Angel "Java" Lopez en Blog

Matemáticas


Publicado el 6 de Abril, 2019, 11:55

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Atención, pregunta: ¿Qué es una integral?
https://francis.naukas.com/2019/02/28/atencion-pregunta-que-es-una-integral/

Logistic map
https://twitter.com/johncarlosbaez/status/1102322497771331584
https://en.wikipedia.org/wiki/Logistic_map

Fifty Years of KdV: An Integrable System
https://arxiv.org/abs/1902.10267
The author discusses integrability of Hamiltonian dynamical systems in the aftermath of KdV.

The Math That Takes Newton Into the Quantum World
http://nautil.us/issue/69/patterns/the-math-that-takes-newton-into-the-quantum-world

The Horgan Surface and the Death of Proof
https://blogs.scientificamerican.com/cross-check/the-horgan-surface-and-the-death-of-proof/
Mathematicians take revenge on the author of a controversial article about proof by naming an object after him

Nash Letters
https://www.nsa.gov/Portals/70/documents/news-features/declassified-documents/nash-letters/nash_letters1.pdf

New Caltech Professor Seeks Order in Chaos
http://www.pasadenanow.com/main/seeking-order-in-chaos/
A Q&A with Caltech's new mathematics professor Maksym Radziwill

Paradox of integration -- Dynamics of two-dimensional status
https://arxiv.org/abs/1903.04291

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 22 de Marzo, 2019, 16:22

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The Death of Proofs
https://pdfs.semanticscholar.org/4e56/c6fea76922082400dfc6e13a3a169ae7b9a6.pdf

Dos problemas sobre primos
https://www.gaussianos.com/dos-problemas-sobre-primos/

¿Por qué el caso n=4 es tan importante?
https://www.gaussianos.com/%C2%BFpor-que-el-caso-n4-es-tan-importante/

Characterizations of Snowflake Metric Spaces
https://www.emis.de/journals/AASF/Vol30/tyson.pdf

19 Women Leading Math and Physics
https://www.quantamagazine.org/19-women-leaders-in-math-and-physics-20170308/

A Movement to Close the Gender Gap in Mathematics
https://www.quantamagazine.org/carolina-araujo-is-building-a-network-of-women-in-mathematics-20190122/

Lo que aprendí resolviendo integrales
https://fuga.naukas.com/2019/02/27/lo-que-aprendi-resolviendo-integrales/

Lo que aprendí resolviendo integrales
https://www.explainxkcd.com/wiki/index.php/2117:_Differentiation_and_Integration

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 8 de Marzo, 2019, 12:01

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Möbius Strips Defy a Link With Infinity
https://www.quantamagazine.org/mobius-strips-defy-a-link-with-infinity-20190220/

Mills' constant
https://en.wikipedia.org/wiki/Mills%27_constant

Chaos on the interval
https://www.math.u-psud.fr/~ruette/articles/chaos-int.pdf

Elliptic Curves Divisors
https://crypto.stanford.edu/pbc/notes/elliptic/divisor.html

A lattice is a set with operations
https://twitter.com/johncarlosbaez/status/1097197827791306752

Yet Another Single Law for Lattices
https://arxiv.org/abs/math/0307284

Lattice (order)
https://en.wikipedia.org/wiki/Lattice_(order)

Formalization of Mathematics in Type Theory
http://drops.dagstuhl.de/opus/volltexte/2019/10237/pdf/dagrep_v008_i008_p130_18341.pdf

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 2 de Marzo, 2019, 14:47

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Maximum Cut
https://en.wikipedia.org/wiki/Maximum_cut

Elliptic Curves
https://crypto.stanford.edu/pbc/notes/elliptic/

For a Black Mathematician, What It"s Like to Be the "Only One"
https://www.nytimes.com/2019/02/18/us/edray-goins-black-mathematicians.html

Unheralded Mathematician Bridges the Prime Gap
https://www.quantamagazine.org/yitang-zhang-proves-landmark-theorem-in-distribution-of-prime-numbers-20130519/

Kant Mathematics
https://plato.stanford.edu/entries/kant-mathematics/

Explaining p-values with puppies
https://hackernoon.com/explaining-p-values-with-puppies-af63d68005d0

