Monday, December 8, 2014

Dessins d'enfants

Grothendieck's "Dessins d'enfants"
Anthony Weaver on Child's Drawings, map subgroups, and curves over number fields.

R.I.P. Alexander Grothendieck (1928 - 2014)

Alexandre Grothendieck. Le génie français des mathématiques n'est plus.

Sunday, November 30, 2014

Mathematics - Breakthrough Prize

"The Breakthrough Prize in Mathematics rewards significant discoveries across the many branches of the subject. The prize was founded by Mark Zuckerberg and Yuri Milner and announced at the 2014 Breakthrough Prize ceremony." 
For more details on the $3 million prize and the 2014 recipients (Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao and Richard Taylor)  - HERE.

Daca totul ar fi atit de simplu... argument pe marginea aplicabilitatii matematicii (Craig vs. Rosenberg)

Profesorul Alex Rosenberg de la Duke Univ. nu poate aduce, ca raspuns silogismului lui William Lane Craig ce se termina in "...deci Dumnezeu exista" un contra-argument bazat pe "exces" (in esenta, supra-abundenta universului matematic, care merge dincolo de ariile direct aplicabile) fara riscul de a submina naturalismul - fundamental pentru sistemul sau de (ne)credinta - care se trezeste, in unele arii, vaduvit de obiectul muncii.
Pe de alta parte solutia lui Craig (desi plauzibila la o prima lectura, si castigatoare in acest caz, macar pentru faptul ca Rosenberg nu intelege argumentul oponentului sau), pentru care Dumnezeu utilizeaza matematica drept instrument pentru "design cosmic", este ne-estetica (aspect in care lasa de dorit, in special pentru crestinii traitori ai frumosului iconic), chiar excesiva pe partea slabiciunii/racelii (s-ar putea argumenta ca idea unui Dumnezeu care face planuri matematice pentru univers submineaza majestatea divina - fundamentala, la rindul sau, pentru crestinism).
Se poate purta un dialog serios, mai complet si mutual ziditor, in materie de matematica si aplicabilitatea acesteia in (sau conexiunea acesteia cu) stiintele fizice? Putem vorbi de o convergenta rezonanta in perceperea estetica in care matematica si cosmosul se prezinta in tandem constiintei? Sigur, insa asta semnalizeaza faptul ca vrem sa o luam pe o linie in care, cel putin intr-un prim pas, constiinta este tratata ca element primordial, sau macar primar ori ireductibil. Insa in acest caz cei ce argumenteaza dinspre tabara ateismului, ar putea chiar accepta ambele (constiinta + estetica) ca primare, non-fizice (sau quasi-fizice intr-o intelegere extinsa a termenului de "fizic") fara sa se simta nevoiti sa accepte logic concluzia silogismului lui Craig.
Cum spuneam... daca totul ar fi atit de simplu... dar nu este.

Wednesday, November 19, 2014

Umor cu Moisil...

In timpul unui curs la Facultatea de Matematica din Iași, în timp ce Moisil scria mare pe tablă și vorbea încet unul dintre studenți îi spune
- Domnule profesor, nu se aude! 
- Nu se aude dar se vede... 
După ce tabla a devenit tot mai încărcată Moisil a început să scrie mai mic, dar să vorbeasca tare, același student îi spune:
 - Domnule profesor, nu se vede! 
 - Nu se vede dar se aude... 
Sursa

OEIS - The Movie!


N. J. A. Sloane Article

Tuesday, November 4, 2014

Ramifications of probability theory

Probability Theory connections with Pure Mathematics, Applied Mathematics, Statistics, Mathematical Finance, Combinatorics, Algebra, Geometry, etc.
Compiled and designed by M.C. - October 27.

The unexpected math behind Van Gogh's "Starry Night"

The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair

Sunday, September 28, 2014

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

Tuesday, September 23, 2014

Why Content Knowledge Matters in Teaching and the Implications for Teacher Education

"This is a talk given by Denise Spangler regarding "mathematical knowledge for teaching." The lecture looks at some examples of student work to see why teachers' mathematical knowledge matters and to think about how using student work in teacher education can help develop mathematical knowledge for teaching."

