The Sand Reckoner
In the problem of the Sand Reckoner, Archimedes tries to prove that the numbers are
infinite in a very indirect way. He uses the number of sand grains that would fill the
earth and the universe, as it was known at that time, to illustrate his point. Many of his
contemporaries thought, “no number has been named which is great enough to exceed
its multitude” where ‘its’ refers to the number of sand grains. Archimedes uses
geometric proofs to show that there is always a number greater than the number of sand
grains in any given container, in this case, the number of grains to fill a globe of the
volume of the earth. In order to do this, he describes an elaborate method of naming and
writing extremely large numbers.