Make a translation of the texts.

Text A. Mathematics is about patterns (2, 000 characters).

The random workings of chance seem to be about as far from patterns as you can get. In fact, one of the current definitions of ‘random’ boils down to ‘lacking any discernible pattern’. Mathematicians had been investigating patterns in geometry, algebra, and analysis for centuries before they realised that even randomness has its own patterns. But the patterns of chance do not conflict with the idea that random events have no pattern, because the regularities of random events are statistical. They are features of a whole series of events, such as the average behaviour over a long run of trials. They tell us nothing about which event occurs at which instant. For example, if you throw a dice1 repeatedly, then about one sixth of the time you will roll 1, and the same holds for 2, 3, 4, 5, and 6 – a clear statistical pattern. But this tells you nothing about which number will turn up on the next throw.

Only in the nineteenth century did mathematicians and scientists realise the importance of statistical patterns in chance events. Even human actions, such as suicide and divorce, are subject to quantitative laws, on average and in the long run. It took time to get used to what seemed at first to contradict free will. But today these statistical regularities form the basis of medical trials, social policy, insurance premiums, risk assessments, and professional sports.

And gambling, which is where it all began. Appropriately, it was all started by the gambling scholar, Girolamo Cardano. Being something of a wastrel, Cardano brought in much needed cash by taking wagers on games of chess and games of chance. He applied his powerful intellect to both. Chess does not depend on chance: winning depends on a good memory for standard positions and moves, and an intuitive sense of the overall flow of the game. In a game of chance, however, the player is subject to the whims of Lady Luck. Cardano realised that he could apply his mathematical talents to good effect even in this tempestuous relationship. He could improve his performance at games of chance by having a better grasp of the odds – the likelihood of winning or losing – than his opponents did. He put together a book on the topic, Liber de Ludo Aleae (‘Book on Games of Chance’). It remained unpublished until 1633. Its scholarly content is the first systematic treatment of the mathematics of probability. Its less reputable content is a chapter on how to cheat and get away with it.

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Mathematical physics	\|	Text B. Mathematical physics (2, 000 characters).

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