Mt

Googolplex (1 followed by a googol of zeros); even using one proton for every zero, it couldn’t be written with all the matter in the universe

5th Ackermann number (of the form n^(n, n times)): cannot be written on a sheet of paper as big as the entire universe… …even if one uses exponential notation

10^(3 638 334 640 024): 4th Ackermann number (of the type n^(n, n times))

A Googol of years (a term coined by mathematician Edward Kasner at the age of 9). After a googol of years the temperature of the Universe is a nearly uniform value very close to absolute zero (0K).

Physicists Giuseppe Mussardo and André LeClair publish an article in which, using physical and not mathematical methods, they demonstrate (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 Artificial Intelligence algorithms (Neural Networks), a particular type of partial differential equations (PDE – Partial Differential Equations): the Navier-Stokes used to describe the motion of incompressible fluids, much more

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

The American Institute of Mathematics with the help of the super-computer Sage of the 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”

Nassim Nicholas Taleb, a Lebanese-born, American-born financial mathematician, introduces the concept of the black swan. The essay is called The Black Swan: How the Improbable Rules Our Lives.

Oxford, England. The day is 3/14, a date written in the American style, or pi. Daniel Tammet, an autistic man with Asperger’s syndrome, recites the first 22,514 digits of pi from memory in 5 hours and 9 minutes, without ever getting one wrong.

Mathematicians announce that RSA174 has also been made to capitulate.

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

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

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

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 the Poincare Conjecture), but shows however that the corrections have no effect on the conclusions

Russian mathematician Grigori “Grisha” Perelman posts a paper to www.arXiv.org in which he presents a proof of the Poincaré Conjecture, formulated in 1904: every compact and simply connected 3-manifold (i.e. on which every closed path can be reduced to a point) is homeomorphic (i.e. topologically

Three Indian mathematicians: Manindra Agrawal, Neeraj Kayal, Nitin Saxena, without presupposing the validity of the Riemann Hypothesis, demonstrate a test similar to the Miller-Rabin one, capable of establishing the primality of a number after a few checks.

Stephen Wolfram, an English physicist and mathematician, publishes “A new kind of science” in which he describes a complex system called a cellular automaton, which can calculate like an algorithm, indeed 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 retired Dutch mathematician and member of te Riele’s team, has not completely recovered from prime number fever, and using three PCs he keeps at home, he demonstrates that the first 10 billion zeros of the Riemann Zeta function fall on

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.

England. The revolutionary contribution in the field of Public Key Cryptography by Ellis, Cocks and Williamson finally becomes public with a “talk” by Cocks. The gigantic steps forward in this field had been made since 1965 at the Government Communication Headquarters (GCHQ) in Cheltenham. Unfortunately

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

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

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

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

Andrew Wiles proves Fermat’s Theorem with a 130-page proof that focuses on the proof of the Shimura-Taniyama Conjecture (Fermat’s Last Theorem: a^n + b^n not equal to c^n for all n>2). The proof will be published in the May 1995 issue of Annals of Mathematics

Mathematicians Arjen Lenstra and Mark Manasse, using the Internet and distributed PCs, crack RSA129 with the quadratic Pomerance sieve. The smallest number that still resists decay now has over 160 digits.

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

Computer scientist Martin Grotschel will calculate at the beginning of the 21st century, that in the period 1988 – 2003 the speed of automatic solution of standard optimization problems, improves by a factor of 43 million. The improvement of the hardware speed contributes by a

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

Ingrid Daubechies, a Belgian physicist and scholar, at Bell Labs in Murray Hill (New Jersey) discovers the right tool for Wavelet Theory: a mother wavelet completely devoid of a tail (previous attempts, at the beginning of the eighties by Jean Morlet, Alexander Grossman, Yves Meyer,

Ken Ribet and Barry Mazur prove the Frey 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 automatically have also proved Fermat’s Last Theorem.

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

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

The work of 420 Navajo Indians encoding and decoding classified military information during World War II is finally being recognized with August 14 being designated “National Navajo Code Talkers Day.” The work was revealed in part starting in 1968 after being classified for decades. The

The Poincaré Conjecture for spheres of dimension 4 is proved by Michael Freedman of the University of California at San Diego. He does this by classifying every compact simply connected 4-dimensional manifold.

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

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 Poincaré Conjecture. Most of the 3-manifolds in 3-space have a hyperbolic structure. The same is true

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

Australian mathematician Richard Brent shows that the first 75 million zeros of the Riemann zeta function fall on the line passing through 1/2.