ICM2014 Benedict Gross, Laudation for Fields Medalist: Manjul Bhargava



The Musical, Magical Number Theorist
The search for artistic truth and beauty has led Manjul Bhargava to some of the most profound recent discoveries in number theory.

Thursday, August 28, 2014

Unreasonable effectiveness, revisited

An interesting take on the 'unreasonable effectiveness' of mathematics is formulated by Michael Barr in his book review that appeared in the last issue (August/September) of The American Mathematical Monthly, and involves the 'ubiquitous' presence of complex numbers in quantum mechanics:
Classical physics was formulated entirely with real numbers. Could quantum mechanics have even been formulated without complex numbers? What could it possibly look like? Isn’t the fact that complex numbers were created long before quantum mechanics required it, another example of the unreasonable effectiveness of mathematics?
(The Outer Limits of Reason. Noson Yanofsky. MIT Press, Cambridge, MA and London, England, 2013 - Reviewed by Michael Barr, The American Mathematical Monthly, Vol. 121, No. 7 (August–September), pp. 658-660)

Thursday, August 14, 2014

Give and take - Brasil loses a FIFA world Cup, but wins a Fields medal!

A Brazilian Wunderkind Who Calms Chaos - Artur Avila’s solutions to ubiquitous problems in chaos theory have earned him Brazil’s first Fields Medal. (Thomas Lin and Erica Klarreich - August 12, 2014)
Artur Avila wins the Fields medal 2014 "for his profound contributions to dynamical systems theory have changed the face of the field, using the powerful idea of renormalization as a unifying principle" (see http://www.icm2014.org/en/awards/prizes/f1 )

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

Monday, June 16, 2014

Joint Statistical Meetings Proceedings - not peer-reviewed

"If you give a presentation at JSM, you may submit a corresponding paper to be published in the conference proceedings. Papers are not peer-reviewed in the same manner as for journals, but authors are encouraged to have others examine their paper before submission. The proceedings are published online around November. Authors retain the right to publish their research later in a peer-reviewed journal."
SOURCE: "What Happens at JSM Should Not Stay at JSM / How to get the most out of the Joint Statistical Meetings"  AMSTAT News - May 2014
http://magazine.amstat.org/wp-content/uploads/2014/02/AN_May2014.pdf

Thursday, May 22, 2014

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 (un judecator conservator din Curtea Suprema a SUA). Intentia nu a fost magulitoare, persoana care a emis aceasta comparatie considerindu-se, in opozitie, ultra-liberala, iar motivul fiind inistenta mea constanta de-a lungul anilor pe cercetarea intreprinsa de personalul didactic, cu accent pe publicatii (fara sa fiu atat de radical incit sa spun "publish a lot or perish" - chiar nu se poate la o universitate de 4 ani fara program graduat, insa macar "publish a few things and everything will be fine"). Insistenta mea a trezit reactii mixte: unii s-au bucurat ("it's about time!"), altii au pedalat putin inapoi, in virtutea faptului ca "suntem o universitate in care teaching-ul este principala componenta" (desi n-au putut sa explice cum cercetarea ar fi exclusa prin aceasta sentinta, mai ales ca cercetarea este plasata pe locul doi dupa predat in documentele oficiale ale Colegiului, fiind astfel recunoscuta oficial inaintea altor activitati cum ar fi dezvoltare profesionala, Serviciu, si Colegialitate), altii (putini, ce-i drept - dar inflacarat de "ultra-liberali") au fost ceva mai ostili, negind orice rol special acordat publicatiilor si incercind in acelasi timp sa extinda aria termenului "cercetare/scholarship" astfel incit sa includa multe alte chestii care nu implica un peer review serios (nice try, though :-) ). In sfirsit, ma bucur ca macar aceasta insistenta a generat ceva auto-reflectie, in acest sens adjudecindu-mi cu mindrie termenul de "conservator". Take it easy!
 

Friday, April 11, 2014

Nature's secrets

"Nature conceals her secrets because she is sublime, not because she is a trickster" 
Albert Einstein, in a letter to Oscar Veblen

Thursday, March 6, 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)

Wednesday, February 26, 2014