Ivar Ekeland Book order

The book delves into the complexities of integrable and nonintegrable systems in celestial mechanics, particularly focusing on periodic solutions. It discusses Poincaré's contributions, including his geometric theorem about area-preserving maps and the significance of the least action principle in Hamiltonian mechanics. The text highlights the historical context of these concepts, from Fermat to Maupertuis, and emphasizes the limited impact of the least action principle until recently, despite its aesthetic appeal and the connection established by Emmy Noether's theorem between symmetries and motion integrals.

Tracing the impact of optimization and the ways in which it has influenced the study of mathematics, biology, economics, and even politics, this title reveals how the idea has driven some of our greatest intellectual breakthroughs.

The story unfolds in a unique hotel where Numbers, including Odds and Evens, fill every room, yet new guests keep arriving. The arrival of Zero sparks a series of room switches, while the unexpected appearance of Letters complicates the situation further. Despite the hotel’s capacity being tested, it remains fully booked. The challenge escalates with the arrival of Fractions, leading to potential chaos. The narrative explores themes of infinity and accommodation, raising the question of whether a clever solution can be devised to house all the guests.

The book presents a series of lectures delivered at the Scuola Normale Superiore, focusing on making complex economic problems and the mathematical theory of exterior differential systems more accessible. It aims to bridge the gap between mathematicians and economic theory, providing a thorough exploration of the subject at a more relaxed pace. The author recognizes that many mathematicians may not be familiar with economic concepts or the works of Elie Cartan, and seeks to clarify these topics for a broader audience.