Mellin Transform
https://en.wikipedia.org/wiki/Mellin_transform

Ceyuan haijing
https://en.wikipedia.org/wiki/Ceyuan_haijing

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 24 de Febrero, 2019, 13:15

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Some Basics of Class Field Theory
https://ahilado.wordpress.com/2017/10/19/some-basics-of-class-field-theory/

More Category Theory: The Grothendieck Topos
https://twitter.com/johncarlosbaez/status/1096813915403505664

Category Theory
https://ahilado.wordpress.com/2016/12/05/category-theory/

Presheaves
https://ahilado.wordpress.com/2016/12/03/presheaves/

Sheaves
https://ahilado.wordpress.com/2016/12/03/sheaves/

Algebraic Numbers
https://ahilado.wordpress.com/2017/01/03/algebraic-numbers/

Why is a mathematical function allowed to have "multiple outputs for single input" but not "multiple inputs for same output"? Is it just a convention or it has a logical reason?
https://www.quora.com/Why-is-a-mathematical-function-allowed-to-have-multiple-outputs-for-single-input-but-not-multiple-inputs-for-same-output-Is-it-just-a-convention-or-it-has-a-logical-reason/answer/Bartosz-Milewski?share=0ce9415c

Foundations Built for a General Theory of Neural Networks
https://www.quantamagazine.org/foundations-built-for-a-general-theory-of-neural-networks-20190131/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 23 de Febrero, 2019, 12:41

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AKS Primality Test
http://mathworld.wolfram.com/AKSPrimalityTest.html
https://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf

The Arithmetic Site and the Scaling Site
https://ahilado.wordpress.com/2018/01/25/the-arithmetic-site-and-the-scaling-site/

Zeta Functions and L-Functions
https://ahilado.wordpress.com/2016/11/23/zeta-functions-and-l-functions/

Basics of Algebraic Geometry
https://ahilado.wordpress.com/2016/12/14/basics-of-algebraic-geometry/

Grothendieck"s Relative Point of View
https://ahilado.wordpress.com/2017/04/25/grothendiecks-relative-point-of-view/

Varieties and Schemes Revisited
https://ahilado.wordpress.com/2017/04/21/varieties-and-schemes-revisited/

Adjoint Functors and Monads
https://ahilado.wordpress.com/2017/06/20/adjoint-functors-and-monads/

The Field with One Element
https://ahilado.wordpress.com/2017/12/20/the-field-with-one-element/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 22 de Febrero, 2019, 13:08

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Congruent Number
https://en.wikipedia.org/wiki/Congruent_number

Birkhoff polytope and Birkhoff–von Neumann theorem
https://en.wikipedia.org/wiki/Doubly_stochastic_matrix#Birkhoff_polytope_and_Birkhoff%E2%80%93von_Neumann_theorem

Assignment problem
https://en.wikipedia.org/wiki/Assignment_problem

Why Mathematicians Can"t Find the Hay in a Haystack
https://www.quantamagazine.org/why-mathematicians-cant-find-the-hay-in-a-haystack-20180917/

Mathematicians Crack the Cursed Curve
https://www.quantamagazine.org/mathematicians-crack-the-cursed-curve-20171207/

Jacques Philippe Marie Binet
https://en.wikipedia.org/wiki/Jacques_Philippe_Marie_Binet

Sobre la conjetura de la suma producto de Erdös y Szemeredi
https://francis.naukas.com/2019/02/11/sobre-la-conjetura-de-la-suma-producto-de-erdos-y-szemeredi/

How a Strange Grid Reveals Hidden Connections Between Simple Numbers
https://www.quantamagazine.org/the-sum-product-problem-shows-how-addition-and-multiplication-constrain-each-other-20190206/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 20 de Febrero, 2019, 12:33

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In the Universe of Equations, Virtually All Are Prime
https://www.quantamagazine.org/in-the-universe-of-equations-virtually-all-are-prime-20181210/

The Beal Conjecture
https://thebealconjecture.wordpress.com/

Love Affairs and Differential Equations
http://ai.stanford.edu/~rajatr/articles/SS_love_dEq.pdf

