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  • The market can stay irrational longer than you can stay solvent. — John Maynard Keynes
  • I'm not so much concerned about the return on my money as the return of my money. — Will Rogers, 1933

Risk and Uncertainty

  • I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all. — קֹהֶלֶת (translation: Ecclesiastes 9:11, King James' Bible)
  • You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician. — Sherlock Holmes / Sir Arthur Conan Doyle, The Sign of Four


  • The job of a financial mathematician is not to predict prices but instead to relate the movements of price in one asset to that of another. — page 4, Mark Joshi, The Concepts and Practice of Mathematical Finance, Cambridge University Press, 2003
  • Mathematical bankers generally search for the arbitrage opportunities under some assumptions. Whilst all of these assumptions can be criticised, they provide a good starting point for modelling. The objective is more to come up with a good model than a perfect description. There is a certain similarity to physics here. Newtonian physics makes certain assumptions about the nature of space and time which are demonstrably wrong. However, bridges are built with Newtonian physics and they do not fall down (or at least not very often). The reason is that Newtonian physics provides a good approximation in the everyday world which only breaks down in the small subatomic world and the huge astronomical scale. Similarly, the models of mathematical finance provide good approximations under what one might call "normal" conditions, but they may perform less well in extremeties. However, just as in physics, the fact that models are not universally valid actually keeps people in work. — page 19, Mark Joshi, The Concepts and Practice of Mathematical Finance, Cambridge University Press, 2003


  • Thales [of Miletus — P.B.], so the story goes, because of his poverty was taunted with the uselessness of philosophy; but from his knowledge of astronomy he had observed while it was still winter that there was going to be a large crop of olives, so he raised a small sum of money and paid round deposits for the whole of the olive-presses in Miletus and Chios, which he hired at a low rent as nobody was running him up; and when the season arrived, there was a sudden demand for a number of presses at the same time, and by letting them out on what terms he liked he realised a large sum of money, so proving that it is easy for philosophers to be rich if they choose, but this is not what they care about. — Aristotle, Politics, 1259a
  • [An] economist steps over a $10 bill that's lying on the ground. His friend asks him why he didn't take the money. "It couldn't possibly be there," he explains. "If it were, somebody would've picked it up!" — This version of the old no-free-lunch/arbitrage joke appeared in Making Capitalism More Creative by Bill Gates (Time Magazine)


  • A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road he is at a stand. Whereas he that is able to reason nimbly and judiciously about figure, force, and motion, is never at rest till he gets over every rub. — Isaac Newton, from a letter dated 25 May, 1694
  • There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning: and when they cannot, it's a sign our knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great a folly to make use of any other, as to grope for a thing in the dark, when you have a candle standing by you. — John Arbuthnot, 1692, Preface, Of the Laws of Chance
  • Logic merely sanctions the conquests of the intuition. — Jacques Hadamard
  • If by knowledge of mathematics, one means an acquaintance with geometry, the calculus, and so forth, then it indeed appears to be true that very little of such knowledge is required [for understanding the essential ideas of game theory] beyond the ability to follow the process of solving some quite simple algebraic equations. However, the issue is not technical mathematical knowledge but rather mathematical background, that is, certain habits of thought usually acquired only through the study of mathematics. Similarly, it is not the ability to play an instrument that is required in order to follow the development of a musical thought, say in a symphony, but rather "musicality", certain habits of listening. The ability to think mathematically is like the ability to listen musically. Some of this ability may be inborn; some may be acquired without technical training; and much of it comes with technical training. — Anatol Rapoport, Two-Person Game Theory
  • Let no one who is unacquainted with geometry enter here. — Plato (an inscription over the entrance to his school of philosophy)
  • Would you have a man reason well, you must use him to it betimes; exercise his mind in observing the connection between ideas, and following them in train. Nothing does this better than mathematics, which therefore, I think should be taught to all who have the time and opportunity, not so much to make them mathematicians, as to make them reasonable creatures; for though we all call ourselves so, because we are born to it if we please, yet we may truly say that nature gives us but seeds of it, and we are carried no farther than industry and application have carried us. — John Locke, Conduct of the Understanding, Sect. 6
  • Empires die, but Euclid's theorems keep their youth forever. — Vito Volterra


  • Essentially, all models are wrong, but some are useful. — George Edward Pelham Box, Norman R. Draper, Empirical Model-Building and Response Surfaces, Wiley, p. 424.
  • The art of model building is to choose assumptions so that the model is unencumbered by less relevant considerations in order to illuminate more important phenomena. A good model provides insight and a guide to action. A good user of a model understands its limitations. — Steven E. Shreve, Did Faulty Mathematical Models Cause The Financial Fiasco?, Analytics Magazine, Spring 2009
  • The right way to engage with a model is to be like a reader of fiction — to suspend disbelief and then push ahead with the model as far as possible. — Emanuel Derman


  • Il semble que la perfection soit atteinte non quand il n'y a plus rien à ajouter, mais quand il n'y a plus rien à retrancher. (Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.) — Antoine de Saint Exupéry, L'Avion, Ch. III, p. 60.
  • The most important single aspect of software development is to be clear about what you are trying to build. — Bjarne Stroustrup
  • Premature optimisation is the root of all evil. — C. A. R. Hoare
  • Belated pessimisation is the leaf of no good. — Len Lattanzi
  • An ancient joke about C++ was that the language is called C++ and not ++C because the language is improved (incremented), but many people still use it as C (the previous value). — Herb Sutter (you must know the difference between the prefix and postfix operators to appreciate the humour of this quote)
  • Assembly language programming is an extravagant waste of human talent and should be avoided whenever possible. — Peter Norton (who wrote several books on the assembly language)



  • Many people would sooner die than think; in fact they do so. — Bertrand Russel
  • Proof by analogy is fraud. — Bjarne Stroustrup
  • People who think they know everything really annoy those of us who know we don't. — Bjarne Stroustrup


  • Quidquid latine dictum sit, altum sonatur.


  • I have made this letter longer than usual, because I lack the time to make it short. — Blaise Pascal


  • ignoranus [ĭg'nə-rā'nəs] — 1. (n.) A person who is both stupid and an a**hole. (


  • A happy man according to Thales of Miletus: "‘ο το μεν σωμα ‘υγιεις, τεν δε ψυχεν ευπορος, τεν δε φυσιν ευπαιδευτος" ("who is healthy in body, resourceful in soul and of a readily teachable nature").
  • Our plans miscarry because they have no aim. When a man does not know what harbour he is making for, no wind is the right wind. — Seneca the Younger
  • There is a tide in the affairs of men,
    Which, taken at the flood, leads on to fortune;
    Omitted, all the voyage of their life
    Is bound in shallows and miseries.
    We must take the current when it serves,
    Or lose our ventures.
    — Shakespeare
  • Luck favours the prepared mind. — Louis Pasteur
  • Ночь, улица, фонарь, аптека,
    Бессмысленный и тусклый свет.
    Живи ещё хоть четверть века —
    Всё будет так. Исхода нет.

    Умрёшь — начнёшь опять сначала,
    И повторится всё, как встарь:
    Ночь, ледяная рябь канала,
    Аптека, улица, фонарь.
    — Александр Блок
    Sometimes, exhausted
    with toil and endeavour,
    I wish I could sleep
    for ever and ever;
    but then this reflection
    my longing allays:
    I shall be doing it
    one of these days. — Piet Hein