Favourite quotations

Here are some of the things that have been said about mathematics that resonate with my own experience, or simply amuse me:

‘Do not worry about your difficulties in mathematics, I assure you that mine are greater.’ (Albert Einstein, 1879–1955)

‘The laws of mathematics are not merely human inventions or creations. They simply “are”; they exist quite independently of the human intellect. The most that any(one) … can do is to find that they are there and to take cognizance of them.’ (Maurits Escher, 1898–1972)

‘One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers.’ (Heinrich Hertz, 1857–94)

‘Mathematics is the art of giving the same name to different things.’ (Henri Poincaré, 1854–1912)

‘Beauty is the first test: there is no permanent place in the world for ugly mathematics.’ (G. H. Hardy, 1877–1947)

‘The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.’ (Aristotle, 384–322 BC)

‘I used to love mathematics for its own sake, and I still do, because it allows for no hypocrisy and no vagueness …’ (Stendhal, 1783–1842)

‘Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.’ (Bertrand Russell, 1872–1970)