The Man Who Counted: A Collection of Mathematical Adventures

Geometry exist everywhere.It is necessary, however, to have eyes to see it, intelligence to understand it , and spirit to wonder at it.The wild Bedouin sees geometric forms but doesn't understand them ; the Sunni understands them but does not admire them; the artist, finally, perceives the perfection of figures, understands beauty, and admires order and harmony.God was the Great Geometer.He geometrized heaven and earth.

Every bird, with its wings outspread, is a book, its pages open to heaven.

Quien no desconfía de sí mismo  no merece la confianza de los otros.

Acautelai-vos - aconselhou - contra os juízos arrebatados pela paixão porque esta desfigura muitas vezes a verdade. Aquele que olha por um vidro de cor vê todos os objetos da cor desse vidro: se o vidro é vermelho, tudo lhe parece rubro; se é amarelo, tudo se lhe apresenta completamente amarelado. A paixão está para nós como a cor do vidro para os olhos. Se alguém nos agrada, tudo lhe louvamos e desculpamos; se, ao contrário, nos aborrece, tudo lhe condenamos, ou interpretamos de modo desfavorável.

A collection of facts is as far from forming a body of knowledge as a mirage in the desert is from being a real oasis.

What is this?" I asked him. "Are you sad? Do you feel a longing for your own country, or are you simply planning new calculations? Is it mathematics or nostalgia?" "My friend..." he replied, "nostalgia and calculations are not unrelated.

A poor wise man is he who seeks out the rich, but a nobler rich man he who seeks out wise men.

Only someone who has been even for a brief moment within the gloomy walls of a dungeon can know how to solve those problems in which numbers form a terrible part of human misery.

Even before the sun shone on us, even before there was air to breathe, the square of the hypotenuse was equal to the sum of the squares on the other two sides.

This is the wisdom of the proud--to find a mere crumb and call it the Himalayas.

Unhappy is he who assumes the burden of a debt whose worth cannot be measured by the simple means of his own intelligence.

The theory that we study today, and that appears to us impractical, might have implications in the future.... Who can imagine the repercussions of an enigma through the centuries?

To cultivate science only for its practical purpose is to despoil the soul of science.

[People] in general are good calculators.... the soldier on campaign who estimates distance in a single glance... the poet who counts syllables and verifies the cadence of his verses... the musician who applies in his compositions the laws of perfect harmony... the painter who draws with the unvarying proportions of perspective in his mind... the humble rug maker who arranges one by one the threads of his labor... All of these, O King, are fine and accomplished calculators.

If you do not know how to calculate exactly, your visions are worth nothing; if you arrive at them through calculation alone, I disbelieve them.

From the uncertainty of calculations comes the undeniable prestige of the mathematician.

It has never occurred to me that counting millions of leaves and swarms of bees could make money. Who could possibly be interested in how many branches there are in a tree, how many birds in a flight that crosses the sky?

El hombre sólo vale por lo que sabe. Saber es poder. Los sabios educan con el ejemplo, y nada hay que conquiste al espíritu humano más profundamente que el ejemplo (...) Socrates, filósofo griego, afirmaba con el peso de la autoridad enorme: "Sólo es útil el conocimiento que nos hace mejores". Séneca, otro pensador famoso, decía incrédulo: "¿Qué importa saber qué es una línea recta, si no se sabe lo que es la rectitud?".

La felicidad es difícil porque somos muy difíciles en materia de felicidad. No hables de felicidad a alguien menos feliz que tú. Cuando no se tiene lo que uno ama, hay que amar lo que se tiene.

Dame, Oh Dios, fuerzas para hacer que mi amor  sea fructífero y útil. Dame fuerzas para no despreciar jamás al pobre  ni plegar mis rodillas ante el poder insolente. Dame fuerzas para levantar el espíritu bien alto,  por encima de las banalidades cotidianas. Dame fuerzas para que me humille, con amor ante ti.

Que tu sabiduría no sea humillación para tu prójimo.  Guarda el dominio de ti mismo  y nunca te abandones a la cólera. Si esperas la paz definitiva,  sonríe al destino que te hiere y no hieras a nadie.

los números hace cuatrocientos años cuando un hindú, cuyo nombre no ha llegado hasta nosotros, creó un signo especial, el cero, para señalar en un número escrito la falta de toda unidad de orden decimal, no efectivamente representada en cifras. Gracias a este invento, todos los signos especiales, las letras y los apóstrofes resultaban inútiles. Así quedaron sólo nueve cifras y el cero. La posibilidad de escribir un número cualquiera por medio de diez caracteres solamente fue el primer gran milagro del cero.