Zaphod Beeblebrox's Brain and the Fifty-ninth Row of Pascal's Triangle
https://dms.umontreal.ca/~andrew/PDF/beeb.pdf

Compositionality for Recursive Neural Networks
https://arxiv.org/abs/1901.10723

Tres historias matemáticas
https://naukas.com/2019/02/01/tres-historias-matematicas/

Pi and the Golden Ratio
https://johncarlosbaez.wordpress.com/2017/03/07/pi-and-the-golden-ratio/

The Physical Meaning of J-Function Elucidates the Monstruous Moonshine Conjeture
https://arturotozzi.webnode.it/_files/200000225-035c7045a7/J-function%20160514%20Monster-R13.pdf

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 21 de Enero, 2019, 12:37

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Machine learning leads mathematicians to unsolvable problem
https://www.nature.com/articles/d41586-019-00083-3

Grigori Perelman documentary
https://www.youtube.com/watch?v=Ng1W2KUHI2s

A note on S(t) and the zeros of the Riemann zeta-function
https://arxiv.org/pdf/math/0511092.pdf

Finally, a Problem That Only Quantum Computers Will Ever Be Able to Solve
https://www.quantamagazine.org/finally-a-problem-that-only-quantum-computers-will-ever-be-able-to-solve-20180621/

Schoof–Elkies–Atkin algorithm
https://en.wikipedia.org/wiki/Schoof%E2%80%93Elkies%E2%80%93Atkin_algorithm

Schoof's algorithm
https://en.wikipedia.org/wiki/Schoof%27s_algorithm

Analysis vs Algebra predicts eating corn?
http://bentilly.blogspot.com/2010/08/analysis-vs-algebra-predicts-eating.html

Mathematicians Seal Back Door to Breaking RSA Encryption
https://www.quantamagazine.org/mathematicians-seal-back-door-to-breaking-rsa-encryption-20181217/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 19 de Enero, 2019, 9:33

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A Characteristic Function for the Primes
https://arxiv.org/abs/1604.08670

Shor
https://mathoverflow.net/questions/48222/applications-of-knot-theory

Quantum money from knots
https://arxiv.org/abs/1004.5127

Knot theory
https://www.maths.ed.ac.uk/~v1ranick/knots/

Reseña: "Apología de un matemático" de G. H. Hardy
https://francis.naukas.com/2017/11/25/resena-apologia-de-un-matematico-de-g-h-hardy/

Michael Atiyah"s Imaginative State of Mind
https://www.quantamagazine.org/michael-atiyahs-mathematical-dreams-20160303/

Algebraic Analysis notes Lecture 2 (9 Jan 2019)
https://joemathjoe.wordpress.com/2019/01/10/algebraic-analysis-notes-lecture-2-9-jan-2019/

Is there an infinite set that's bigger than the set of integers but smaller than the set of real numbers?
https://twitter.com/johncarlosbaez/status/1083047483368890368

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 2 de Enero, 2019, 12:14

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El proyecto GIMPS encuentra un nuevo primo de Mersenne
https://francis.naukas.com/2018/12/25/el-proyecto-gimps-encuentra-un-nuevo-primo-de-mersenne/

¿Sorpresa sobre los números primos?
https://francis.naukas.com/2016/03/16/numeros-primos/

¡Cuidado con el método de inducción «a ojo»!
https://francis.naukas.com/2018/12/27/cuidado-con-el-metodo-de-induccion-a-ojo/

Prime Zeta Function
https://en.wikipedia.org/wiki/Prime_zeta_function

Summing over General Functions of Primes and an Application to Prime ζ Function
https://math.stackexchange.com/questions/115230/summing-over-general-functions-of-primes-and-an-application-to-prime-zeta-fun

How does ∑p<xp−s grow asymptotically for Re(s)<1?
https://math.stackexchange.com/questions/49383/how-does-sum-px-p-s-grow-asymptotically-for-textres-1

A note on S(T) and the zeros of the Riemann zeta-function
https://arxiv.org/abs/math/0511092

The distribution of prime numbers
https://dms.umontreal.ca/~koukoulo/documents/notes/primes.pdf

