 'Spectacular' discovery hailed

17 March 2014
Cosmic inflation: 'Spectacular' discovery hailed
By Jonathan Amos Science correspondent, BBC News


NY Times - Space & Cosmos 
Detection of Waves in Space Buttresses Landmark Theory of Big Bang 
By DENNIS OVERBYE, MARCH 17, 2014

Why the brain sees maths as beauty (BBC News)

Mathematics: Why the brain sees maths as beauty 
By James Gallagher
Health and science reporter, BBC News
12 February 2014

"What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating." (P. A. M. Dirac)

'On Ducci Sequences with Primes' - Fibonacci Quarterly

http://www.fq.math.ca/Abstracts/52-1/caragiu.pdf
Mihai Caragiu, Alexandru Zaharescu, and Mohammad Zaki 
On Ducci Sequences with Primes 
Fibonacci Quart. 52 (2014), no. 1, 32-38.

Miami University Fall Conference on Undergraduate Research in Mathematics

Abstract of my presentation:

More than twelve years ago, a talk on "Ducci games" delivered jointly by two Ohio Northern University students at the 2001 Ohio MAA Spring meeting initiated a fairly long streak of undergraduate research in the area of number theory at our school. Since then, Ohio Northern University students presented 40 talks and posters in the broad area of number theory at various mathematics meetings, and were co-authors of 11 research articles in number theory which appeared in peer-reviewed mathematics journals. We were especially pleased to see our research on "greatest prime factor sequences" (published in Fibonacci Quarterly in 2010) featured alongside other "noteworthy variations on the Fibonacci numbers" in the keynote talk at the 15th International Conference on Fibonacci Numbers held in Budapest (June 25-30, 2012), and cited in various other journals. In the light of the speaker's experience as an undergraduate research advisor, we will try to address some issues of interest regarding the impact of undergraduate research in the outside mathematical community. This "impact" may be viewed as a long-sought fulfillment or closure of the combined efforts of faculty and students engaged in undergraduate research, which ultimately takes a life of its own. We will explore open-ended difficult questions such as: What does it mean to make an impact? Are there specific strategies for smaller schools? Can presentations make an impact? What is the relationship between undergraduate research and faculty research? Is it harder for pure mathematics?

Alba Iulia 2013

My talk (abstract) at the 2013 RMS-AMS Special Session of Discrete Mathematics and Theoretical Computer Science in Alba Iulia:
Uniform distribution for a class of k-paradoxical oriented graphs 
By using estimates for incomplete character sums with polynomial arguments, we provide uniform distribution results for the dominating sets in a class of k-paradoxical regular oriented graphs, including the Paley tournaments. Moreover, we will explore a method of quasi-random tournament generation from fi nite sets of natural numbers, by using the greatest prime factor function.

Work on Stirling numbers honored with an Allendoerfer Award (2013)

Khristo N. Boyadzhiev (Ohio Northern University) - 2013 Carl B. Allendoerfer Award for the paper "Close Encounters with the Stirling Numbers of the Second Kind" - Mathematics Magazine, 85:4 (2012), pp. 252-266.
More at: http://www.maa.org/news/2013-maa-awards-recipients-announced

A parametric curve with... Bach's Prelude in G major

http://youtu.be/IvNQbTYSON8