Angel "Java" Lopez en Blog

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Programming with Categories - Lecture 0
https://www.youtube.com/watch?v=NUBEB9QlNCM&feature=emb_logo

Cuánto da 0 elevado a la 0
https://perlitasmatematicas.wordpress.com/2020/01/14/cuanto-da-0-elevado-a-la-0/

This is the largest known Fibonacci number that's also prime
https://twitter.com/fermatslibrary/status/1217800668385284096

About Noether's Theorem
https://twitter.com/InertialObservr/status/1217545021810888706

Programming with Categories - Lecture 6
https://www.youtube.com/watch?v=xStrvUgN51A&feature=emb_logo

Tai-Danae Bradley: Modeling Language with Tensor Networks
https://www.youtube.com/watch?v=12j8OV-ptC4

Berstein Polynomial
https://en.wikipedia.org/wiki/Bernstein_polynomial

Choose 2 numbers at random - here's the probability they will have no common factor
https://twitter.com/fermatslibrary/status/1216350626055184385

Nos leemos!

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

Y comienza un nuevo año. Resultado de las resoluciones de diciembre:

- Escribir sobre Matemáticas [completo] ver post
- Escribir sobre Física [pendiente]
- Escribir sobre Historia de las Matemáticas [pendiente]
- Escribir sobre Historia de la Ciencia [pendiente]
- Estudiar blues en guitarra [completo]
- Estudiar dibujo/pintura [completo] evidencia

Sigo con las mismas resoluciones (espero esta vez escribir algo sobre curvas elípticas, sea historia o desarrollo):

- Escribir sobre Matemáticas
- Escribir sobre Física
- Escribir sobre Historia de las Matemáticas
- Escribir sobre Historia de la Ciencia
- Estudiar blues en guitarra
- Estudiar dibujo/pintura

Nos leemos!

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

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Rectangular Billiard
https://mobile.twitter.com/fermatslibrary/status/1208018727318544384

Almost all orbits of the Collatz map attain almost bounded values
https://arxiv.org/abs/1909.03562

Primer avance en décadas en un problema aparentemente imposible
https://elpais.com/elpais/2020/01/08/ciencia/1578499346_232520.html

Strassen Algorithm
https://en.wikipedia.org/wiki/Strassen_algorithm

Chaos Machine
https://twitter.com/henryseg/status/1215224040345960449

Science history: Al-Khwarizmi, master of maths
https://cosmosmagazine.com/mathematics/science-history-al-khwarizmi-master-of-maths

Facebook's AI mathematician can solve university calculus problems
https://www.newscientist.com/article/2228399-facebooks-ai-mathematician-can-solve-university-calculus-problems/

Mathematicians explain an uncertain law of physics
https://cosmosmagazine.com/physics/mathematicians-provide-explanation-for-an-uncertain-law-of-physics

Nos leemos!

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

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Folding a piece of paper into a ellipse
https://twitter.com/fermatslibrary/status/1202232094241501184

Mathematician Terence Tao and the Collatz conjecture
https://www.quantamagazine.org/mathematician-terence-tao-and-the-collatz-conjecture-20191211/

Here's a proof that e^π is transcendental
https://twitter.com/fermatslibrary/status/1206575467014348800

La conjetura ABC y el último teorema de Fermat
https://www.gaussianos.com/la-conjetura-abc-y-el-ultimo-teorema-de-fermat/

El teorema clausura complemento de Kuratowski
https://www.gaussianos.com/el-teorema-clausura-complemento-de-kuratowski/

The equation XAX=B is surprisingly simple to solve on the set of positive matrices
https://twitter.com/gabrielpeyre/status/1207541067756818434

El mapa de las matemáticas
https://www.gaussianos.com/el-mapa-de-las-matematicas/

The Suble Art of the Mathematical Conjecture
https://www.quantamagazine.org/the-subtle-art-of-the-mathematical-conjecture-20190507/

Nos leemos!

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

En su libro The Principles of Mathematics, Bertrand Russel describe lo que considera matemáticas puras:

Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.

