Very large numbers!
In science as well as in everyday life, we are led to encounter large numbers. The way to name them then depends, according to countries, on the choice of the scale used, long or short. The imagination of scientists, particularly mathematicians, being boundless, techniques for designating even larger numbers have been developed. This is the case, from Antiquity, with Archimedes' The Sand Reckoner. More recently, in the 20th century, John Conway and Donald Knuth developed new notations for numbers immensely larger than the number of elementary particles in the universe. And what is even more surprising, is that they are found in certain theories!
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Long and short scales: billion, trillion, milliard—how to name large numbers
From colossal fortunes to the limits of mathematical language, words struggle to keep pace as numbers explode. From long and short scales, through international conventions, to mathematicians' bold inventions, the way we name extremely large quantities tells a story in which language, science and imagination meet.
Knuth and Conway notations for mind-boggling numbers
When it comes to representing extremely large numbers, the standard operations, including exponentiation, are no longer enough. With considerable imagination, Donald Knuth and John Conway devised notations to overcome this limitation.
Archimedes' Sand Reckoner: counting the grains of sand in the universe
If the universe is finite, then it can be filled with grains of sand. Yes, it would take a great many, but the quantity required would still be a finite number—one that can be expressed. Drawing on the most advanced astronomical knowledge of his time, Archimedes set out to do just that.
Ackermann-Péter function: recursion without bounds
With a surprisingly simple definition, the Ackermann–Péter function generates numbers of a staggering size. This mathematical construction, born out of research into computability, shows how quickly a recursive procedure can exceed all the usual bounds.
Edward Kasner: the man behind googol and googolplex
Staggeringly large numbers invented by an eccentric mathematician that would inspire an iconic domain name...
Google: an almost accidental choice
In 1996, when they launched the famous search engine, Sergey Brin and Larry Page called it BackRub internally, a reference to its ability to identify and index even the most deeply hidden links (backlinks).
Skewes's numbers: enormous bounds in number theory
Skewes's numbers are among the large numbers encountered in arithmetic.
Mersenne primes: discover perfect numbers
The search for Mersenne primes very quickly leads us to examine gigantic numbers.