Ivar Ekeland

Ivar Ekeland (born 2 July 1944, Paris) is a French mathematician of Norwegian descent. Ekeland studied at the École Normale Supérieure (1963–1967). He is a Senior Research Fellow at the French National Centre for Scientific Research (CNRS). He obtained his doctorate in 1970. He teaches mathematics and economics at the Paris Dauphine University, at the École Polytechnique, at the École Spéciale Militaire de Saint-Cyr, and at the University of British Columbia in Vancouver.

The Best of All Possible Worlds (2006)

 * The optimist believes that this is the best of all possible worlds, and the pessimist fears that this might be the case.
 * Introduction, p. 1.


 * We do not discover mathematical truths; we remember them from our passages through this world outside our own.
 * Chapter 1, Keeping The Beat, p. 6.


 * The world is full, at every scale, and every scale ignores the higher and lower ones.
 * Chapter 2, The Birth of Modern Science, p. 34.


 * So every possible reality, once God gives it existence, will reveal its own identity. Its life will unfold slowly, whereas God encompasses it at a single glance.
 * Chapter 2, The Birth of Modern Science, p. 39.


 * Nowadays, however, we are much more aware of the fact that the best proof in the world is worth no more than its premises: every scientific theory is transitory and provisional, in wait for a better one, and accepted only as long as the experimental results conform to its predictions.
 * Chapter 3, The Least Action Principle, p. 48.


 * It is a testimony to the power of education that classical mechanics could operate for so long under a mistaken conception. Teaching and research concentrated on integrable systems, each feeding the other, until in the end we had no longer the tools nor the interest for studying nonintegrable systems.
 * Chapter 4, From Computation To Geometry, p. 84.
 * The transition from integrable to non integrable systems is quiet interesting to observe.
 * Chapter 4, From Computation To Geometry, p. 100.


 * If there is a God, he has left no tracks in the laws of physics; or if he has, he has covered them up very well.
 * Chapter 6, Pandora's Box, p. 122.


 * Chaos cuts with two edges. We have seen how it is impossible to retrieve past history from current observations. We will now show that it is impossible to predict future states from the current observations.
 * Chapter 6, Pandora's Box, p. 127.


 * Many great failures and many great successes are due to chance and not to human folly or ingenuity.
 * Chapter 7, May The Best One Win, p. 138.


 * An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory.
 * Chapter 7, May The Best One Win, p. 141.


 * In the struggle for life, or in the struggle for power, there is no reason why their victory would make the world better than it was. There is no invisible hand guiding these processes, dealing out victory to the most deserving. Chance is their leader.
 * Chapter 7, May The Best One Win, p. 144.


 * The measurement of time was the first example of a scientific discovery changing the technology.
 * Chapter 8, The End of Nature, p. 150.


 * The moment when the scientists became engineers was a historical turning point.
 * Chapter 8, The End of Nature, p. 152.


 * The social world is not driven by natural laws and randomness alone, as the physical world is, but also by human wills.
 * Chapter 8, The End of Nature, p. 162.
 * Power is no linger seen as inheriting its legitimacy from some divine authority; it is a mere convention which we adhere to because we are born and educated into it, and because we see others conform to it. Its strength lies in the fact that we believe that others believe in it: power is no more than the illusion of power. The exercise of power is a constant fight to keep up appearances.
 * Chapter 8, The End of Nature, p. 164.


 * Well, it has been a long time since manna last fallen from from heaven. We cannot live alone; we rely on others to produce the stuff of our material and intellectual life, and we have to organize society so that its members will cooperate toward the common good.
 * Chapter 9, The Common Good, p. 167.


 * What is needed is courage: it is always so much easier to accept what you are being told than to think for yourself.
 * Chapter 10, A Personal Conclusion, p. 188.