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20-ott-20

20-ott-20

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Researchers from Caltech and Purdue University reveal that they have solved in the Fourier domain, with algorithms (Neural Newtorks) of Artificial Intelligence, a particular type of partial differential equations (PDE – Partial Differential Equations): the Navier-Stokes used to describe motion of incompressible fluids, much more

lug-07

lug-07

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Jonathan Schaeffer of the University of Alberta in Edmonton demonstrates that the game of chess, if played perfectly (ie without making mistakes – see Zermelo’s Theorem -), then it is a no-win situation, that is, it always ends “draw”

March 19, 2007

March 19, 2007

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The American Institute of Mathematics with the help of the super-computer Sage of Washington University manages to complete, after 4 years of work, the mapping of the E8 to explain its symmetry, it is a 248-dimensional object belonging to a Lie group (the “E8” in

2007

2007

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Nassim Nicholas Taleb, an expert in financial mathematics, born in Lebanon and naturalized American, introduces the concept of the black swan. The essay is called The Black Swan: how the improbable rules our life.

March 14, 2004

March 14, 2004

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Oxford, England. The day is 3/14, date written in the American style, or pi Greek. Daniel Tammet, autistic with Asperger’s syndrome, recites the first 22514 digits of pi from memory in 5 hours and 9 minutes, without ever making a mistake.

ago-03

ago-03

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Tobias Colding and William Minicozzi find an even simpler, more geometric proof of the Poincare Conjecture than the one presented just a month earlier by Grigori “Grisha” Perelman in his third article at ‘www.arXiv.org’

July 17, 2003

July 17, 2003

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Grigori “Grisha” Perelman sends the third article to ‘www.arXiv.org’; in it he presents a further analytical result that allows him to use the first and less difficult half of his second article to directly prove Poincare’s Conjecture ‘.

April 7, 2003

April 7, 2003

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In Cambridge, Massachussets, the Russian mathematician Grigori “Grisha” Perelman presents the proof of the Poincare ‘Conjecture, formulated in 1904: every compact and simply connected 3-manifold (on which every closed path can be reduced to a point ) is homeomorphic (ie topologically identical) to the 3-sphere;

March 10, 2003

March 10, 2003

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Grigori “Grisha” Perelman sends the second article to ‘www.arXiv.org’; in it he corrects the statement of two results reported in the first article (in which he presented the proof of Poincare’s Conjecture ‘), but nevertheless shows that the corrections have no effect on the conclusions

November 11, 2002

November 11, 2002

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The Russian mathematician Grigori “Grisha” Perelman sends an article to www.arXiv.org in which he presents the proof of the Poincare ‘conjecture, formulated in 1904: every compact and simply connected 3-manifold (on which every closed path can ‘to be reduced to a point) is homeomorphic (i.e.

2002

2002

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Stephen Wolfram, English physicist and mathematician, publishes “A new kind of science” in which he describes a complex system called a cellular automaton, which can compute like an algorithm, indeed they can replace a computer.

ago-02

ago-02

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Three Indian mathematicians: Manindra Agrawal, Neeraj Kayal, Nitin Saxena, without assuming the validity of the Riemann Hypothesis, demonstrate a test similar to that of Miller-Rabin, able to establish the primality of a number after a few checks.

nov-01

nov-01

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Canadian student Michael Cameron discovers a prime number with over 4 million digits. It is 2 ^ 13466917 – 1.

2001

2001

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Jan van de Lune, Dutch mathematician part of Te Riele’s team, retired, is not completely cured of prime number fever, and using three PCs that he keeps at home, he proves that the first 10 billion zeros of Riemann’s Zeta function they fall on the

ago-99

ago-99

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With the Sieve of the Numerical Field, RSA155 is also capitulated. The result is achieved by a network of mathematicians gathered under the name of Kabalah.

giu-99

giu-99

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Nayan Hajratwala of Plymouth, Michigan discovers the first prime number with more than a million digits. It is 2 ^ 6972593 – 1 with 2098960 digits.

April 7, 1997

April 7, 1997

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A bombshell goes around the world: the Riemann hypothesis has been demonstrated! It will then be discovered that it was an April Fool of Prof. Enrico Bombieri, one of the leading researchers involved, at the Institute for Advanced Study in Princeton.

