Our Featured event for the week is the ZetaTrek Expedition, an online event organized by Rohit Gupta. In this guest post, Rohit updates us on the mysteries that his team of 21 participants has set out to explore.
Update From The ZetaTrek Expedition:
Ancient mysteries continue to haunt the team of 21 participants from 7 countries who have joined this quest thus far. More than two thousand years ago, for instance, the Greeks realized that the number 496 is a sum of its own proper divisors:
496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
Such a number they called a perfect number. Till this day, we do not know whether there is an infinite number of them. All the 47 known perfect numbers until the year 2011 are also even (multiples of 2), the largest number having 25956377 digits. Nor do we know if there exists a perfect number which is odd. We know that if an odd perfect number exists, it is many orders of magnitude larger than the estimated number of atoms in the observable universe. Another elementary observation, 496 is also the sum of all numbers below 31.
496 = 1 + 2 + 3 + 4……28 + 29 + 30 + 31
Here is a snapshot from the opening pages of the monumental book by
L. E. Dickson, History Of The Theory of Numbers Vol. I ( 1919 edition):
In 1984, it was discovered by physicists Michael Green and John Schwarz that superstring theory only makes sense if the dimension of a certain “gauge group” is the number 496. The link between numbers and cosmology that originated in mystical thought eons ago continues to bedazzle us today.