Es una definición seca, llevada a la base de toda la matemática pura, pero que deja afuera (o al menos lejos) a cantidad de ramas activas y fructíferas de las matemáticas, puras o no. Pero en aquellos años (1903 fue publicado por primera vez ese libro), Russel buscaba los fundamentos de la matemática, que habían entrado en cierta crisis (recordemos la crítica de Russel al libro sobre conjuntos y lógica de Frege). En su infancia, había encontrado en las matemáticas una roca firme, donde la verdad era clara, en medio quizás de un mundo humano cambiante. Pero para fines del siglo XIX, los fundamentos de las matemáticas no estaban claros ni firmes.

Desde entonces, se ha avanzado, y hoy, gran parte de los matemáticos no se preocupan de los fundamentos, sino del gran juego que es el pensamiento matemático. No lo hacen en general por ser arriesgados, mas bien los fundamentos de la matemática se han ido desarrollando en el siglo XX en varias ramas, desde una teoría de conjuntos más elaborada, hasta teoría de categorías, pasando por el formalismo de Hilbert,  los teoremas de Gödel y la evolución de la lógica matemáticas más allá de verdadero o falso. No es un tema que ha quedado abandonado, sino que sigue siendo bien atendido. Pero hay tantas ramas interesantes y activas, que muchos matemáticos simplemente descansan sobre los hombros de los colegas que se ocupan de los fundamentos.

Nos leemos!

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

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Rank of an elliptic curve
https://en.wikipedia.org/wiki/Rank_of_an_elliptic_curve

Mathematics
https://twitter.com/pickover/status/1213096691513122817

From sequences to nets
https://twitter.com/johncarlosbaez/status/1213165193703804929

Beal Conjecture
https://twitter.com/fermatslibrary/status/1213100462389547009

Subnet
https://en.wikipedia.org/wiki/Subnet_(mathematics)

An Essay towards solving a Problem in the Doctrine of Chance
https://en.wikipedia.org/wiki/An_Essay_towards_solving_a_Problem_in_the_Doctrine_of_Chances

Lo que considero lo mejor de 2019 en gaussianos
https://www.gaussianos.com/lo-que-yo-considero-lo-mejor-de-2019-en-gaussianos/

Decoding the ancient greek astronomical calculator known as the antikythera mechanism
https://fermatslibrary.com/s/decoding-the-ancient-greek-astronomical-calculator-known-as-the-antikythera-mechanism

Nos leemos!

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

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Apolo, Pitágoras y la Música
https://twitter.com/pgroisma/status/1197826329346863104

Thirty-Six Unsolved Problems in Number Theory
https://arxiv.org/abs/math/0010143

Circular Prime
https://twitter.com/fermatslibrary/status/1212382480717754369

Solution Randomness from Deteterminism
https://www.quantamagazine.org/solution-randomness-from-determinism-20191122/

George Dantziq
https://en.wikipedia.org/wiki/George_Dantzig

Simplex Algorithm
https://en.wikipedia.org/wiki/Simplex_algorithm

In 1947 W. H. Mills proved that there is a number A, such that the following number is prime for all integer values of n
https://twitter.com/fermatslibrary/status/1197877654285889541

On Computing the Rank of Elliptic Curves
https://www.math.colostate.edu/~achter/math/brown.pdf

Nos leemos!

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

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Erdős–Rényi_model
https://en.wikipedia.org/wiki/Erdős–Rényi_model

Matthias Goerner made an in-space viewer for hyperbolic 3-manifolds
https://twitter.com/henryseg/status/1211226130167910400

The Central Limit Theorem and its misuse
https://lambdaclass.com/data_etudes/central_limit_theorem_misuse/

Transportation theory (mathematics)
https://en.wikipedia.org/wiki/Transportation_theory_(mathematics)

Gaspard Monge
https://en.wikipedia.org/wiki/Gaspard_Monge

Compositionality First Issue
https://johncarlosbaez.wordpress.com/2019/12/30/compositionality-first-issue/

Compositionality Journal
https://compositionality-journal.org/

Start with 82 and go backwards to 1
https://twitter.com/fermatslibrary/status/1197153129646694406

Nos leemos!

