#mathematics

May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life. ↗

— James Joseph Sylvester

#dream #feels #life #mathematician #mathematics

The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence. ↗

— James Joseph Sylvester

#human intelligence #intelligence #intelligible #laws #mathematics

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics. ↗

— Edsger Dijkstra

#clumsy #consider #elegance #essential #further

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations. ↗

— Paul Lockhart

#math #mathematics #art

Real mathematics must be justified as art if it can be justified at all. ↗

— G.H. Hardy

#mathematics #art

The only problem i had with literature that I simply couldn't figure out was that the correct answer was the first thing that comes to your mind after reading the question, the most obvious one. I can only blame math for that. ↗

— Blin Varfi

#exams #highschool #humor #irony #literature

One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul. ↗

— Herbert S. Gaskill

#beauty

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos. ↗

— Gary William Flake

#mathematics #beauty

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. ↗

— Bertrand Russell

#beauty #math #mathematics #sculpture #art

My first feeling was that there was no way to continue. Writing isn't like math;in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel changes everything. ↗

— Stephenie Meyer

#mathematics #sadness #writing #change