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.

1st7th 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
 CharlesAnge 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 uparrow 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 26,790digit 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
 KirbyParis hydra was defined.^{[19]}

1983
 SteinhausMoser notation was invented.^{[20]} Douglas Hofstader promoted the "luring lottery" or "largestnumber game" in Scientific American.^{[21]}

1987
 Buchholz hydra was defined.^{[22]}

1991
 Sbiis Saibian invents his polycell notations, a precursor to the modern ExtensibleE System.

November 25, 1994
 Poincaré recurrence time of a Lindetype superinflationary 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. ExtensibleE System (Saibian's Array Notation) is developed in this book.

November 19, 2011
 Sbiis Saibian introduced HyperE (E#) and Extended HyperE 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 CascadingE 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 CascadingE 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.