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

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In 1919, Viggo Brun proved that the sum of the reciprocals of twin primes converges to Brun's constant
https://twitter.com/fermatslibrary/status/1189900586365464588

Computer Science and Biology Explore Algorithmic Evolution
https://www.quantamagazine.org/computer-science-and-biology-explore-algorithmic-evolution-20181129/

Stackelberg competition
https://en.wikipedia.org/wiki/Stackelberg_competition
 
James Sylvester
https://twitter.com/johncarlosbaez/status/1191041537531973632

Why the Sum of Three Cubes Is a Hard Math Problem
https://www.quantamagazine.org/why-the-sum-of-three-cubes-is-a-hard-math-problem-20191105/

158,962,555,217,826,360,000 (Enigma Machine) - Numberphile
https://www.youtube.com/watch?v=G2_Q9FoD-oQ&feature=youtu.be

Neutrinos Lead to Unexpected Discovery in Basic Math
https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/

La física de los neutrinos inspira cómo calcular los autovectores de matrices hermíticas
https://francis.naukas.com/2019/11/14/la-fisica-de-los-neutrinos-inspira-como-calcular-los-autovectores-de-matrices-hermiticas/

Nos leemos!

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

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A Proof from "The Book": The limit of sin(x)/x as x → 0
https://twitter.com/TamasGorbe/status/1207788896622403584

The determinant is log-concave function
https://twitter.com/gabrielpeyre/status/1210440170530463744

John ellipsoid
https://en.wikipedia.org/wiki/John_ellipsoid

Musical Isomorphism
https://en.wikipedia.org/wiki/Musical_isomorphism

Problem 2
https://solvemymaths.com/2015/01/19/proof-problem-2/

About Yoneda Lemma
https://twitter.com/davidad/status/1210308612276408320

Go Cellular Automata
http://xahlee.info/cmaci/ca/go_cellular_automata.html

Knitting, Chinese Knots, Braid Theory
http://xahlee.info/math/math_knitting_chinese_knots.html

Nos leemos!

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

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Fast Fourier Transform
https://en.wikipedia.org/wiki/Fast_Fourier_transform

Visual Knitting Machine Programming
https://www.youtube.com/watch?v=9ms5uEUC_js

Anudado espontáneo de una cuerda agitada
https://twitter.com/emmaiarussi/status/1209554742441062402

Spontaneous knotting of an agitated string
https://www.pnas.org/content/104/42/16432

In any category we can define the concepts of "product" and "coproduct"
https://twitter.com/johncarlosbaez/status/1206257622480904193

Posible demostración de la veracidad de la conjetura ABC
https://www.gaussianos.com/posible-demostracion-de-la-veracidad-de-la-conjetura-abc/

Hay funciones continuas que no son derivables en ningún punto
https://twitter.com/pgroisma/status/1189877205960183808

Mathematicians Cut Apart Shapes to Find Pieces of Equations
https://www.quantamagazine.org/mathematicians-cut-apart-shapes-to-find-pieces-of-equations-20191031/

Nos leemos!

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

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Revisiting Ramanujan
https://blogs.royalsociety.org/history-of-science/2018/10/02/revisiting-ramanujan/

Circular law for random matrices
https://www.johndcook.com/blog/2018/07/27/circular-law/

Wigner's Semicircle Law
http://mathworld.wolfram.com/WignersSemicircleLaw.html

Random Matrices: The circular Law
https://arxiv.org/abs/0708.2895

Montgomery's pair correlation conjecture
https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture

Bayes theorem, and making probability intuitive
https://www.youtube.com/watch?v=HZGCoVF3YvM&feature=youtu.be

A practical type theory for symmetric monoidal categories
https://twitter.com/johncarlosbaez/status/1209177768241483776

The Year in Math and Computer Science
https://www.quantamagazine.org/quantas-year-in-math-and-computer-science-2019-20191223/

Nos leemos!

