Definition:Graham's Number/Historical Note
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Historical Note on Graham's Number
Ronald Lewis Graham arrived at his number as an upper bound to the solution to a certain problem in Ramsey theory.
Strictly speaking, the number used by Graham is somewhat smaller than the number described here, but is less easily described.
This version is the one given to Martin Gardner, who then publicised it in his Mathematical Games column in Scientific American.
It entered the record books as the largest number ever used in a mathematical proof.
Amusingly, given that Graham's number is an upper bound, the actual solution to the problem in question, according to certain experts, may well be $6$.
Sources
- November 1977: Martin Gardner: Mathematical Games (Scientific American Vol. 237, no. 5: pp. 18 – 28)
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3 \uparrow \uparrow \uparrow 3$ etc., etc.
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3 \uparrow \uparrow \uparrow 3$ etc., etc.