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 27 de Diciembre, 2018, 15:23

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Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/
Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

Solomon W. Golomb
https://en.wikipedia.org/wiki/Solomon_W._Golomb

The most beautiful and important mathematical equations
https://www.zmescience.com/other/feature-post/mathematical-equations-beautiful-30112018/

Zipf's law
https://simple.wikipedia.org/wiki/Zipf%27s_law

What's so special about characteristic 2?
https://math.stackexchange.com/questions/1573308/whats-so-special-about-characteristic-2

Relojes matemáticos: el modelo «123» y otros a cuál más curiosos
https://www.microsiervos.com/archivo/ciencia/relojes-matematicos-123-pi-curiosos.html

Amusing Permutation Representations of Group Extensions
https://arxiv.org/abs/1812.08475

All right triangles with integer sides are multiples of these! 
https://twitter.com/johncarlosbaez/status/1076865258050904065

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 2 de Diciembre, 2018, 14:50

Siempre vuelvo a estudiar la vida y la obra de Paul Erdös. En estos días estoy disfrutando de una biografía de este gran matemático, publicada en la serie de matemáticos de editorial RBA. Espero poder escribir sobre historias que encontré ahí.

Hoy quiero recorder un tema que a Erdös le importaba mucho: su idea de que hay un Libro, donde están todas las demostraciones matemáticas, expresadas de forma simple y bella. El decía que siempre que buscaba una prueba, quería alcanzar la version "del Libro". Encuentro este párrafo en el libro "Proof of THE BOOK" de Martin Aigner y Günter Ziegler:

Paul Erdös liked to talk about The Book, in which God maintains the perfect proofs for mathematical theorems, following the dictum of G.H.Hardy that there is no permanent place for ugly mathematics. Erdös also said that you need not believe in God but, as a mathematician, you should believe in The Book.

En el libro, los autores muestran unas 44 demostraciones, de diversos campos como la teoría de números, teoría de grafos, combinatoria, análisis, geometría. Me llama la atención que expongan SEIS demostraciones sobre la infinitude de los números primos. La representación de números como la suma de dos cuadrados, es un clásico (estuve escribiendo serie de posts, debería retomar) así como la ley de reprocidad cuadrática. Me gusta que exista para los autores al menos una demostración del postulado de Bertrand que se acerque a la version del libro: el enunciado es tan simple, dado n >=1 siempre hay un primo entre n y 2n.

Podría estar horas describiendo brevemente las pruebas aportadas. Realmente una lectura muy interesante, y siempre, tratando de encontrar pruebas por nuestro propio esfuerzo, antes de llegar a estudiar la prueba DEL LIBRO.

Ver también

https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Publicado el 2 de Octubre, 2018, 13:04

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A Master of Numbers and Shapes Who Is Rewriting Arithmetic
https://www.quantamagazine.org/peter-scholze-becomes-one-of-the-youngest-fields-medalists-ever-20180801/

A Poet of Computation Who Uncovers Distant Truths
https://www.quantamagazine.org/computer-scientist-constantinos-daskalakis-wins-nevanlinna-prize-20180801/

The Universal Pattern Popping Up in Math, Physics and Biology
https://www.quantamagazine.org/the-universal-pattern-popping-up-in-math-physics-and-biology-20180823/

A Number Theorist Who Bridges Math and Time
https://www.quantamagazine.org/fields-medalist-akshay-venkatesh-bridges-math-and-time-20180801/

How Network Math Can Help You Make Friends
https://www.quantamagazine.org/how-network-math-can-help-you-make-friends-20180820/

Tinkertoy Models Produce New Geometric Insights
https://www.quantamagazine.org/tinkertoy-models-produce-new-geometric-insights-20180905/

The Strange Numbers That Birthed Modern Algebra
https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/
Quaternions

Why Mathematicians Can"t Find the Hay in a Haystack
https://www.quantamagazine.org/why-mathematicians-cant-find-the-hay-in-a-haystack-20180917/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 1 de Octubre, 2018, 14:41

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Four Is Not Enough
https://www.quantamagazine.org/the-numbers-and-geometry-behind-a-math-coloring-puzzle-20180618/
How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?