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

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‘Noise’ in the Brain Encodes Surprisingly Important Signals
https://www.quantamagazine.org/noise-in-the-brains-vision-areas-encodes-body-movements-20191107/

Longevity Linked to Proteins That Calm Overexcited Neurons
https://www.quantamagazine.org/longevity-linked-to-proteins-that-calm-overexcited-neurons-20191126/

Penrose diagrams
https://twitter.com/JannaLevin/status/1199042297087897600

Generador hardware de números aleatorios más rápido del mundo, basado en un diodo láser en régimen caótico
https://francis.naukas.com/2009/07/16/generador-hardware-de-numeros-aleatorios-mas-rapido-del-mundo-basado-en-un-diodo-laser-en-regimen-caotico/

The Inspection Paradox is Everywhere
https://towardsdatascience.com/the-inspection-paradox-is-everywhere-2ef1c2e9d709

Imágenes icónicas de la ciencia
https://twitter.com/SdeStendhal/status/1165926802474393601

Why an Old Theory of Everything Is Gaining New Life
https://www.quantamagazine.org/why-an-old-theory-of-everything-is-gaining-new-life-20180108/

¿Eran los dinosaurios como los hemos imaginado?
https://www.vozpopuli.com/altavoz/next/dinosaurios-imaginado_0_1067294935.html

Nos leemos!

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

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Can maths predict the universe?
https://www.prospectmagazine.co.uk/arts-and-books/the-universe-speaks-in-numbers-graham-farmelo-marcus-chown

Un horizonte sin límites clave para la humanidad
https://www.lanacion.com.ar/sociedad/un-horizonte-sin-limites-clave-para-la-humanidad-nid2311527

A group of our Homo erectus ancestors suffered a mysterious mass death more than 107,000 years ago. It's their last appearance in the fossil record
https://www.businessinsider.com/homo-erectus-mass-death-java-2019-12

Where is comet Borisov?
https://www.nytimes.com/interactive/2019/12/07/science/comet-borisov-tracker.html

Even In A Quantum Universe, Space And Time Might Be Continuous, Not Discrete
https://www.forbes.com/sites/startswithabang/2019/11/08/even-in-a-quantum-universe-space-and-time-might-be-continuous-not-discrete/#59ac6eb23598

Neutrinos Lead to Unexpected Discovery in Basic Math
https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/

Black hole 'so big it should not exist' has been discovered
https://news.sky.com/story/black-hole-so-big-it-should-not-exist-has-been-discovered-11873235

Paul Dirac and the Nobel Prize in Physics
https://physicstoday.scitation.org/doi/10.1063/PT.3.4342

Nos leemos!

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

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Evariste Galois
https://www.youtube.com/watch?v=BAmhQle-uvA

Hipatia la verdad en las matemáticas
https://www.gaussianos.com/comic-hipatia-la-verdad-en-las-matematicas/

A problem of Ramanujan
https://fermatslibrary.com/s/a-problem-of-ramanujan

Mathematician makes Euler equations blow up
https://www.quantamagazine.org/mathematician-makes-euler-equations-blow-up-20191218/

John Baez December 15th, Category Theory
http://math.ucr.edu/home/baez/diary/december_2019.html#december_15

Is there a set with 2.5 elements?  No!  But here's a "groupoid" with 2.5 elements
https://twitter.com/johncarlosbaez/status/1207711861732335616

Engel relations in 4-manifold topology
https://arxiv.org/abs/1412.5024

What color is Shinoy"s hat?
https://twitter.com/brilliantorg/status/1207299869846724608

Nos leemos!

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

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To colour any map on a torus you just need 7 colours
https://twitter.com/fermatslibrary/status/1185541866080624640

El artículo de matemáticas que Terence Tao publicó con solo 8 años
https://francis.naukas.com/2019/12/08/el-articulo-de-matematicas-que-terence-tao-publico-con-solo-8-anos/

Infinitve Powers
https://twitter.com/unbalancedparen/status/1203786359409917958

La Estadística o el curso para sacar muelas
http://anabelforte.com/2019/12/03/la-crisis-de-la-significatividad-estadistica/

Galactic Algorithm
https://en.wikipedia.org/wiki/Galactic_algorithm

Van Emde Boas tree
https://en.wikipedia.org/wiki/Van_Emde_Boas_tree

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

Inverse distance weighting
https://en.wikipedia.org/wiki/Inverse_distance_weighting

Nos leemos!

