5 reasons why Graham's Number is the most mind-boggling

Graham's number is a gigantic natural number that was defined by a man named Ronald Graham, a mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years".

Graham was solving a problem in an area of mathematics called Ramsey theory. He proved that the answer to his problem was smaller than Graham's number.

Graham's number is one of the biggest numbers ever used in a mathematical proof and mathematicians believe there is not enough space in the whole universe to transcribe all of the digits, or in other words - it cannot be represented in the observable universe.

Ronald Graham juggling a four ball fountain (1986)


1. Guinness Book Of World Records

The number was published in the 1980 Guinness Book of World Records after the popular science writer Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977 as "a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof."

2. At The Time Of Its Creation...

Graham's number was the largest specific positive integer ever to have been used in a published mathematical proof at the time of its introduction.

3. Close Enough To Infinity

Many scientists describe it to be probably "close enough" to infinity!

4. Your Head Would Collapse Into a Black Hole?!

The basis of this mind-bending theory is that only so much information can be stored within a finite space, according to the laws of physics.

Physics Astronomy's website writes, "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," and many others agree with the same.

5. The Mind-Boggling Up-Arrows...

  • In order to be able to write Graham's number down, we have to use Knuth's up-arrow notation in which a sequence of numbers are used to define the following ones
  • When we reach the 64th number, it will be Graham's mind-boggling number
  • However, what's stunning is that this process of up-arrows extends to a scale that could fill up the universe and beyond.

For example:

Conclusion: Don't try to memorize Graham's number at home folks ... this number could do some serious harm! :)

Take a moment to celebrate some of the amazing achievements from people who had virtually no education at all.

He isn’t the one to let something like being the fourth richest man on the planet stop him from getting a good deal.

There is no Nobel Prize for mathematics, but there are equivalents...