Wiki Googologie
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Wiki Googologie
Date Event
c. 287 - 212 BCE Archimède publie L'Arénaire et définit le système de notation des nombres jusqu'à .[1]
190 BCE Apollonius de Perga "le grand géomètre" a écrit Conics, et a inventé la notation en superscription pour les nombres supérieurs en chiffres romains.
1st-7th century CE Un nombre proche de 10^10^37 a été écrit dans les écritures bouddhistes Avataṃsaka sūtra.[2]
1484 Nicolas Chuquet a écrit un article intitulé Triparty en la science des nombres, le premier ouvrage d'une série systématique et étendue de noms se terminant par -llion.[3]
1631 Le système numérique japonais a été défini jusqu'à 無量大数 (muryoutaisuu) dans 塵劫記 (Jinkoki).[4]
1706 John Machen découvre le centième chiffre de π.[5]
1808 Christian Kramp utilise le symbole ! pour les factorielles.[6]
1811 Chernac liste les facteurs premiers jusqu'à 1020000.[7][8]
1856 Crelle lists 6 million primes.
1857 First known use of vigintillion.[9]
1861 Zacharias Dase lists 9 million primes.
1893 D. H. Lehmer lists 50847534 primes.
1904 L'hiérarchie de Hardy was defined.[10]
1906 Charles-Ange Laisant calculates \(^{3}9\) has 369,693,100 digits.[11]
1928 Fonction d'Ackermann was published.[12]
1933 Stanley Skewes proved that, assuming the Riemann Hypothesis, there exists a number \(x\) less than \(e^{e^{e^{79}}} \approx 10^{10^{10^{34}}}\) where \(\pi (x) > li(x)\).[13] Notable for possibly being the largest number published in a serious mathematical proof at the time, and this number is now known as the first nombre de Skewes.
1938 Googol was named.[14]
1944 Suite de Goodstein was defined and Goodstein's theorem was proved.[15]
1947 Goodstein named tétration, pentation and hexation.[16]
1949 John Wrench and L. R. Smith were the first to use an electronic computer (the ENIAC) to calculate \(\pi\). It took 70 hours to calculate 2037 digits. It is also attributed to Reitwiesner.[17]
1955 Stanley Skewes proves that, without assuming the Riemann Hypothesis, there exists a number, \(x\), less than \(e^{e^{e^{e^{7.705}}}} \approx 10^{10^{10^{963}}}\) where \(\pi (x) > li(x)\).[18] Notable for being a record holder for "largest number in a professional mathematics paper", and this number is now known as the second nombre de Skewes.
1962 Castor affairé was defined.[19]
1971 Graham's paper, describing the number now known as Little Graham, was published.[20]
1976 Knuth devised notation des puissances itérées.[21].
1977 Gardner wrote about the modern nombre de Graham in Scientific American, popularizing it to the general public.[22] He also wrote about nombre de Folkman.
1978 High school students Laura Ariel Nickel and Landon Cole Noll discovered 25th and 26th nombre de Mersenne premier.[23] As the 26th Mersenne prime is 2^23209-1, 2^23208(2^23209-1) ≈ 8.1 × 10^13972 is a perfect number.
1979 Harry L. Nelson, puzzle developer, discovered 26,790-digit perfect number; Cormack and Williams discovered titanic prime \(25^{23,314}\) - 1.
1980 nombre de Graham was listed in Guinness World Records as the highest number ever used in a mathematical proof.
1982 Hydre de Kirby-Paris was defined.[24]
1983 Notation de Steinhaus-Moser was invented.[25] Douglas Hofstader promoted the "luring lottery" or "largest-number game" in Scientific American.[26]
1987 Hydre de Buchholz was defined.[27]
1991 Sbiis Saibian invents his poly-cell notations, a precursor to the modern système extensible-E.
November 25, 1994 Poincaré recurrence time of a Linde-type super-inflationary universe was calculated to be \(10^{10^{10^{10^{10^{1.1}}}}}\) years.[28]
1995 Conway invented notation des flèches chaînées.[29] Pickover defined en:Superfactorial and en:Leviathan number.[30] Sloane defined another type of superfactorial.[31]
1996 Robert Munafo's large number site was created.
February 26, 1998 The en:lynz was defined.