Her Key to Modeling Brains: Ignore the Right Details
https://www.quantamagazine.org/mathematician-carina-curto-thinks-like-a-physicist-to-solve-neuroscience-problems-20180619/

Mathematics Shows How to Ensure Evolution
https://www.quantamagazine.org/mathematics-shows-how-to-ensure-evolution-20180626/

Mathematicians Tame Turbulence in Flattened Fluids
https://www.quantamagazine.org/mathematicians-tame-turbulence-in-flattened-fluids-20180627/

The Peculiar Math That Could Underlie the Laws of Nature
https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/
New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called "octonions."

A Math Theory for Why People Hallucinate
https://www.quantamagazine.org/a-math-theory-for-why-people-hallucinate-20180730/

A Traveler Who Finds Stability in the Natural World
https://www.quantamagazine.org/alessio-figalli-a-mathematician-on-the-move-wins-fields-medal-20180801/

An Innovator Who Brings Order to an Infinitude of Equations
https://www.quantamagazine.org/caucher-birkar-who-fled-war-and-found-asylum-wins-fields-medal-20180801/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 28 de Septiembre, 2018, 13:30

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Más artículos sobre la prueba presentada por Michael Atiyah. Como comentaba en el anterior post, el punto principal es las cualidades de la función T, que o no parecen cumplirse, o no parecen probadas. No parece que la discusión pase por la adecuación de la función T con la constante de estructura fina, que es el resultado principal del "paper" de enero, pero que parece accesorio a la prueba de RH de este septiembre.

The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12?
https://medium.com/@marktdodds/the-ramanujan-summation-1-2-3-1-12-a8cc23dea793

Did a mathematician really solve a million-dollar math problem?
https://www.usatoday.com/story/news/nation-now/2018/09/25/riemann-hypothesis-mathematician-said-he-solved-1-m-math-problem/1418487002/

Reading Into Atiyah"s Proof
https://rjlipton.wordpress.com/2018/09/26/reading-into-atiyahs-proof/

Atiyah Riemann Hypothesis proof: final thoughts
https://aperiodical.com/2018/09/atiyah-riemann-hypothesis-proof-final-thoughts/

Retired mathematician rocks math world with claim that he's solved $1 million problem
https://www.nbcnews.com/mach/science/retired-mathematician-rocks-math-world-claim-he-s-solved-1-ncna914046

Mathematician claims to have solved 160-year-old Reimann hypothesis
https://www.independent.co.uk/news/uk/home-news/riemann-hypothesis-uk-mathematics-solved-claim-sir-michael-atiyah-a8557656.html

Mathematician may have cracked $1 million riddle
https://nypost.com/2018/09/25/mathematician-may-have-cracked-1-million-riddle/

Mathematicians Skeptical of Supposed Million-Dollar Proof
https://gizmodo.com/mathematicians-skeptical-of-supposed-million-dollar-pro-1829301425

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 25 de Septiembre, 2018, 12:12

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Más sobre el caso Atiyah Hipótesis de Riemann. El punto débil parece la función T (de Todd), si su aplicación en la prueba DEPENDE de su relación con la constant de estructura fina, entonces es bastante dudosa. Si el tema de la constant de estructura fina es accesorio, tal vez haya algo interesante. Veremos.

Explainer: Has Michael Atiyah conquered the Everest of mathematics?
https://www.irishtimes.com/news/world/explainer-has-michael-atiyah-conquered-the-everest-of-mathematics-1.3639725

Top Mathematician Says He's Solved a 160-Year-Old Maths Problem Worth $1 Million
https://www.sciencealert.com/top-mathematician-sir-michael-atiyah-solved-a-160-year-old-1-million-maths-problem-riemann-hypothesis

Skepticism surrounds renowned mathematician"s attempted proof of 160-year-old hypothesis
https://www.sciencemag.org/news/2018/09/skepticism-surrounds-renowned-mathematician-s-attempted-proof-160-year-old-hypothesis

Atiyah's Lecture on the Riemann Hypothesis
https://www.reddit.com/r/math/comments/9igc4d/atiyahs_lecture_on_the_riemann_hypothesis/

