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Date Event
c. 287 - 212 BCE Archimedes published The Sand Reckoner and defined unit of numbers up to \(10^{8 \cdot 10^{16}}\).
190 BCE Apollonius of Perga "the Great Geometer" wrote Conics, invented superscription notation for higher numbers in Roman numerals.
1st-7th century CE Number close to \(10^{10^{32}}\) was written in Buddhist scripture Avatamsaka Sutra.
1484 Nicolas Chuquet wrote an article Triparty en la science des nombres, the earliest work of a systematic, extended series of names ending in -illion.
1631 Japanese number system was defined up to muryoutaisuu in Jinkoki.[1]
1706 John Machen discovers hundredth digit of \(\pi\).[2]
1808 Christian Kramp uses the symbol ! for factorials.[3]
1811 Chernac lists prime factors to 1,020,000.
1856 Crelle lists 6 million primes.
1857 First known use of vigintillion.[4]
1861 Zacharias Dase lists 9 million primes.
1893 D. H. Lehmer lists 50,847,534 primes.
1904 Hardy hierarchy was defined.[5]
1906 Charles-Ange Laisant calculates \(^{3}9\) has 369,693,100 digits.[6]
1928 Ackermann function was published.[7]
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).[8] 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 Skewes Number.
1938 Googol was named.[9]
1944 Goodstein sequence was defined and Goodstein's theorem was proved.[10]
1947 Goodstein named tetration, pentation and hexation.[11]
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.[12]
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).[13] Notable for being a record holder for "largest number in a professional mathematics paper", and this number is now known as the second Skewes Number.
1962 Rado's sigma function was defined.[14]
1971 Graham's paper, describing the number now known as Little Graham, was published.[15]
1976 Knuth devised up-arrow notation.[16].
1977 Gardner wrote about the modern Graham's number in Scientific American, popularizing it to the general public.[17] He also wrote about Folkman's number.
1978 High school students Laura Ariel Nickel and Landon Cole Noll discovered 25th and 26th Mersenne primes.[18] As the 26th Mersenne prime is \(2^{23209}-1\), \(2^{23208}(2^{23209}-1)\ \approx 8.1 \cdot 10^{13972}\) 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 Graham's number was listed in Guinness World Records as the highest number ever used in a mathematical proof.
1982 Kirby-Paris hydra was defined.[19]
1983 Steinhaus-Moser notation was invented.[20] Douglas Hofstader promoted the "luring lottery" or "largest-number game" in Scientific American.[21]
1987 Buchholz hydra was defined.[22]
1991 Sbiis Saibian invents his poly-cell notations, a precursor to the modern Extensible-E System.
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.[23]
1995 Conway invented chained arrow notation.[24] Pickover defined Superfactorial and Leviathan number.[25] Sloane defined another type of superfactorial.[26]
1996 Robert Munafo's large number site was created.
February 26, 1998 The lynz was defined.
June 1, 2000 The Block subsequence theorem was invented.[27]
December, 2001 marxen.c and loader.c were created for Bignum Bakeoff.
2002 Array Notation and Extended Array Notation were invented.
June 29, 2002 Fish number 1 was created.[28][29]
2006 Bird's Array Notation was invented.
2007 Bowers considerably expanded Array Notation, inventing BEAF.[30]
January 26, 2007 Rayo's number was defined at Big Number Duel.
March, 2008 Meameamealokkapoowa oompa was defined.[31]
December 5, 2008 Googology Wiki was established.
December 9, 2008 One to Infinity[32] was published. Extensible-E System (Saibian's Array Notation) is developed in this book.
November 19, 2011 Sbiis Saibian introduced Hyper-E (E#) and Extended Hyper-E Notation (xE#).
March 16, 2012 Dmytro Taranovsky defined an ordinal notation up to the second order arithmetic.[33]
January 6, 2013 Adam P. Goucher defined Xi function.[34]
January 22, 2013 Sbiis Saibian introduced Cascading-E Notation (E^).
April, 2013 Hyperfactorial array notation was invented.
May, 2013 Bracket Notation (Dollar Function) was defined.
June 5, 2013 Wythagoras published the first version of Dollar Function.
September 11, 2013 Japanese googological webcomic Sushi Kokuuhen started.
November 10, 2013 Hyp cos defined R notation.
January 30, 2014 Sbiis Saibian introduced Extended Cascading-E Notation (xE^).
August 14, 2014 BASIC programs of primary sequence number and pair sequence number, which will later upgrade to Bashicu matrix system, were posted on Japanese BBS.
October 30, 2014 BIG FOOT was defined.
July 9, 2015 Hyp cos defined strong array notation.
January 5, 2017 Emlightened defined Little Bigeddon.
March 27, 2017 Emlightened defined sasquatch.

