Quotes About Mathematics

An algebraic integer of degree two is simply a root of a quadratic polynomial of the form X2 + aX + b with a, b ordinary integers.

the second derivative conveys just the idea we want—a comparison between the value at x and the average value near x. It is worth noting that if f is linear, then the average of f(x - h) and f(x + h) will be equal to f(x), which fits with the familiar fact that the second derivative of a linear function f is zero.

there are only four units in the ring R-1 of Gaussian integers, namely ±1 and ±i; multiplication by any of these units effects a symmetry of the infinite square tiling

Fundamental to understanding the arithmetic of Rd is the following question: which ordinary prime numbers p are irreducible elements of Rd and which ones factorize as products of irreducible elements in Rd? We will see shortly that if a prime number does factorize in Rd, it must be expressible as the product of precisely two irreducible factors.

if, for each t, we write u(t) for the function from to that takes x to u(x, t), then it describes how the function u(t) "evolves" over time. The Cauchy problem for an evolution equation is the problem of determining this evolution from knowledge of its initial value u(0).

A3 0 is an additive identity: 0 + a = a for any number a. That is all you need to know about 0. Not what it means – just a little rule that tells you what it does.

Mathematics is the supreme judge; from its decisions there is no appeal.

I always thought that I was okay with arithmetic.

My older brother was the person who got me interested in science in general. He used to tell me what he learned in school. My first memory of mathematics is probably the time that he told me about the problem of adding numbers from 1 to 100.

Mathematicians among my readers do not need to be informed that . . . is the algebraical sign representing a blend of wheeze, croak, and hiccough.

And with which numbers does the ant subtract its dead soldiers? Y con que cifras va restando la hormiga sus soldados muertos?

PHI is one H of a lot cooler than PI!

When the ancients discovered 'Phi', they were certain they had stumbled across God's building block for the world.

The mathematics of Malthus? A quick Internet search led him to information about a prominent nineteenth-century English mathematician and demographist named Thomas Robert Malthus, who had famously predicted an eventual global collapse due to overpopulation.

Ever since I was a child, I've had the gut sense that there's a consciousness behind the universe. When I witness the precision of mathematics, the reliability of physics, and the symmetries of the cosmos, I don't feel like I'm observing cold science; I feel as if I'm seeing a living footprint…the shadow of some greater force that is just beyond our grasp.

As we mathematicians like to say: PHI is one H of a lot cooler than PI!

However, when they try to look back to the instant when the Big Bang occurred—where T equals zero—the mathematics all goes mad, describing what seems to be a mystical speck of infinite heat and infinite density.

based on a single variable! Every single line on this graph

desde un punto de vista meramente científico, atendiendo sólo a la lógica, no a los sentimientos, puedo asegurarte que, si no tiene lugar un cambio drástico, el fin de nuestra especie se acerca. Y ocurrirá con rapidez. No consistirá en fuego, azufre, el Apocalipsis o una guerra nuclear..., sino en el colapso total a causa de la cantidad de gente que habita el planeta. Las matemáticas son indiscutibles.

Cineva trebuie s? duc? acest r?zboi, altfel, ?sta-i viitorul nostru. Matematica îl garanteaz?. Omenirea se complace acum într-un purgatoriu al nehot?rârii, al procastin?rii È™i al l?comiei personale... dar cercurile iadului aÈ™teapt? imediat sub picioarele noastre, gata s? ne înghit? pe toÈ›i.

She knew the computer's processors auditioned thirty million keys per second – one hundred billion per hour. If TRANSLTR was still counting, that meant the key had to be enormous – over ten billion digits long.

When I witness the precision of mathematics, the reliability of physics, and the symmetries of the cosmos, I don't feel like I'm observing cold science; I feel as if I'm seeing a living footprint…the shadow of some greater force that is just beyond our grasp.

Outside the port, the slashed rock of the unnamed asteroid tumbled and spun in dynamics known only to the gods of chaos mathematics.

In 1792 their decimal calendar replaced the 7-day week by a 10-day week called a décade, each day of which was given a Latin numerical name, three of which comprised a month. The day was divided into ten hours, each consisting of 100 minutes, each minute of 100 seconds.