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

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III Carnaval de Matemáticas: Toda la verdad sobre la anécdota de Gauss, el niño prodigio, su profesor y la suma de 1 a 100
https://francis.naukas.com/2010/04/15/iii-carnaval-de-matematicas-toda-la-verdad-sobre-la-anecdota-de-gauss-el-nino-prodigio-su-profesor-y-la-suma-de-1-a-100/

This question was asked by Toeplitz in 1911 and remains unsolved to this day
https://twitter.com/fermatslibrary/status/1204400428554838021

Who cares about topology? (Inscribed rectangle problem)
https://www.youtube.com/watch?v=AmgkSdhK4K8

"Screw theory" was invented by a guy named Ball
https://twitter.com/johncarlosbaez/status/1185234370690310144

Benford's law
https://twitter.com/fermatslibrary/status/1185179983939096580

A Collector of Math and Physics Surprises
https://www.quantamagazine.org/tadashi-tokieda-collects-math-and-physics-surprises-20181127/

From open learners to open games
https://arxiv.org/abs/1902.08666

Cross-sections of a regular octahedron
https://twitter.com/brilliantorg/status/1185541449963704320

Nos leemos!

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

Se termina el año. Repaso de las resoluciones del mes anterior:

- Escribir sobre Matemáticas [pendiente]
- Escribir sobre Física [pendiente]
- Escribir sobre Historia de las Matemáticas [pendiente]
- Escribir sobre Historia de la Ciencia [pendiente]
- Estudiar blues en guitarra [completo]
- Estudiar dibujo/pintura [completo] evidencia

Las resoluciones para el nuevo mes:

- Escribir sobre Matemáticas
- Escribir sobre Física
- Escribir sobre Historia de las Matemáticas
- Escribir sobre Historia de la Ciencia
- Estudiar blues en guitarra
- Estudiar dibujo/pintura

Nos leemos!

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

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Why mathematicians just can"t quit their blackboards
https://www.theguardian.com/artanddesign/2019/oct/12/mathematicians-blackboards-academics-photographer-jessica-wynne-do-not-erase

Villani and Ávila: Two Men that Count
https://news.cnrs.fr/articles/villani-and-avila-two-men-that-count

A Different Way to Solve Quadratic Equations
https://www.youtube.com/watch?v=ZBalWWHYFQc

"Para hacer matemáticas no hace falta ser un bicho raro"
https://elpais.com/elpais/2019/11/25/ciencia/1574678450_142554.html

How Randomness Can Arise From Determinism
https://www.quantamagazine.org/how-randomness-can-arise-from-determinism-20191014/

The Mandelbulb
https://twitter.com/Rainmaker1973/status/1184424960523227137

Three number systems
https://twitter.com/johncarlosbaez/status/1184492139897507840

The Laplace Transform
https://archive.org/details/in.ernet.dli.2015.201038

Nos leemos!

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

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El sentido de la vida, el universo y todo lo demás… resuelven x³+y³+z³ = 42
https://francis.naukas.com/2019/09/07/el-sentido-de-la-vida-el-universo-y-todo-lo-demas-resuelven-x³y³z³-42/

Fourier was trying to do something completely unrelated when he stumbled on Fourier series
https://twitter.com/AlexKontorovich/status/1171519369089667072

El "icónico" número 42 ya se sabe expresar como de tres cubos enteros
https://www.gaussianos.com/el-iconico-numero-42-ya-se-sabe-expresar-como-suma-de-tres-cubos-enteros/

Enumerative Geometry Genealogy (Or The Sex Life of Points and Lines)
https://twitter.com/johncarlosbaez/status/1179135794478321664

La conjetura de Steinberg es falsa
https://www.gaussianos.com/la-conjetura-de-steinberg-es-falsa/

Outside In, Turning Number
https://www.youtube.com/watch?v=wO61D9x6lNY

Sphere Eversion
https://en.wikipedia.org/wiki/Sphere_eversion

The Lambda Calculus is Algebraic
https://www.mscs.dal.ca/~selinger/papers/combinatory.pdf

Nos leemos!

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