Irrational Numbers Quotes

God made integers, all else is the work of man.

The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.

Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.

Nature never uses prime numbers. But mathematicians do.

There are infinite numbers between 0 and 1.

There might be a hidden structure in pi that we simply haven't discovered.

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.

Transcendental [numbers], They transcend the power of algebraic methods.

The soul may not be destroyed. The soul goes on forever. Like the number pi, it is without cessation or conclusion. Like pi it is a constant. Pi is an irrational number, incapable of being made into a fraction, impossible to divide from itself. So, too, the soul is an irrational, indivisible equation that perfectly expresses one thing: you.

Perfect numbers like perfect men are very rare.

It is impossible for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.

Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.

I chose the name Pi because it's an irrational number (one with no discernable pattern). Yet scientists use this irrational number to come to a "rational" understanding of the universe. To me, religion is a bit like that, "irrational" yet with it we come together we come to a sound understanding of the universe.

The fun little proofs that you can do with algebra - they are sort of like crowd pleasers in a way. Like, the .9 repeating equaling one. It doesn't take a lot of algebra to prove that, and it's really fun. It kind of wows people. It's like they're watching magic happen right before their eyes.

A prime number is one (which is) measured by a unit alone.

God may not play dice with the universe, but something strange is going on with the prime numbers.

If equations are trains threading the landscape of numbers, then no train stops at pi.

But it is impossible to divide a cube into two cubes, or a fourth power into fourth powers, or generally any power beyond the square into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it.