128 Quotes Tagged: mathematics

Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works.

"While ritual, emotion and reasoning are all significant aspects of human nature, the most nearly unique human characteristic is the ability to associate abstractly and to reason. Curiosity and the urge to solve problems are the emotional hallmarks of our species; and the most characteristically human activities are mathematics, science, technology, music and the arts — a somewhat broader range of subjects than is usually included under the "humanities." Indeed, in its common usage this very word seems to reflect a peculiar narrowness of vision about what is human. Mathematics is as much a "humanity" as poetry."

Just as we talk of poetic beauty, so we should also talk of mathematical beauty and medicinal beauty. But we do not talk like that for the very good reason that we know what the object of mathematics is, namely proof; and what the object of medicine is, namely cure; but we do not know what constitutes the attraction which is the object of poetry.

[...] Queste difficoltà possono essere risolte nel modo migliore facendo buon viso a cattivo gioco. I ritardi possono essere tollerati accettandoli ed elaborando una scansione temporale che li preveda. Si può poi tollerare una certa imprecisione nella risposta pensando in termini di <>. Così invece di dire: <>, noi diremo: <>. Le varie classi devono essere del tutto distinte e ben lontane dal sovrapporsi, cioé - topologicamente parlando - potremmo dire che devono avere tra loro una distanza finita. Con una decisione del genere avremo introdotto una ben definita divisione del lavoro tra il matematico e l'ingegnere, che permetterà a ognuno dei due di andare avanti senza preoccuparsi se le sue assunzioni siano in accordo con quelle dell'altro.

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.

In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is concern for content.

6.1 The propositions of logic are tautologies.
6.2 Mathematics is a logical method. The propositions of mathematics are equations, and therefore pseudo-propositions.
6.3 The exploration of logic means the exploration of everything that is subject to law. And outside logic everything is accidental.
6.4 All propositions are of equal value.
6.5 When the answer cannot be put into words, neither can the question be put into words. The riddle does not exist. If a question can be framed at all, it is also possible to answer it.

The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

We do not know space. We do not see it, we do not hear it, we do not feel it. We are standing in the middle of it, we ourselves are part of it, but we know nothing about it.

Une méthode est un truc qui a été utilisé plusieurs fois

A good notation should be unambiguous, pregnant, easy to remember.

You ask me if an ordinary person — by studying hard — would get to be able to imagine these things like I imagine. Of course. I was an ordinary person who studied hard. There's no miracle people. It just happens they got interested in this thing, and they learned all this stuff. They're just people. There's no talent or special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields that comes without practice and reading and learning and study. So if you take an ordinary person who's willing to devote a great deal of time and study and work and thinking and mathematics, then he's become a scientist.

Dejando de lado la metáfora, pienso que la filosofía de los antiguos griegos nos atrae hoy porque nunca antes o desde entonces, en ningún lugar del mundo, se ha establecido nada parecido a su altamente avanzado y articulado sistema de conocimiento y especulación sin la fatídica división que nos ha estorbado durante siglos y que ha llegado a hacerse insufrible en nuestros días.

Математика и опыт - вот подлинные основания достоверного, естественного, разумного живого познания.

But in my opinion, all things in nature occur mathematically.