Riemann hypothesis, the fine structure constant, and the Todd function
https://www.johndcook.com/blog/2018/09/24/riemann-hypothesis-the-fine-structure-constant-and-the-todd-function/
https://news.ycombinator.com/item?id=18059880

Discussion about Atiyah's Paper
https://news.ycombinator.com/item?id=18054890

Proof of Riemann hypothesis, Generalized Riemann hypothesis and Ramanujan τ-Dirichlet series hypothesis
https://arxiv.org/abs/1703.03827

What is the definition of the function T used in Atiyah's attempted proof of the Riemann Hypothesis?
https://mathoverflow.net/questions/311280/what-is-the-definition-of-the-function-t-used-in-atiyahs-attempted-proof-of-the

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 24 de Septiembre, 2018, 18:13

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6th HLF – Lecture: Sir Michael Francis Atiyah
https://www.youtube.com/watch?v=jXugkzFW5qY

The Fine Structure Constant, Michael Atiyah
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view

The Riemann Hypothesis, Michael Atiyah
https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view

A Mathematician May Have Just Solved a A 160-Year-Old, $1 Million Problem
https://motherboard.vice.com/en_us/article/d3j3kk/a-mathematician-may-have-just-solved-a-a-160-year-old-dollar1-million-problem

Top mathematician says he solved the 'single most important open problem' in math after 160 years
https://www.thisisinsider.com/riemann-hypothesis-solved-by-sir-michael-atiyah-after-160-years-he-says-2018-9

Riemann hypothesis likely remains unsolved despite claimed proof
https://www.newscientist.com/article/2180504-riemann-hypothesis-likely-remains-unsolved-despite-claimed-proof/

The Riemann Hypothesis and Atiyah
https://twitter.com/johncarlosbaez/status/1043975994246291456

Has the Riemann hypothesis been 'solved'? Who is Michael Atiyah? Why is it so important?
https://www.standard.co.uk/news/uk/has-the-riemann-hypothesis-been-solved-who-is-michael-atiyah-a3944486.html

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 23 de Septiembre, 2018, 18:50

La hipótesis de Riemann podría considerarse como el problema del siglo. Es uno de los problemas matemáticos pendientes de solución más famosos. Mientras que el Ultimo Teorema de Fermat y la Conjetura de Poincare fueron probados. la hipótesis de Riemman se resiste todavía, luego de más de siglo y medio de haber sido formulada.

Cuéntase que el matemático Hardy, cuando tenia que cruzar el Atlántico, enviama un telegrama al otro declarando que tenia una prueba de la hipótesis. De esta forma, esperaba que ninguna divinidad dejaría que le pasara algo en el viaje.

Hilbert lo propuso como uno de los problemas de su lista de 1900. Es uno de los pocos que pasado el siglo veinte todavía no tiene solución. Hilbert decía que si se durmiera tres mil años y se despertara, lo primero que preguntaría es si se había resuelto el problema. Del siglo XX al XXI pasó a ser uno de los problemas del milenio, según el instituto de matemáticas Clay.

Yo estoy tratando de explicar la hipótesis en mi serie La Hipótesis de Riemman. Ya a fines del siglo XIX se vió que no era necesaria su verdad para probar el teorema de los números primos, (ver teorema de Hadamard y de la Vallée-Poussin) pero se espera que si es verdad, la distribución de los primos sea la esperada.

Ver también:

https://en.wikipedia.org/wiki/Riemann_hypothesis
https://en.wikipedia.org/wiki/Prime_number_theorem 
https://en.wikipedia.org/wiki/Riemann_hypothesis#Function_fields_and_zeta_functions_of_varieties_over_finite_fields notablemente se demostró la hipótesis para otros campos, y hay varias generalizaciones

En estos días el mundo matemático está esperando la conferencia de Michael Atiyah, medallista Field, anunciada para mañana lunes 24 de septiembre. Ver

Famed mathematician claims proof of 160-year-old Riemann hypothesis
https://www.newscientist.com/article/2180406-famed-mathematician-claims-proof-of-160-year-old-riemann-hypothesis/

News regarding ABC conjecture and Riemann Hypothesis
https://www.johndcook.com/blog/2018/09/20/abc-conjecture-riemann-hypothesis/

