Quick: Whatâ€™s the biggest number you can think of? Okay, timeâ€™s up. Mine was 85. Iâ€™m proud of it. But as it turns out, there are even larger numbers. In a recent post at the explainer blog *Wait But Why*, Tim Urban teaches readers about Grahamâ€™s Number, one of the largest figures commonly referenced in mathematics.

Urban approaches Grahamâ€™s Number by going beyond multiplication (e.g., 3 times 3) and exponentiation (3^3) into stranger realms of tetration, pentation, and hexation. With care and enthusiasm, Urban details these mathematical processes and how they eventually lead to Grahamâ€™s Number, which once held the world record for the largest number cited in a â€śserious mathematical proofâ€ť (until it was superseded, presumably, by Grahamâ€™s Number + 1).

Grahamâ€™s Number is so big that itâ€™s impossible to explicitly compute, let alone write down. We actually can figure out the last few digits, but thatâ€™s itâ€”nobody knows how it begins, so you couldnâ€™t write it down in decimal form. We can talk about it, though, and express it in more abstract terms. As you might imagine, getting at Grahamâ€™s Number involves some mind-bending mathematics. Urbanâ€™s explanation includes images like thisâ€¦

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â€¦and thisâ€¦

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â€¦but if you take it slow, you should be able to follow along. Once the outlandish vastness of Grahamâ€™s Number is fomenting a deep existential terror within you, then youâ€™re getting the idea.

If Urbanâ€™s article doesnâ€™t do it for you, here is mathematician Ron Graham himself explaining the origin of the number with his name on it:

And hereâ€™s another video in which Graham talks about how the number is calculated:

I still think 85 is pretty big.

[via *Kottke.org*]

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