June 1, 2000 The en:Block subsequence theorem was invented.[32]
December, 2001 marxen.c and loader.c were created for Bignum Bakeoff.
2002 Jonathan Bowers invented Array Notation and Extended Array Notation.
June 29, 2002 Premier nombre de Fish was created.[33][34]
2006 Bird's Array Notation was invented.
2006 Harvey Friedman discovers TREE(3).
2007 Bowers considerably expanded array notation, inventing BEAF.[35]
January 26, 2007 Agustin Rayo defined nombre de Rayo at Big Number Duel.
March, 2008 Jonathan Bowers defined Meameamealokkapoowa oompa.[36]
June 10, 2008 Sbiis Saibian began working on One to Infinity.
December 5, 2008 en:Googology Wiki was established.
December 9, 2008 One to Infinity[37] was published. La système extensible-E (Saibian's Array Notation) is developed in this book.
November 19, 2011 Sbiis Saibian introduced notation hyper-E (E#) and Extended Hyper-E Notation (xE#).
March 16, 2012 Dmytro Taranovsky defined an ordinal notation conjecturally up to the second order arithmetic.[38]
January 6, 2013 Adam P. Goucher defined en:Xi function.[39]
January 22, 2013 Sbiis Saibian introduced Cascading-E Notation (E^).
April, 2013 Lawrence Hollom invented Hyperfactorial array notation.
May, 2013 Bracket Notation (Dollars Function) was defined.
June 5, 2013 Wythagoras published the first version of Dollar Function.
September 11, 2013 Japanese googological webcomic Sushi Kokuu Hen started.
November 10, 2013 Hyp cos defined R notation.
December 12, 2013 This site, French version of Wiki Googologie, was established.
January 30, 2014 Sbiis Saibian introduced Extended Cascading-E Notation (xE^).
February 25, 2014 SammySpore creates en:Sam's Number, a notable "fake number" and an in-joke within the googology community.[40]
May 28, 2014 Pointless Large Number Stuff was created.[41]
August 14, 2014 BASIC programs of primary sequence number and the number of séquence de la paire, which will later upgrade to système de matrice de Bashicu, were posted on Japanese BBS.
October 30, 2014 LittlePeng9 defined en:BIG FOOT.
July 9, 2015 Hyp cos defined en:strong array notation.
November 11, 2016 Peter Trueb computed \(\pi\) to 22,459,157,718,361 digits.[42]
January 5, 2017 Emlightened defined en:Little Bigeddon.
March 27, 2017 Emlightened defined en:sasquatch.
June 12, 2019 Special issue of large numbers was published in a Japanese mathematical journal 数学セミナー (Volume 693, July, 2019).
November 28, 2019 Special issue of large numbers was published in a Japanese mathematical contemporary philosophy journal 現代思想 (December, 2019).

Sources

  1. Henry Mendell, English translation of Archimedes, Sand-Reckoner (Arenarius)
  2. 大方広仏華厳経巻第四十五 阿僧祇品第三十
  3. Nicolas Chuquet (1484) Triparty en la science des nombres.
  4. Yoshida, M. (1631) "Jinkoki (塵劫記)"
  5. Jovanovic, R. (2005) Machin's Formula (archive)
  6. Kramp, C. (1808) Élémens d'arithmétique universelle, Cologne.
  7. Derrick N. Lehmer (1867-1938), University of California
  8. Derrick N. Lehmer (1909), Factor table for the first ten millions, Carnegie Institution of Washington, Washington, D.C.
  9. Vigintillion - Merriam-Webster Online
  10. Hardy, G.H. (1904), "A theorem concerning the infinite cardinal numbers", Quarterly Journal of Mathematics 35: 87–94.
