The speaker discusses Graham's number, a massive number developed by mathematician Ronald Graham in 1971. Graham's number is the solution to a problem involving combinatorics and graph theory. It is so large that it cannot be written out in standard numerical notation, requiring instead the use of arrow notation. The number is constructed by iteratively applying the operation of exponentiation, with each step producing a number that is exponentially larger than the previous one. The speaker explains that Graham's number is so enormous that it is difficult to comprehend, with its last digit being 7 and its last 500 digits being known. The actual value of the number is between 11 and Graham's number, and mathematicians consider this range to be a precise answer. The speaker also mentions that Graham's number is not the largest number used in mathematics, but it is still an incredibly large number that is often cited as an example of a massive number.
Here are the key facts extracted from the text:
1. Graham's number is the largest number ever used constructively in mathematics.
2. If you tried to picture all the graves in the world, your head would collapse into a black hole.
3. The maximum amount of information that can be stored in your head is related to the size of a black hole the size of your head.
4. The entry of a black hole the size of your head carries less information than it would take to write out Graham's number.
5. If you started to try to write out Graham's number in your head, your head would eventually collapse into a black hole.
6. Arrow notation is used to represent extremely large numbers.
7. Three to the power of 27 is approximately 7.6 trillion.
8. Graham's number was developed in 1971 as the maximum possible number of people needed to guarantee a certain condition.
9. The smallest number of people required for this condition to be true is between 6 and Graham's number.
10. Graham's number is so large that it cannot be described using traditional notation.
11. We do not know what the first digit of Graham's number is.
12. The last digit of Graham's number is 7.
13. We know the last 500 digits of Graham's number.
14. Recently, mathematicians have narrowed down the range of possible numbers to between 11 and Graham's number.
15. Graham's number is not the largest number ever used in mathematics, but it is still extremely large.
16. Ronald Graham, the mathematician who developed Graham's number, was also a circus performer.