Kurt Godel dies, starving himself to death. He suffered from hypochondriac personality disorders that led him to not eat for fear of being poisoned

Ronald Rivest, Adi Shamir, Leonard Adleman, make public the RSA, an asymmetric cryptography system. They do it through an article by Martin Gardner in Scientific American, entitled “A new kind of cipher that would take millions of years to break”. The basic mechanism is based

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

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

The American NSA (National Security Agency) adopts the 56-bit version of the Lucifer code by Horst Feistel (a German emigrant to the United States, an IBM employee), and calls it DES (Data Encryption Standard). It will remain the standard for encrypted communication for several decades.

New York, National Computer Conference. The audience of cryptography experts is astonished by the presentation of the Diffie-Hellman-Merkle exchange scheme, which enables two interlocutors (usually called Alice and Bob) to exchange a secret through a public discussion. Whitfield Diffie (Distinguished Engineer at Sun Microsystems, graduate

Two mathematicians from the University of Illinois, Kenneth Appel and Wolfgang Haken, solve the four-color problem. or: is it possible to draw a political map with a minimum number of colors greater than four? (without two countries bordering on more than one point having the

A formula for calculating the complete list of prime numbers is written out in full for the first time. It contains 26 variables (that is, it must use all 26 letters of the English alphabet). Random values are inserted into the variables and the result

JM Smith, GR Price publish “The Logics of Animal Conflict” in Game Theory

A famous calculation shows that the first 3 million zeros of the Riemann zeta function fall on the straight line passing through 1/2.

Yuriy Matijasievic finds the last piece of the puzzle and proves Julia Robinson’s assertion and thus Hilbert’s tenth problem: there is no program that can determine whether any equation has a solution.

The 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 (by the year

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

Beatrice and Allen Gardner are able to teach the deaf-mute language, American Sign Language, to the shimpanzee Washoe; he uses words like “open” even when applied to contexts as diverse as a door or a peanut

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

Whitfield Diffie, Martin Hellman, Ralph Merkle will become famous for Public Key Cryptography, while Ronald Rivest, Adi Shamir, Leonard Adleman, will become famous for RSA, the most practical implementation of Public Key Cryptography. But, it will be discovered many years later, that in England, they

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 fractional numbers and less than real numbers, and, at the same time, it is impossible to

Paul Cohen of Stanford University discovers specific questions in mathematics that are undecidable, in accordance with Gödel’s Theorem; one of the questions is the continuum hypothesis, which David 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 into nested hierarchies of repeated subunits.

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

Japanese Mathematician Yutaka Taniyama Commits Suicide

John von Neumann dies. He had been diagnosed with bone cancer and underwent emergency surgery two years earlier. Edward Teller, who was with him frequently during his final days, reports that John was not only dedicated to thinking but benefited from it. Perhaps like no

New York City. The Game of the Century: American Bobby Fischer, 13, plays and wins at chess against Donald Byrne, the top seed in the national rankings and 13 years his senior. The 13-year-old Fischer makes two dramatic apparent sacrifices early in the game: first

John Nash becomes famous by solving the Riemann Embedding Problem. He soon after falls into a deep schizophrenic psychosis. The Riemann Embedding Problem: Is it possible to embed every surface, and more generally every manifold with a metric in the Riemannian sense, into some n-dimensional

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

Rand Corporation Mathematicians Publish “A Million Random Digits” After Years of Research

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 prime numbers thin out found by Gauss, for sufficiently large figures, was underestimated; the first of these figures must be less than 10^10^100000000000000000000000000000000000000000; if a person played chess with all the particles existing in the universe, where

John von Neumann collapses while on the phone with Lewis Strauss. He will be diagnosed with bone cancer and undergo emergency surgery. He will be confined to a wheelchair, but will continue to produce and work, writing the book “The computer and the brain” published

Mathematician Derek Lawden mathematically describes the flyby

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

Desert Inn, Las Vegas. A casino customer manages to hit 28 consecutive correct dice rolls. A priori, there is a 1 in 10 million chance. (But obviously with tens of millions of games played over so many decades, one would expect at least one case

John Nash studies Non-Cooperative Game Theory and Bargaining Theory

John von Neumann summarizes in a letter the Monte Carlo method, which he developed with Stanislaw Ulam: a way to solve problems that would otherwise be intractable (or difficult to solve in a timely manner), with the laws of chance. A first use case is

The Air Force establishes the start of the RAND project (Research And Development – although some jokingly call it Research And No Development). On May 2nd it will produce a first report: “Preliminary Design of an Experimental World-Circling Spaceship”, in practice an artificial satellite. It

United States. John von Neumann publishes the book “Theory of games and economic behavior”, the book that will change social sciences forever and will profoundly influence political and economic decisions starting from the 50s of the twentieth century.

United States. The book “Theory of games and economic behavior” is finally finished by John von Neumann and Oskar Morgenstern. 1200 pages sent to the publisher for publication. It will be published in 1944. The book will change social sciences forever and will profoundly influence