I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe. Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.
Marcus du SautoyRelated topics
arithmetic beginning built discovery eternal example humankind hydrogen indivisible mathematics mind multiplying number numbers oxygen prime prove pure teach thought universe world years greeksRelated quotes
To me there are two Hitlers: one who existed until the end of the French war; the other begins with the Russian campaign. In the beginning he was genial and pleasant. He would have extraordinary willpower and unheard-of influence on people. The important thing to remember is that the first Hitler, the man who I knew until the end of the French war, had much charm and goodwill. He was always frank. The second Hitler, who existed from the beginning of the Russian campaign until his suicide, was always suspicious, easily upset, and tense. He was distrustful to an extreme degree.
Hermann Göring
We live together, we act on, and react to, one another; but always and in all circumstances we are by ourselves. The martyrs go hand in hand into the arena; they are crucified alone. Embraced, the lovers desperately try to fuse their insulated ecstasies into a single self-transcendence; in vain. By its very nature every embodied spirit is doomed to suffer and enjoy in solitude. Sensations, feelings, insights, fancies - all these are private and, except through symbols and at second hand, incommunicable. We can pool information about experiences, but never the experiences themselves. From family to nation, every human group is a society of island universes.
Aldous Huxley
If... God highly exalted Christ because He humbled Himself, suffered dishonour, was tempted and endured a shameful cross and death for our sake, how will He save, glorify and raise us up if we neither choose humility, nor show love to our fellows, nor gain our souls by enduring temptation (cf. Lk. 21:19), nor follow the saving Guide through the 'strait gate' and along the 'narrow way' leading to eternal life (Mt. 7:14)? To this end we were called, says Peter, the chief Apostle, ' Because Christ also suffered for us, leaving us an example that we should follow His steps' (I Pet. 2:21).
Gregory Palamas
Arithmetic and geometry, according to Plato, are the two wings of the mathematician. The object indeed of all mathematical questions, is to determine the ratios of numbers, or of magnitudes ; and it may even be said, to continue the comparison of the ancient philosopher, that arithmetic is the mathematician's right wing; for it is an incontestable truth, that geometrical determinations would, for the most part, present nothing satisfactory to the mind, if the ratios thus determined could not be reduced to numerical ratios. This justifies the common practice, which we shall here follow, of beginning with arithmetic.
Jacques Ozanam
It is our endeavour to remove all kinds of divides-those between the high and low, touchables and untouchables-as well as other aspects of discrimination which have filled people's hearts with conflicts and divided the entire humanity into fragments...Rishi Valmiki taught us that in order to make progress in society, you have to take along Shabari with you; if you want your society to progress, you have to ensure that even vanars stand by you. If you want to move ahead, you have to embrace Kevat. ...We have come together at this place to express our commitment to follow his message.
Narendra Modi
