On Numbers: Perfect Numbers II

"It is the greatest that will ever be discovered, for, as they [perfect numbers] are merely curious without being useful, it is not likely that any person will attempt to find one beyond it." (Peter Barlow, "Theory of Numbers", 1811)

“The Perfect numbers are also like the virtues, few in number; whilst the other two classes are like the vices - numerous, inordinate and indefinite.” (W Wynn Westcott, “Numbers: Their Occult Power and Mystic Virtues”, 1911)

“The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. ‘Perfect numbers’ certainly never did any good, but then they never did any particular harm.” (John E Littlewood, “A Mathematician’s Miscellany”, 1953)
”Maybe some simple combination of a dozen or so primes in fact yield an odd perfect number!” (Stan Wagon, “The evidence: perfect numbers”, Mathematical Intelligencer 7(2), 1985)

”Yet, I believe the problem stands like a unconquerable fortress. For all that is known, it would be almost by luck that an odd perfect number would be found. On the other hand, nothing that has been proved is promising to show that odd perfect numbers do not exist. New ideas are required.” (Paulo Ribenboim, “The New Book of Prime Number Records”, 1996)

“We should not leave unmentioned the principal numbers […] those which are called ‘perfect numbers’. These have parts which are neither larger nor smaller than the number itself, such as the number six, whose parts, three, two, and one, add up to exactly the same sum as the number itself. For the same reason twenty-eight, four hundred ninety-six, and eight thousand one hundred twenty-eight are called perfect numbers.” (Stanley J Bezuszka & Margaret J Kenney, ”Even perfect numbers”, Math. Teacher 90, 1997)

”Throughout both ancient and modern history the feverish hunt for perfect numbers became a religion.” (Clifford A Pickover, “Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning”, 2001)

"One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery - and more totally useless - than the perfect numbers." (Martin Gardner)

Resources:Wikipedia (2018) List of perfect numbers [Online] Available from: https://en.wikipedia.org/wiki/List_of_perfect_numbers