1997

1997

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Mertone Scholes win the Nobel Prize in Economics (Fischer Black died in 1997), for the Black-Scholes equation which describes the price trend of a derivative financial instrument. The formula will then be used and abused, forgetting the conditions of its validity, contributing to subsequent financial

June 27, 1996

June 27, 1996

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Andrew Wiles collects the Wolfskehl prize for having solved Fermat’s Last Theorem, Wolfskehl whose problem saved his life, renewing his passion for life the night before a planned suicide, had opened the competition for the prize on 27 June 1908, worth 100,000 marks. In 1996,

1996

1996

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Paul Gage and David Slowinski announce the discovery, via the Cray supercomputer of the Lawrence Livermore Lab in California, of their seventh record prime number: 2 ^ 1257787 – 1 consisting of 378632 digits. From this moment on, the era of the domination of supercomputers

19-set-94

19-set-94

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Andrew Wiles proves Fermat’s Theorem with a 130-page proof focused on the proof of the Shimura-Taniyama Conjecture (Fermat’s Last Theorem: a ^ n + b ^ n different from c ^ n for every n> 2). The proof will be published in the May 1995

apr-94

apr-94

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To the mathematicians Arjen Lenstra and Mark Manasse, through the use of the internet and distributed PCs, they capitulate RSA129 with the quadratic sieve of Pomerance. The smallest number that still resists decomposition now has over 160 digits.

mag-93

mag-93

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First attempt of proof by Andrew Wiles of the Taniyama-Shimura conjecture, and therefore of Fermat’s Last Theorem, but the proof is undermined by an inappropriate application of the Kolyvagin-Flach method.

1988

1988

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Harvard’s Naom Elkies refutes Euler’s conjecture: there may be integer solutions to the equation x ^ 4 + y ^ 4 + z ^ 4 = w ^ 4. A solution is 2682440 ^ 4 + 15365639 ^ 4 + 18796760 ^ 4 = 20615673

1987

1987

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Ingrid Daubechies, Belgian physicist and physicist, at Bell Labs in Murray Hill (New Jersey) discovers the right tool for Wavelet Theory: an entirely tailless mother wavelet (previous attempts, in the early 1980s by Jean Morlet, Alexander Grossman, Yves Meyer, had led to mother wavelets, but

1984

1984

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Gerhard Frey, a mathematician from Saarbrucken, makes a conjecture: if someone were able to prove the Taniyama-Shimura conjecture on the equivalence of elliptic forms and modular equations, he would have automatically proved Fermat’s Last Theorem as well.

1984

1984

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The New Zealand mathematician Vaughan Frederick Randal Jones, expert in knot theory, invents the Jones Polynomial, the invariant of knots. This will win him the Fields Medal in 1990. This will pave the way for other node invariants, including the generalization called HOMFLY-PT, from the

1984

1984

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The American Robert Axelrod publishes in Science “The Evolution of Cooperation” or a Prisoner Dilemma tournament open to all scholars: each submitted algorithm can cooperate (cooperate) or pass-to-enemy / attack (defect): the winning strategy turns out to be the TIT-FOR-TAT (blow for blow) of prof.

1982

1982

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Poincare’s conjecture for spheres of dimension 4 is proved by Michael Freedman of the University of California at San Diego. It does this by classifying each compact 4 dimensional variety simply connected.

1982

1982

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The work of classification of all the finite simple groups is completed: they are some families of classical groups and some exceptional groups of which the largest, known as “the monster”, has order 808017424794512875886459904961710757005754368000000000

1982

1982

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The American William Thurston completes the Geometrization Conjecture: in dimension 3 there are only 8 different geometries, instead of the 3 found in dimension 2. The Geometrization Conjecture implies the Poincare’s Conjecture ‘. Most of the 3 manifolds in 3 space have a hyperbolic structure.

1979

1979

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A team led by Dutchman Herman te Riele and Australian Richard Brent demonstrates that the first 200 million zeros of Riemann’s Zeta function fall on the straight line through 1/2. However, there was a pending bet between Zagier and Bombieri (two bottles of excellent bordeaux)

1978

1978

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The Australian mathematician Richard Brent demonstrates that the first 75 million zeros of the Riemann Zeta function fall on the straight line through 1/2.

1977

1977

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Ronald Rivest, Adi Shamir, Leonard M. Addelman of MIT conceive a practical implementation of the idea known as RSA, i.e. the encryption and decryption algorithm based on the fact that decomposing a large number into its prime factors is a so-called problem. intractable

1977

1977

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Ronald Rivest, Adi Shamir, Leonard Adleman, of MIT, realize that prime numbers are the ideal basis for cryptography

1976

1976

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Two University of Illinois mathematicians, Kenneth Appel and Wolfgang Haken, solve the four-color problem. o: Is it possible to draw an imaginative political map with a minimum number of colors greater than four? (without two neighboring countries in more than single points having the same

1976

1976

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It is written in full for the first time, a formula to calculate the complete list of prime numbers, it contains 26 variables (ie it must use all 26 letters of the Anglo-Saxon alphabet). We insert random values

February 15, 1970

February 15, 1970

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Jurij Matijasievic finds the last piece of the puzzle and proves Julia Robinson’s assertion and therefore Hilbert’s tenth problem: there is no program that allows us to establish whether any equation has a solution

1970

1970

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American mathematician Stephen Cook, while completing his PhD in Computer Science at the University of California at Berkeley, discovers the SAT (Satisfiability) for NP-Complete (Non-deterministic, Polynomially time bounded) problems: solving any NP-complete problem is equivalent to solving any instance of SAT (over 2000 different NP-complete

70’s

70’s

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Cryptography: Whitfield Diffie and Martin Hellman find a mathematical procedure easy to perform in one direction but incredibly difficult in the other, or perfect coding

