The Biggest Numbers Our Brains Can Fathom

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Graham's number (named after mathematician Ronald Graham) is the biggest number that's been used constructively -- but it's too big to even begin to think about. In fact, Graham's number is so big that it's impossible even to discuss the number of digits within it, or the number of digits within that number. But Graham's number wasn't always the biggest. Explore other massive numbers below.

Graham's Number, Explained By Ronald Graham

Hear about math's biggest number from the man who came up with it.

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Key Facts In This Video

  1. If you tried to picture Graham's number, your head would collapse into a black hole because your head cannot store the information required to imagine it. 00:30

  2. Three to the power of three to the power of three would be written as 3^(3^3), and the sum exceeds 7 trillion. 01:52

The Largest Number Before Graham

Hear about the math problem that led to this enormous number.

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Key Facts In This Video

  1. Before Graham's number, the largest number to be used in a mathematical proof was Skewes's number. 00:30

  2. Skewes' Number is trillions and trillions and trillions of digits long. A googol is only 100 digits long. 00:47

  3. Here's the problem the mathematicians were solving with this number. 02:10

What's The Difference Between a Googol and a Googolplex?

They're not the biggest numbers in the universe, but they are impressively massive.

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Key Facts In This Video

  1. A googol is 10 raised to the power of 100—in other words, a 1 with 100 zeroes after it. 00:33

  2. A googolplex is 10 raised to the power of googol. 02:53

  3. A universe that was a googolplex meters across would likely contain repeated versions of yourself. 03:56

The Story of Math's Biggest Numbers

There's a strange coincidence hiding in one large number.

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Key Facts In This Video

  1. Avogadro's number tells us how many atoms are in a lump of material. 01:32

  2. 10^40, or just N, corresponds to two important principles in physics. 03:15

  3. Here's how Robert Dicke sorted out the strange coincidence of 10^40 corresponding to both of these principles. 06:23