Googolplex (1 followed by a googol of zeros); even using a proton for each zero, it could not be written with all the matter in the universe
5th Ackermann number (of the type n ^ (n, n times)): cannot be written on a sheet of paper as big as the whole universe … … even if exponential notation is used
10 ^ (3 638 334 640 024): 4th Ackermann number (of the type n ^ (n, n times))
A Googol of years (term coined by the mathematician Edward Kasner at the age of 9). After a googol of years, the temperature of the Universe is an almost uniform value very close to absolute zero (0K).
Physicists Giuseppe Mussardo and André LeClair publish an article in which, using physical rather than mathematical methods, they demonstrated (mathematically!) That “while a violation of the Riemann Hypothesis (RH) is strictly speaking not impossible, it is however extremely improbable. “; that is, it is technically possible
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
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”
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
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.
Oxford, England. The day is 3/14, a 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.
The mathematicians announce that RSA174 has also been capitulated.
Tobias Colding and William Minicozzi find an even simpler, more geometric proof to the Poincare Conjecture than the one presented just a month earlier by Grigori “Grisha” Perelman in his third article at ‘www.arXiv.org’
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 ‘.
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; he
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
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.
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.
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.
Canadian student Michael Cameron discovers a prime number with over 4 million digits. It is 2 ^ 13466917 – 1.
Jan van de Lune, a 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 the Riemann Zeta function they fall
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.
Nayan Hajratwala of Plymouth, Michigan discovers the first prime number with more than a million digits. It is 2 ^ 6972593 – 1 with 2098960 digits.
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, despite
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.
Mertone Scholes won the Nobel Prize in Economics (Fischer Black died in 1997), for the Black-Scholes equation which describes the price trend of a financial derivative. The formula will then be used and abused, forgetting the conditions of its validity, contributing to the subsequent financial collapses.
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 supercomputer domination sets and the
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 issue
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.
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.
Harvard’s Naom Elkies refutes Euler’s conjecture: there may be integer solutions to the equation x ^ 4 + y ^ 4 + z ^ 4 = w ^ 4. One solution is 2682440 ^ 4 + 15365639 ^ 4 + 18796760 ^ 4 = 20615673 ^
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
Ken Ribet and Barry Mazur prove Frey’s conjecture thus linking the Tanyiama-Shimura conjecture to Fermat’s Last Theorem
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.
The New Zealand mathematician Vaughan Frederick Randal Jones, expert in knot theory, invents the Jones Polynomial, the invariant of knots. This will make him win the Fields Medal in 1990. This will open the way to other invariants of the nodes, including the generalization called HOMFLY-PT,
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. Anatol
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.
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
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. The same
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) on
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.
Kurt Godel dies, allowing himself to be killed by hunger. In fact, he suffered from hypochondriacal personality disorders that led him not to eat for fear of being poisoned.
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
Ronald Rivest, Adi Shamir, Leonard Adleman, of MIT, realize that prime numbers are the ideal basis for cryptography
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 higher than four? (without two neighboring countries in more than single points having the same color). Appel and
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 in the variables and look at the result:
JM Smith, GR Price publish “The Logics of Animal Conflict” as part of Game Theory
A famous calculation shows that the first 3 million zeros of the Riemann Zeta function fall on the line passing through 1/2.
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
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
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
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
The FFT algorithm (Fast Fourier Transform, discrete version of the Fourier Transform) is developed
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
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.
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.
The Hungarian mathematician Tibor Rado invents the Busy Beaver Problem: given a Turing machine that stops, how many “1s” 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 computable
Japanese mathematician Yutaka Taniyama commits suicide
New York City. The Game of the Century: 13-year-old American Bobby Fischer plays and wins chess against Donald Byrne, seeded in the national rankings and 13 years older than him. 13-year-old Fischer makes two dramatic apparent sacrifices at the start of the game: first he exposes a
John Nash became famous by solving the Riemann Immersion Problem. Shortly thereafter 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 Euclidean space
DH Lehmer shows that the first 25,000 zeros of the Zeta function satisfy the Riemann hypothesis
Rand Corporation mathematicians after years of research publish the text “A million random digits”
At an international mathematics conference in Tokyo, the young Yutaka Taniyama suggests a curious relationship between modular forms and elliptic equations
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 were to play chess with all particles in
Mathematician Derek Lawden mathematically describes the flyby
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
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 so many decades, at least one case is expected to happen …)
John Nash studies Non-Cooperative Game Theory and Bargaining Theory (bargaining theory)
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.
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 down
The Institute for Advanced Study in Princeton is moved to a new location
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
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 the sum of no more than 4
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.
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
Alan Mathison Turing describes the simplest calculating machine capable of calculating any computable function
Emmy Noether dies at the age of 57
Kurt Godel commutes between Vienna and the Princeton Institue for Advanced Study
Kolmogorov: axiomization of probability theory
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 largest number
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.