1966

1966

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Beatrice and Allen Gardner manage to teach the language of the deaf-dumb, American Sign Language, at the Washoe shimpanze; uses words like “open” also applied to different contexts such as a door or a peanut

1965

1965

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The FFT algorithm (Fast Fourier Transform, discrete version of the Fourier Transform) is developed

1963

1963

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The continuum hypothesis is solved by Paul Cohen, or Hilbert’s first problem: it is impossible to prove that there exists a set of numbers with a dimension greater than fractionals and smaller than reals, and, at the same time, it is impossible to prove that

1963

1963

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Paul Cohen of Stanford University, discovers specific questions of mathematics that are undecidable, in accordance with Godel’s Theorem; one of the questions is the continuum hypothesis, which Davide Hilbert had included among the 23 most important problems in mathematics.

1962

1962

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Simon publishes The Architecture of Complexity in which he explains the reasons why complex organizations of any kind, biological or artificial, tend to self-organize in nested hierarchies of repeated sub-units.

1962

1962

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The Hungarian mathematician Tibor Rado invents the Busy Beaver Problem: given a Turing machine that stops, how many “1’s” can it write before it stops? If the Turing machine in question has n states, this number is denoted S (n) and grows faster than any

1956

1956

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John Nash became famous by solving the Riemann Immersion Problem. Soon after, he falls into a profound schizophrenic psychosis. The Riemann Immersion Problem: It is possible to immerse every surface, and more generally every manifold with a metric in the Riemannian sense, in some n-dimensional

1956

1956

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DH Lehmer shows that the first 25,000 zeros of the Zeta function satisfy the Riemann hypothesis

1955

1955

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Rand Corporation mathematicians after years of research publish the text “A million random digits”

1955

1955

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At an international mathematics conference in Tokyo, the young Yutaka Taniyama suggests a curious relationship between modular forms and elliptic equations

1955

1955

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S. Skewes shows that the frequency with which the prime numbers thin out, found by Gauss, for sufficiently high figures was underestimated; the first of these figures must be less than 10 ^ 10 ^ 10000000000000000000000000000000000; if a person played chess with all particles in

January 30, 1952

January 30, 1952

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Raphael Robinson, at Berkeley, writes a program for the Standard Western Automatic Computer (SWAC) which calculates a huge Mersenne prime number (Mersenne’s Primes): 2 ^ 521 – 1. A few hours later it produces an even bigger one: 2 ^ 607 – 1. The same

11-giu-50

11-giu-50

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Desert Inn, Las Vegas. A casino customer manages to hit 28 consecutive right shots on the dice. A priori, there’s a one in 10 million chance. (but obviously with tens of millions of plays over many decades, at least one case is expected to happen

February 14, 1943

February 14, 1943

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Hilbert dies after a fall in the streets of Göttingen. For the German town, already marked by the Nazi purges, this event marks the end of its role as mecca of mathematics. German mathematics will no longer be what it was.

apr-40

apr-40

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Following the invasion of Denmark by Germany, the South African mathematician John Kerrich, who happened to be in Copenhagen, was also imprisoned. The mathematician will use the free time (a lot) of the years of imprisonment to flip a coin 10 thousand times and write

gen-40

gen-40

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Kurt Godel and his wife leave Vienna for Princeton, USA, they reached it with the trans-Siberian, through Japan from which they sailed for San Francisco reaching their destination only in March 1940; Godel would never set foot on European soil again

1937

1937

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The Russian Vinogradov demonstrates that any sufficiently large odd number can be represented as the sum of no more than 3 primes (for example 1937 = 641 + 643 + 653); therefore every even number can be represented as a sum of no more than

1936

1936

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Alan Turing publishes his most important article: “On computable numbers with an application to the Entscheidungsproblem” introducing what will be remembered as the Turing Machine, and the Universal Turing Machine, which are the basis of every digital computer.

1936

1936

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The American logician Alonzo Church demonstrates the Tarski-Church-Turing theorem: There is no foolproof method to discriminate true statements of arithmetic from false statements

1935

1935

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Alan Mathison Turing describes the simplest calculating machine capable of calculating any computable function

1933

1933

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A Littlewood student, Stanley Skewes, estimates that only when counting prime numbers no less than 10 ^ 10 ^ 10 ^ 34 can one witness the underestimation of the number of primes by the Gaussian integral logarithm. This is an incredibly large number. Probably the

1932

1932

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The Institute for Advanced Study in Princeton is founded, which will take up the baton of the mecca of mathematics, dropped by Göttingen in 1943.

1931

1931

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The Russian mathematician Schnirelmann demonstrates that any number, even or odd, can be represented as the sum of no more than 300,000 primes

1931

1931

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Kurt Godel’s Theorem: “In every mathematics there are statements that cannot be proved true” published under the title of On Formally Undecidable Propositions of Principia Mathematica and Related Systems; the mathematician John Von Neumann, who was giving a cycle of lectures in America, cancels the