  11. Laisant, C. A. (1906) Initiation mathématique: ouvrage étranger à tout programme dédié aux amis de l'enfance. Hachette & Cie, Paris. Paperback reprint.
  12. Ackermann, W. (1928). "Zum Hilbertschen Aufbau der reellen Zahlen". Mathematische Annalen 99: 118–133. doi:10.1007/BF01459088.
  13. Skewes, S. (1933) "On the Difference pi(x)-li(x)." J. London Math. Soc. 8, 277-283. doi:10.1112/jlms/s1-8.4.277
  14. Kasner, E. and Newman, J. R. (1989) Mathematics and the Imagination. Redmond, WA: Tempus Books, pp. 20-27.
  15. Goodstein, R. L. (1944). "On the restricted ordinal theorem". Journal of Symbolic Logic 9 (2): 33-41. doi:10.2307/2266486. JSTOR 2268019.
  16. Goodstein, R. L. (1947). "Transfinite Ordinals in Recursive Number Theory". Journal of Symbolic Logic 12 (4): 123–129. doi:10.2307/2266486. JSTOR 2266486.
  17. Reitwiesner, G. (1950) "An ENIAC determination of Pi and e to more than 2000 decimal places," MTAC, v. 4, 1950, pp. 11–15"
  18. Skewes, S. (1955) "On the Difference pi(x)-li(x). II." Proc. London Math. Soc. 5, 48-70.
  19. Rado, T. (1962) "On Non-Computable Functions." Bell System Technical J. 41, 877-884. doi:10.1002/j.1538-7305.1962.tb00480.x
  20. Graham, R. L. and Rothschild, B. L. (1971) "Ramsey's Theorem for n-Parameter Sets." Trans. Amer. Math. Soc. 159, 257-292.
  21. Knuth, D. E. (1976) "Mathematics and Computer Science: Coping with Finiteness." Science 194, 1235-1242. doi:10.1126/science.194.4271.1235
  22. Gardner, M. (1977) "Mathematical games: In which joining sets of points leads into diverse (and diverting) paths" Scientific American 237(5), 18-28. doi:10.1038/scientificamerican1177-18.
  23. Noll, C. and Nickel, L. (1980)The 25th and 26th Mersenne Primes, Mathematics of Computation, vol. 35, No. 152 (1980), pp. 1387–1390
  24. Kirby, L. and Paris, J. (1982) "Accessible independence results for Peano arithmetic" Bulletin of the London Mathematical Society 14: 285–293.
  25. Steinhaus-Moser Notation - MathWorld
  26. Hofstader, D. (1983) "The Largest Number Game" Scientific American.
  27. Buchholz, W. (1987) "An independence result for \(\Pi_1^1-\textrm{CA}+\textrm{BI}\)" Ann. Pure Appl. Logic 33 131-155.
  28. Page, D. N. (1994) "Information loss in black holes and/or conscious beings?", preprint for "Heat Kernel Techniques and Quantum Gravity", edited by S. A. Fulling (Discourses in Mathematics and Its Applications, No. 4, Texas A&M University Department of Mathematics, College Station, Texas, 1995)
  29. Conway, J. H. and R. Guy (1995) Book of Numbers, Copernicus.
  30. Pickover, C. A. (1995) Keys to Infinity Wiley, New York.
  31. Sloane, N. J. A. (1995) Sequence A000178/M2049 in "The On-Line Encyclopedia of Integer Sequences."
  32. Friedman, H. M. (2000) "Enormous integers in real life".
  33. Archive of Japanese BBS discussing large numbers in 2002
  34. Fish (2013) Googology in Japan - exploring large numbers
  35. Bowers, J. (2007) Exploding Array Function
  36. Bowers, J. (2007) Infinity Scrapers
  37. Saibian, S. (2008) One to Infinity: A Guide to the Finite
  38. Taranovsky, D. (2012) Ordinal Notation
  39. Goucher, A. P. (2013) The Ξ function
  40. Sam's Number (old revision)
  41. Older Updates - Pointless Large Number Stuff
  42. [1]
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