Quotable Mathematics

The following two quotes from Carl Friedrich Gauss are frequently met in books on Mathematics and Science (sometimes with slight differences...

"A great deal of misunderstanding is avoided if it be remembered that the terms infinity, infinite, zero, infinitesimal must be interpr...

"Number theory is revealed in its entire simplicity and natural beauty when the field of arithmetic is extended to the imaginary number...

"It is the greatest that will ever be discovered, for, as they [perfect numbers] are merely curious without being useful, it is not lik...

"Factoring big numbers is a strange kind of mathematics that closely resembles the experimental sciences, where nature has the last and...

"[Number theory] produces, without effort, innumerable problems which have a sweet, innocent air about them, tempting flowers; and yet…...

"We do not perceive any quantity such as that its square is negative!" (Bhāskara II, "Bijaganita", 12th century) ...

"On the basis of what has been proved so far, it remains possible that there may exist (and even be empirically discoverable) a theorem...

“On the basis of what has been proved so far, it remains possible that there may exist (and even be empirically discoverable) a theorem-prov...

“A perfect number is that which is equal to the sum of its own parts.” (Euclid, “Elements”, cca. 300 BC) “ If as many numbers as we please...

“Since primes are the basic building blocks of the number universe from which all the other natural numbers are composed, each in its own un...

"The prime numbers are useful in analyzing problems concerning divisibility, and also are interesting in themselves because of some of ...

"[…] in the science of numbers ought to be preferred as an acquisition before all others, because of its necessity and because of the g...

“A prime number is one (which is) measured by a unit alone.” (Euclid, “The Elements”, Book VII)  “Numbers prime to one another are those w...

"The prime numbers are useful in analyzing problems concerning divisibility, and also are interesting in themselves because of some of ...