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La Lettre
© Photo Researchers, Inc - Alamy
Artist’s view of Ceres
© ESO
Carl Friedrich Gauss (1777-1855)
dear to me: in 1933, Torsten Carleman conducted the first mathematical study on the Boltzmann equation,
describing and predicting the statistical evolution of a gas that experiences unceasing collisions; today, the
mathematical literature on this topic is tens of thousand of pages long.
And mathematicians may now be counted by hundreds of thousand, operating within highly organized
research systems and publishing more than ever – and probably too much – in hundreds of specialized
journals, most of the time in collaboration with others; they gather all over the world, in a relentless
ballet of conferences, symposia and emails. The roles of mathematicians within the industry has been
acknowledged; they have been praised and reviled, and by times called criminals. The time of craft, of
Newton and his colleagues, is far away; and yet their questions are still ours, so as their unremitting desire
to understand and predict the phenomena, with is sometimes fulfilled, other times held in check.
Thus, to the question raised by Newton – Is the solar system stable? – after three hundred and fifty years
of work, the introduction of linear algebra, dynamical systems, probability theory, chaos theory, perturbed
Hamiltonian systems, symplectic schemes and the contributions of such sacred monsters as Laplace,
Lagrange, Poincaré and Kolmogorov – to this question, we may now confidently answer: “
Perhaps
!”
This “perhaps” is nothing we should be ashamed of, as it may be
quantified in probability terms, and as we know it is not
possible to do better: the outcome of the universe is
ruled by a set of probabilities, for lack of an infinite,
unreachable precision. Ultimately, in Newton’s
problem, we are faced with two well-known
conceptual monsters: chance and the infinite.
Prediction and unpredictability are two
themes entwined in each other throughout
this long story, which is not unlike a great
novel, with its share of ironic twists and
turns. Indeed, when Gauss managed to find
the lost orbit of the asteroid Ceres, then to
master Vesta’s, its little sister, the world seemed
most predictible; yet, some two centuries later,
our fellow Jacques Laskar would demonstrate
the perturbing effect Ceres and Vesta has
on the whole solar system, forbidding any
prediction beyond 60 million years. And as for