... the German army invaded a large part of France that included Paris, and there followed in the spring and summer of 1940 a southward exodus of civilians. Paulette and her family took refuge in Lyons, where she was able to sit for two examinations. She then travelled to Toulouse to sit for additional examinations. She returned to Paris with her family in autumn. Part of the École had moved to Paris after the German troops occupied the building in Sèvres, and she prepared for the agrégation while living with her family.

With a kind of black humour, Paulette Libermann used to say that the anti-Semitic laws had been lucky for her, since Élie Cartan, who was teaching these young ladies, suggested that she start research instead [of becoming a teacher].

The equivalence problem is a general problem and has been investigated by many including Élie Cartan. Roughly speaking, the question is to classify, up to local isomorphism, structures on manifolds. For instance, all the manifolds of the same dimension are equivalent (this is a local question). But this is not true anymore if the manifolds are endowed with Riemannian metrics: a (curved) sphere is not locally isometric to a (flat) plane.

When the Faculty of Science of the University of Paris split after 1968, mostly along ideological lines, she chose Paris VII in accordance with her left-leaning convictions.

She was quietly daring but also very faithful: to Élie Cartan of course, whose vision of the world was perpetuated by her seminar with Yvette Kosmann, during a period where his viewpoint was a bit out of fashion; and even more significantly to Ehresmann, gradually marginalised after having occupied a central focus in the mathematics of his time. At the Kosmann-Libermann seminar, the 'a fortiori' marginalised students of this great mind could express themselves. Paulette Libermann was in a good position to understand the meaning of both their work and exclusion. Perhaps due to the help that she had received from Élie Cartan as a beginner, she was always ready to welcome and encourage previously unknown young mathematicians, including Michèle Audin, Daniel Bennequin, Jean-Pierre Françoise and the author of this article [Marc Chaperon].

During the last two centuries, analytical mechanics have occupied a prominent place among scientists' interests. The work in this field by such mathematicians as Euler, Lagrange, Laplace, Hamilton, Jacobi, Poisson, Liouville, Poincaré, Carathéodory, Birkhoff, Lie and Élie Cartan has played a major role in the development of several important branches of mathematics: differential geometry, the calculus of variations, the theory of Lie groups and Lie algebras, and the theory of ordinary and partial differential equations. During the last thirty years, the study of the geometric structures which form the basis of mechanics (symplectic, Poisson and contact structures) has enjoyed renewed vigour. The introduction of modern methods of differential geometry is one of the reasons for this renewal; it has permitted a formulation of global problems and furnished tools with which to solve them. Even though there are already a number of books that treat this subject, the authors believe that it is of value to provide readers with an approach to these methods and to permit them to familiarise themselves with certain recent developments which are not mentioned in the other textbooks in this field, and to acquire the information necessary in order to pursue current research. They have also expounded and employed the methods of exterior algebra which were introduced by E Cartan.

The present work is an advanced textbook which gives a systematic exposition of the theory of symplectic, Poisson and contact manifolds, and their applications in Hamiltonian mechanics. ... The book, which was written by two well-known specialists with important contributions in the field (also reflected in this book) is very well written, updated, and it supplies a valuable contribution to the geometric-mechanical literature.

The authors have clearly achieved their main aim: to give a systematic, accurate and largely self-contained account of the geometric foundations of classical mechanics for graduate students in mathematics. In doing so, they have written an excellent and lasting book.

Mademoiselle Libermann, as everyone called her, left us on 10 July 2007, after an exceptionally long and fruitful mathematical life. For example, till the end she actively participated in our seminar of Hamiltonian geometry, organised by her friend and collaborator Charles-Michel Marle; during the ensuing lunches, we benefited from her remarkable knowledge of mathematics and mathematicians but also from her stimulating vision of the world. I do not think she had changed substantially nor lost in vivacity since her admission in 1938 to the École Normale Supérieure de Jeunes Filles.

Tiny, energetic, smiling, chatty, sometimes caustic, she was also a memory of the mathematical community. She liked to speak of those who helped her, either personally or professionally: Cartan's family, Jacqueline Ferrand, Ehresmann, anonymous others ... and she also liked to speak of those who did not help her. She participated, almost until the end, in conferences all around the world. The last time we met, in April, I was leaving for Vietnam. "I cannot go", she told me, "too tiring, I am getting old". She was 87.