Quotes About Mathematics

How many of you have broken no laws this month? That's the kind of society I want to build. I want a guarantee - with physics and mathematics, not with laws - that we can give ourselves real privacy of personal communications.

Now, I'd like to ask people in the room, please raise your hand if you have not broken a law, any law, in the past month... That's the kind of society I want to build. I want to guarantee — with physics and mathematics, not with laws — that we can give ourselves real privacy of personal communications.

The lack of solutions to the Three-Body Problem is not caused by our human deficiencies as mathematicians, it is build into the laws of mathematics.

You know, people think mathematics is complicated. Mathematics is the simple bit. It's the stuff we can understand. It's cats that are complicated. I mean, what is it in those little molecules and stuff that make one cat behave differently than another, or that make a cat? And how do you define a cat? I have no idea.

How does the industry seek to master the risks? Through mathematics. The common-sense version of what sophisticated investors do is diversification, a technique so old it's mentioned in the Talmud, where the strategy advocated is to have a third of your assets in trade, a third in cash and a third in land.

We see that music, like the world, is formed from unchanging mathematical principles deployed in time, creating complexity, variety and beauty.

Ludwig Schlafi (1814-1895) proved that there are six regular four-dimensional polytopes (generalisations of polyhedra): the 5-cell made of tetrahedra, the 8-cell or tesseract made of cubes, the 16-cell made of tetrahedra, the 24-cell made of octahedra, the 120-cell made of dodecahedra, and the 600-cell made of tetrahedra.

If you kept on spiraling you would eventually discover, as the Chinese did long ago, that 53 perfect fifths (or Lu) almost exactly equal 31 octaves. The first five fifths produce the pattern of the black notes on a piano, the Eastern pentatonic scale.

The rhombic dodecahedron is a three-dimensional shadow of the four-dimensional tesseract analogous to the hexagon as a two-dimensional shadow of the cube.

Schlafi also proved that in five or more dimensions the only regular polytopes are the simplex, or generalized tetrahedron, the hypercube, or generalized cube, and the orthoplex, or generalized octahedron.

Many familiar objects from cassettes to credit cards and Georgian front doors are Phi (1.618...) rectangles.

When one circle is drawn over another like this so that they pass through each others' centers, then an important almond shape, the vesica piscis, literally 'fish's bladder' is formed. It is one of the first things that circles can do. Christ is often depicted inside a vesica.

The dodecagon is also made from six squares and six equilateral triangles fitted around a hexagon

Twelve is the number which fits around one in three dimensions in the same way that six fits around one in two dimensions. The New Testament is a story of a teacher surrounded by twelve disciples.

Eleven is important as the first number that allows us to begin to comprehend the measure of a circle. This is because, for practical purposes, a circle measuring seven across will measure eleven halfway around.

The ancient Maya were superb stargazers. Their calendar synchronized not just the Sun and Moon, byt also Venus and Mars. They worked out that 81 (or 3X3X3X3) full moons occur exactly every 2,392 (or 8X13X23) days, an astonishingly accurate gearing.

Once you absorb the maths, it's all perfectly clear.

The only God is in the numbers and the fire; in the equations and the furnace

Patty felt another blush stain her cheeks as she drew her knees up and, hurrying her feet under her bulk, hid herself in differential equations again.

Mathematicians need to understand a problem only for themselves; math teachers need both to know the math and to know how 30 different minds might understand (or misunderstand) it. Then they need to take each mind from not getting it to mastery. And they need to do this in 45 minutes or less.

One wanted children; had them, and brought them up: and then, in spite of all the calculations of time and care, they defeated one by producing a result which seemed, to say the least, almost mathematically incorrect.

Though my love for you is infinitesimal, your eyes are as dewey as any old decimal.

Poetry, architecture, music, philosophy and mathematics all intrigued him and he was patron of them all, surrounding himself with men of genius: the poet and satirist Juvenal, the architect Apollodorus, the historians Tacitus, Suetonius and Arrian, the writers Pliny the Younger, Pausanias and Plutarch.

And as his research continued in Syracuse, Archimedes made sure word of what he was doing got back to friends in Alexandria. Among his correspondents was a former Croton pupil named Dositheusa to whom Archimedes would send one major treatise after another that would revolutionize mathematics. There was Quadrature of the Parabola, then two books on Sphere and Cylinder, one on Spiral Lines, and finally a treatise on Conoids and Spheroids.27