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.