Quotes About Theorem

Thus the hexagon argument demonstrates ? > 3.

In other words, the diagonal of that square is irrational—and nowadays we recognize that number as the square root of two.

All polynomials of degree n-those that have a leading term of x^n- split into n distinct terms. This is the fundamental theorem of algebra.

The theorem is a hack on discrete number theory that simultaneously disproves the Church-Turing hypothesis (wave if you understood that) and worse, permits NP-complete problems to be converted into P-complete ones. This has several consequences, starting with screwing over most cryptography algorithms—translation: all your bank account are belong to us—and ending with the ability to computationally generate a Dho-Nha geometry curve in real time. This

As a rule of thumb, the sample size must be at least 30 for the central limit theorem to hold true.) This

Statistical inference is really just the marriage of two concepts that we've already discussed: data and probability (with a little help from the central limit theorem).

The central limit theorem tells us that a large sample will not typically deviate sharply from its underlying population

The central limit theorem tells us that the sample means will be distributed roughly as a normal distribution around the population mean.

Dullards would have you believe that once you have eliminated the impossible, whatever remains, however improbable, must be the truth... but to a mathematical mind, the impossible is simply a theorem yet to be solved. We must not eliminate the impossible, we must conquer it, suborn it to our purpose.

What she did pay attention to was that same sense of rightness, possessed by every theorem she learned, as insistent as the tiles' physicality, and as exact as their fit.

Finally, the third law of thermodynamics, initially formulated in 1906 as Walther Nernst's (1864–1941) heat theorem, states that all processes come to a stop (and entropy shows no change) only when the temperature nears absolute zero (–273°C).

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.

I took a break from acting for four years to get a degree in mathematics at UCLA, and during that time I had the rare opportunity to actually do research as an undergraduate. And myself and two other people co-authored a new theorem: Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Two Dimensions, or Z2.

You know, in formal logic, an inconsistent set of axioms can be used to prove anything at all. Once you have a single contradiction, A and not A, there's nothing you can't derive from it.

In PM, as Gödel said, "one can prove any theorem using nothing but a few mechanical rules.

Fermat's last theorem,

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

a continuous curve that goes from the lower half-plane to the upper half-plane must cross the horizontal axis at some point.

The oscillations-or waves-mandated by the Goldstone theorem originate in the application of symmetry operations to small domains.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[A] machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

Leonhard Euler

The story does what no theorem can quite do. It may not be "like real life" in the superficial sense: but it sets before us an image of what reality may well be like at some more central region.

I think I have met nearly all the Laureates in Economics. Among the few I haven't met, I suppose I'd most like to meet Ronald Coase because of his legendary power to persuade his colleagues of the validity of the Coase Theorem.

To analyse present-day systems in their catastrophic reality, to consider not only their failures and aporias but also the way in which they sometimes succeed only too well and get lost in the delusion of their own functioning, is to come face to face at every turn with the theorem or equation of the accursed share, and to find its indestructible symbolic power confirmed every time.