Timeline of googology

== Pre-Googology Wiki ==
Date 	Event
c. 287 - 212 BCE 	Archimedes published 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.
c. 200 BCE - 100 AD	The Anuyoga Dwara Sutra likely defines Jaghanya Parīta Asaṃkhyāta as approximately \(10\uparrow \uparrow (1.285 \times 10^{136})\).
1st-7th century CE 	Number close to \(10^{10^{32}}\) was written in Buddhist scripture Avatamsaka Sutra.
1484 	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.Yoshida, M. (1631) "Jinkoki (塵劫記)"
1706 	John Machen discovers hundredth digit of \(\pi\).Jovanovic, R. (2005) Machin's Formula archived 2010-02-09.
1808 	Christian Kramp uses the symbol ! for factorials.Kramp, C. (1808) Élémens d'arithmétique universelle, Cologne.
1811 	Chernac lists prime factors to 1,020,000.
1856 	Crelle lists prime factors to 6 million.
1857 	First known use of vigintillion.Vigintillion - Merriam-Webster Online
1861 	Zacharias Dase lists prime factors to 9 million.
1893 	D. H. Lehmer lists 50,847,534 primes.
1904 	Hardy hierarchy was defined.Hardy, G.H. (1904), "A theorem concerning the infinite cardinal numbers", Quarterly Journal of Mathematics 35: 87–94.
1906 	Charles-Ange Laisant calculates \(^{3}9\) has 369,693,100 digits.Laisant, C. A. (1906) Initiation mathématique: ouvrage étranger à tout programme dédié aux amis de l'enfance. Hachette & Cie, Paris. Paperback reprint.
1928 	Ackermann function was published.Ackermann, W. (1928). "Zum Hilbertschen Aufbau der reellen Zahlen". Mathematische Annalen 99: 118–133. doi:10.1007/BF01459088.
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 \(\pi (x) > li(x)\).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 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.Kasner, E. and Newman, J. R. (1989) Mathematics and the Imagination. Redmond, WA: Tempus Books, pp. 20-27.
1944 	Goodstein sequence was defined and Goodstein's theorem was proved.Goodstein, R. L. (1944). "On the restricted ordinal theorem". Journal of Symbolic Logic 9 (2): 33-41. doi:10.2307/2266486. JSTOR 2268019.
1947 	Goodstein named tetration, pentation and hexation.Goodstein, R. L. (1947). "Transfinite Ordinals in Recursive Number Theory". Journal of Symbolic Logic 12 (4): 123–129. doi:10.2307/2266486. JSTOR 2266486.
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.Reitwiesner, G. (1950) "An ENIAC determination of Pi and e to more than 2000 decimal places," MTAC, v. 4, 1950, pp. 11–15"
1951 	Steinhaus wrote about mega and megiston in Mathematical Snapshots,Hugo Steinhaus. Mathematical Snapshots Oxford University Press, 1951. ISBN 9780486409146 which is a base of Steinhaus-Moser notation.Steinhaus-Moser Notation - MathWorld Note that it is not confirmed if it appears in 1938 edition.
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 \(\pi (x) > li(x)\).Skewes, S. (1955) "On the Difference pi(x)-li(x). II." Proc. London Math. Soc. 5, 48-70. 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 	The busy beaver function was defined by Tibor Radó and its first two values were computed.Rado, T. (1962) "On Non-Computable Functions." Bell System Technical J. 41, 877-884. doi:10.1002/j.1538-7305.1962.tb00480.x
1963 	The third value of the busy beaver function was proven by Shen Lin.Lin, Shen; Radó, Tibor (April 1965). "Computer Studies of Turing Machine Problems". Journal of the ACM. 12 (2): 196–212. https://doi.org/10.1145/321264.321270
1971 	Graham's paper, describing the number now known as Little Graham, was published.Graham, R. L. and Rothschild, B. L. (1971) "Ramsey's Theorem for n-Parameter Sets." Trans. Amer. Math. Soc. 159, 257-292.
1974 	The fourth value of the busy beaver function was proven by Allen Brady.Brady, Allen H. (April 1983). "The determination of the value of Rado's noncomputable function Σ(k) for four-state Turing machines". Mathematics of Computation. 40 (162): 647–665. doi:10.1090/S0025-5718-1983-0689479-6. JSTOR 2007539. He does not publish his result until 1983.Brubaker, Ben (2024-07-02). "Amateur Mathematicians Find Fifth 'Busy Beaver' Turing Machine". Quanta Magazine. Retrieved 2024-07-03.
1976 	Knuth devised up-arrow notation.Knuth, D. E. (1976) "Mathematics and Computer Science: Coping with Finiteness." Science 194, 1235-1242. doi:10.1126/science.194.4271.1235 .