Michael Atiyah claims proof of Riemann Hypothesis
https://aperiodical.com/2018/09/michael-atiyah-claims-proof-of-riemann-hypothesis/

Hay algún escepticismo sobre la validez de la prueba, que no fue publicada todavía. No se espera que Atiyah haya encontrado el éxito donde otros muchos matemáticos fracasaron. Pero esperemos a maña. Me he referido a Atiyah varias veces en este blog, por ejemplo en relación a un teorema de Hilbert. Ver su entrevista en

https://www.lavanguardia.com/lacontra/20111228/54241694041/sir-michael-atiyah-el-camino-mas-corto-para-crear-es-un-largo-rodeo.html

Pero hay un dato interesante en las noticias publicadas sobre el tema. En Aperiodical leo:

Atiyah will speak at the HLF on Monday at 9am CEST, and his abstract, available to read through the HLF conference app, claims he will present "a simple proof using a radically new approach […] based on the work of Von Neumann (1936), Hirzebruch (1954) and Dirac (1928)."

Hirzebruch es conocido por el teorema de Hirzebruch–Riemann–Roch, luego opacado en parte por el trabajo novedoso de Gothrendieck, que lo extendió más allá del resultado original. Ver

Friedrich Hirzebruch
https://en.wikipedia.org/wiki/Friedrich_Hirzebruch

Atiyah trabajó con Hirzebruch, en sus años jóvenes, y será interesante ver qué camino aprovechó de los descubrimientos de su maestro para llegar a su proclamada prueba. Pero en el párrafo que mencioné arriba, mencionan a Von Neumann y a Dirac, dos "habitué" de este blog. Eso da una pista, y acá apuesto que la prueba tiene que ver con:

MATRICES HERMITIANAS

usadas tanto en la mecánica cuántica que tanto Von Neumann como Dirac ayudaron a desarrollar. No es un camino nuevo en los intentos de demostración de este problema. La idea es que la hipótesis afirma que la función zeta de Riemman

z(x + iy) 

tiene TODOS sus ceros no triviales en x = 1/2. Pero eso equivale a que, haciendo cambio de variables (rotación 90 grados y desplazamiento 1/2), todas los ceros no triviales de otra función:

h(y + ix - i/2)

SON REALES. El camino de las matrices hermitianas, mostraría que existe una matriz "infinita" M, que sea hermitiana (igual a su transpuesta conjugada), tal que el determinante de M - wI, o sea su polinomio característico, sea igual a la función h de arriba.

Se sabe que las matrices hermitianas solo tienen autovalores (los ceros de su polinomio característico) reales. Con eso se completaría la demostración. Claro que una cosa es decirlo, y otra es encontrar esa matriz M infinita que cumpla con todo eso. Pero bien podría Atiyah haber encontrado un camino nuevo en este forma de solucionar el problema: una forma de "armar" esa matriz para obtener la función h, transformada de la zeta. Pero lo mío es solo un albur, veremos si es así.

Vivimos tiempos interesantes.

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 22 de Septiembre, 2018, 17:47

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Hay novedades sobre la Hipótesis de Riemman

Legendre's Theorem, Lagrange's Descent
https://public.csusm.edu/aitken_html/notes/legendre.pdf

Symmetry of second derivatives
https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives

Patterns That Eventually Fail
https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/

News regarding ABC conjecture and Riemann Hypothesis
https://www.johndcook.com/blog/2018/09/20/abc-conjecture-riemann-hypothesis/

Hirzebruch–Riemann–Roch theorem
https://en.wikipedia.org/wiki/Hirzebruch%E2%80%93Riemann%E2%80%93Roch_theorem

Friedrich Hirzebruch
https://en.wikipedia.org/wiki/Friedrich_Hirzebruch

Famed mathematician claims proof of 160-year-old Riemann hypothesis
https://www.newscientist.com/article/2180406-famed-mathematician-claims-proof-of-160-year-old-riemann-hypothesis/

Michael Atiyah claims proof of Riemann Hypothesis
https://aperiodical.com/2018/09/michael-atiyah-claims-proof-of-riemann-hypothesis/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

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