“The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done.”

- R. Askey, The American Mathematics Monthly

“...throughout the city, artists sharpen pencils and dip brushes and tune guitars. Others (mathematicians), with their theorems and equations revel just as much in the world’s possibilities. / The world needs artists. Into words and pictures, notes and numbers each transforms their portion of the night. A mathematician at his desk glimpses something hitherto invisible. He is about to turn darkness into light.”

- Daniel Tammet, Thinking in Numbers

“No branch of education is considered so valuable a preparation for household management and politics, and all arts and crafts, sciences and professions, as arithmetic; best of all by some divine art it arouses the dull and sleepy brain, and makes it studious, mindful and sharp.”

-Plato, on why the understanding of mathematics was critical to entering the Academy

“If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.”

- Galileo Galilei

“The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”

- Charles Celeb Cotton

“One of the most amazing things about mathematics is the people who do math aren’t usually interested in application, because mathematics itself is truly a beautiful art form. It’s structures and patterns, and that’s what we love, and that’s what we get off on.”

- Danica McKellar

“A lot of music is mathematics. It’s balance.”

- Mel Brooks

“The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.”

- Gottfried Wilhelm Leibniz

“Mathematics is the door and key to the sciences.”

- Roger Bacon

“Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world.”

- Roger Bacon

“As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.”

- Joseph Louis Lagrange

“This, therefore, is Mathematics: She reminds you of the invisible forms of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings to light our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth…”

- Diadochus Proclus

“The understanding of mathematics is necessary for a sound grasp of ethics.”

- Socrates

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”