1977 	Gardner wrote about the modern Graham's number in Scientific American, popularizing it to the general public.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. He also wrote about Folkman's number.
1978 	High school students Laura Ariel Nickel and Landon Cole Noll discovered 25th and 26th Mersenne primes.Noll, C. and Nickel, L. (1980)The 25th and 26th Mersenne Primes, Mathematics of Computation, vol. 35, No. 152 (1980), pp. 1387–1390 As the 26th Mersenne prime is \(2^{23,209}-1\), \(2^{23,208}(2^{23,209}-1)\ \approx 8.1 \cdot 10^{13,972}\) 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 as the highest number ever used in a mathematical proof.
1982 	Kirby-Paris hydra was defined.Kirby, L. and Paris, J. (1982) "Accessible independence results for Peano arithmetic" Bulletin of the London Mathematical Society 14: 285–293.
January 5-7, 1983 	A contest is held to find lower bounds for the fifth busy beaver. It is determined that Σ(5) ≥ 501 and S(5) ≥ 134,467.Ludewig, Jochen et al. Chasing the Busy-Beaver - Notes and Observations on a Competition to Find the 5-state Busy Beaver
1983 	Douglas Hofstader promoted the "luring lottery" or "largest-number game" in Scientific American.Hofstader, D. (1983) "The Largest Number Game" Scientific American.
1987 	Buchholz hydra was defined.Buchholz, W. (1987) "An independence result for \(\Pi_1^1-\textrm{CA}+\textrm{BI}\)" Ann. Pure Appl. Logic 33 131-155.
1990 	The Turing machine now known to be the five-state busy beaver is discovered by Heiner Marxen.Marxen, Heiner; Buntrock, Jürgen (February 1990). "Attacking the Busy Beaver 5". Bulletin of the EATCS. 40: 247–251.
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.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)
1995 	Conway invented chained arrow notation.Conway, J. H. (1995) The Book of Numbers. Copernicus. Pickover defined Superfactorial and Leviathan number.Pickover, C. A. (1995) Keys to Infinity Wiley, New York. Sloane defined another type of superfactorial.Sloane, N. J. A. (1995) Sequence A000178/M2049 in "The On-Line Encyclopedia of Integer Sequences."
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.Friedman, H. M. (2000) "Enormous integers in real life".
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.Archive of Japanese BBS discussing large numbers in 2002Fish (2013) Googology in Japan - exploring large numbers
2006 	Bird's Array Notation was invented.
2006 	Harvey Friedman discovers TREE(3).
2007 	Bowers considerably expanded Array Notation, inventing BEAF.Bowers, J. (2007) Exploding Array Function
January 26, 2007 	Agustin Rayo defined Rayo's number at Big Number Duel.
March, 2008 	Jonathan Bowers defined Meameamealokkapoowa oompa.Bowers, J. (2007) Infinity Scrapers
June 10, 2008 	Sbiis Saibian began working on One to Infinity.
== Googology Wiki era ==
Date 	Event
December 5, 2008 	Googology Wiki was established.
December 9, 2008 	One to InfinitySaibian, S. (2008) One to Infinity: A Guide to the Finite 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 conjecturally up to the second order arithmetic.Taranovsky, D. (2012) Ordinal Notation
January 6, 2013 	Adam P. Goucher defined Xi function.Goucher, A. P. (2013) The Ξ function
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 Kokuuhen started.
November 10, 2013 	Hyp cos defined R notation.
January 30, 2014 	Sbiis Saibian introduced Extended Cascading-E Notation (xE^).
February 25, 2014 	SammySpore creates Sam's Number, a notable "fake number" and an in-joke within the googology community.Sam's Number (old revision)
May 28, 2014 	Pointless Large Number Stuff was created.Older Updates - Pointless Large Number Stuff
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 	LittlePeng9 defined BIG FOOT.
July 9, 2015 	Hyp cos defined strong array notation.
November 11, 2016 	Peter Trueb computed \(\pi\) to 22,459,157,718,361 digits.Trueb, P. (2016) Digit Statistics of the First 22.4 Trillion Decimal Digits of Pi. arXiv:1612.00489
January 5, 2017 	Emlightened defined Little Bigeddon.
March 27, 2017 	Emlightened defined 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).
December 3, 2019 	P進大好きbot defined Large Number Garden Number.
March 7, 2022 	DeepLineMadom pointed out Sam's Number as an actually non-number and has been removed from list of googolisms/Uncomputable numbers.
May 10, 2024 	BBChallenge user mxdys proves the fifth value of busy beaver.ccz181078. Coq-BB5. GitHub.
== Sources ==
ja:巨大数の年表
Category:Time