Sources Edit

  1. Yoshida, M. (1631) "Jinkoki (塵劫記)"
  2. Jovanovic, R. (2005) Machin's Formula
  3. Kramp, C. (1808) Élémens d'arithmétique universelle, Cologne.
  4. Vigintillion - Merriam-Webster Online
  5. Hardy, G.H. (1904), "A theorem concerning the infinite cardinal numbers", Quarterly Journal of Mathematics 35: 87–94.
  6. Laisant, C. A. (1906) Initiation mathématique: ouvrage étranger à tout programme dédié aux amis de l'enfance. Hachette & Cie, Paris. Paperback reprint.
  7. Ackermann, W. (1928). "Zum Hilbertschen Aufbau der reellen Zahlen". Mathematische Annalen 99: 118–133. doi:10.1007/BF01459088.
  8. 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
  9. Kasner, E. and Newman, J. R. (1989) Mathematics and the Imagination. Redmond, WA: Tempus Books, pp. 20-27.
  10. Goodstein, R. L. (1944). "On the restricted ordinal theorem". Journal of Symbolic Logic 9 (2): 33-41. doi:10.2307/2266486. JSTOR 2268019.
  11. Goodstein, R. L. (1947). "Transfinite Ordinals in Recursive Number Theory". Journal of Symbolic Logic 12 (4): 123–129. doi:10.2307/2266486. JSTOR 2266486.
  12. Reitwiesner, G. (1950) "An ENIAC determination of Pi and e to more than 2000 decimal places," MTAC, v. 4, 1950, pp. 11–15"
  13. Skewes, S. (1955) "On the Difference pi(x)-li(x). II." Proc. London Math. Soc. 5, 48-70.
  14. Rado, T. (1962) "On Non-Computable Functions." Bell System Technical J. 41, 877-884. doi:10.1002/j.1538-7305.1962.tb00480.x
  15. Graham, R. L. and Rothschild, B. L. (1971) "Ramsey's Theorem for n-Parameter Sets." Trans. Amer. Math. Soc. 159, 257-292.
  16. Knuth, D. E. (1976) "Mathematics and Computer Science: Coping with Finiteness." Science 194, 1235-1242. doi:10.1126/science.194.4271.1235
  17. 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.
  18. Noll, C. and Nickel, L. (1980)The 25th and 26th Mersenne Primes, Mathematics of Computation, vol. 35, No. 152 (1980), pp. 1387–1390
  19. Kirby, L. and Paris, J. (1982) "Accessible independence results for Peano arithmetic" Bulletin of the London Mathematical Society 14: 285–293.
  20. Steinhaus-Moser Notation - MathWorld
  21. Hofstader, D. (1983) "The Largest Number Game" Scientific American.
  22. Buchholz, W. (1987) "An independence result for \(\Pi_1^1-\text{CA}+\text{BI}\)" Ann. Pure Appl. Logic 33 131-155.
  23. 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)
  24. Conway, J. H. (1995) Book of Numbers PDF
  25. Pickover, C. A. (1995) Keys to Infinity Wiley, New York.
  26. Sloane, N. J. A. (1995) Sequence A000178/M2049 in "The On-Line Encyclopedia of Integer Sequences."
  27. Friedman, H. M. (2000) "Enormous integers in real life".
  28. Archive of Japanese BBS discussing large numbers in 2002
  29. Fish (2013) Googology in Japan - exploring large numbers
  30. Bowers, J. (2007) Exploding Array Function
  31. Bowers, J. (2007) Infinity Scrapers
  32. Saibian, S. (2008) One to Infinity: A Guide to the Finite
  33. Taranovsky, D. (2012) Ordinal Notation
  34. Goucher, A. P. (2013) The Ξ function

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