Here is an accurate and readable translation of a seminal article by Henri Poincare that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincare applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. Poincare wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

Here is an accurate and readable translation of a seminal article by Henri Poincare that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincare applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. Poincare wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

A member of the Academie francaise, Henri Poincare (1854 1912) was one of the greatest mathematicians and theoretical physicists of the late nineteenth and early twentieth centuries. His discovery of chaotic motion laid the foundations of modern chaos theory, and he was acknowledged by Einstein as a key contributor in the field of special relativity. He earned his enduring reputation as a philosopher of mathematics and science with this elegantly written work, which was first published in French as three separate essays: Science and Hypothesis (1902), The Value of Science (1905), and Science and Method (1908). Poincare asserts that much scientific work is a matter of convention, and that intuition and prediction play key roles. George Halsted's authorised 1913 English translation retains Poincare's lucid prose style, presenting complex ideas for both professional scientists and those readers interested in the history of mathematics and the philosophy of science."

During his lifetime, Henri Poincare published three major philosophical books which achieved great success: "La science et l'hypothese" (1902), "La valeur de la science" (1905) and "Science et methode" (1908). After his death in 1913, a fourth volume of his philosophical works was published by his heirs as "Dernieres pensees" (1913). The four books constitute the core of Poincare's philosophic works and were given an ovation by scientific and general public. Around 1919, Gustave Le Bon wrote to Poincare's widow. As the director of the "Bibliotheque de Philosophie Scientifique at Flammarion," he asked her permission to publish a second posthumous volume. "L'Opportunisme scientifique" was intended to be the fifth and final volume of Poincare's philosophical writings. Louis Rougier had elaborated the project, with the collaboration of Gustave Le Bon, and the approval of the philosopher Emile Boutroux and his son Pierre. Because of the reservations of the mathematician's heirs, this book was never published and Dernieres pensees remained his last philosophical book. Nevertheless Poincare's correspondence - which is kept in the Poincare Archives at University Nancy 2 - contains a large amount of documents concerning the project, its justification and the discussions between Louis Rougier and the mathematician's heirs. The aim of this book is to restore this episode, which gives some crucial informations about editorial practices of Poincare and about the posterity of his philosophic thinking."

by John Stillwell I. General Reaarb , Poincare's papers on Fuchsian and Kleinian I1'OUps are of Il'eat interest from at least two points of view: history, of course, but also as an inspiration for further mathematical proll'ess. The papers are historic as the climax of the ceometric theory of functions initiated by Riemann, and ideal representatives of the unity between analysis, ceometry, topololY and alcebra which prevailed during the 1880's. The rapid mathematical prOll'ess of the 20th century has been made at the expense of unity and historical perspective, and if mathematics is not to disintell'ate altogether, an effort must sometime be made to find its , main threads and weave them tocether 81ain. Poincare's work is an excellent example of this process, and may yet prove to be at the core of a . new synthesis. Certainly, we are now able to gather up , some of the loose ends in Poincare, and a broader synthesis seems to be actually taking place in the work of Thurston. The papers I have selected include the three Il'eat memoirs in the first volumes of Acta Math. -tice, on* Fuchsian groups, Fuchsian , functions, and Kleinian groups (Poincare [1882 a,b,1883]). These are the papers which made his reputation and they include many results and proofs which are now standard. They are preceded by an , unedited memoir written by Poincare in May 1880 at the height of his , creative ferment.

During his lifetime, Henri PoincarA(c) published three major philosophical books which achieved great success: "La science et l'hypothA]se" (1902), "La valeur de la science" (1905) and "Science et mA(c)thode" (1908). After his death in 1913, a fourth volume of his philosophical works was published by his heirs as "DerniA]res pensA(c)es" (1913). The four books constitute the core of PoincarA(c)'s philosophic works and were given an ovation by scientific and general public. Around 1919, Gustave Le Bon wrote to PoincarA(c)'s widow. As the director of the "BibliothA]que de Philosophie Scientifique at Flammarion," he asked her permission to publish a second posthumous volume. "L'Opportunisme scientifique" was intended to be the fifth and final volume of PoincarA(c)'s philosophical writings. Louis Rougier had elaborated the project, with the collaboration of Gustave Le Bon, and the approval of the philosopher A0/00mile Boutroux and his son Pierre. Because of the reservations of the mathematician's heirs, this book was never published and DerniA]res pensA(c)es remained his last philosophical book. Nevertheless PoincarA(c)'s correspondence - which is kept in the PoincarA(c) Archives at University Nancy 2 - contains a large amount of documents concerning the project, its justification and the discussions between Louis Rougier and the mathematician's heirs. The aim of this book is to restore this episode, which gives some crucial informations about editorial practices of PoincarA(c) and about the posterity of his philosophic thinking.

by John Stillwell I. General Reaarb , Poincare's papers on Fuchsian and Kleinian I1'OUps are of Il'eat interest from at least two points of view: history, of course, but also as an inspiration for further mathematical proll'ess. The papers are historic as the climax of the ceometric theory of functions initiated by Riemann, and ideal representatives of the unity between analysis, ceometry, topololY and alcebra which prevailed during the 1880's. The rapid mathematical prOll'ess of the 20th century has been made at the expense of unity and historical perspective, and if mathematics is not to disintell'ate altogether, an effort must sometime be made to find its , main threads and weave them tocether 81ain. Poincare's work is an excellent example of this process, and may yet prove to be at the core of a . new synthesis. Certainly, we are now able to gather up , some of the loose ends in Poincare, and a broader synthesis seems to be actually taking place in the work of Thurston. The papers I have selected include the three Il'eat memoirs in the first volumes of Acta Math. -tice, on* Fuchsian groups, Fuchsian , functions, and Kleinian groups (Poincare [1882 a,b,1883]). These are the papers which made his reputation and they include many results and proofs which are now standard. They are preceded by an , unedited memoir written by Poincare in May 1880 at the height of his , creative ferment.

Science and Hypothesis is a classic text in history and philosophy of science. Widely popular since its original publication in 1902, this first new translation of the work in over a century features unpublished material missing from earlier editions. Addressing errors introduced by Greenstreet and Halsted in their early 20th-century translations, it incorporates all the changes, corrections and additions Poincare made over the years. Taking care to update the writing for a modern audience, Poincare's ideas and arguments on the role of hypotheses in mathematics and in science become clearer and closer to his original meaning, while David J. Stump's introduction gives fresh insights into Poincare's philosophy of science. By approaching Science and Hypothesis from a contemporary perspective, it presents a better understanding of Poincare's hierarchy of the sciences, with arithmetic as the foundation, geometry as the science of space, then mechanics and the rest of physics. For philosophers of science and scientists working on problems of space, time and relativity, this is a much needed translation of a ground-breaking work which demonstrates why Poincare is still relevant today.

Science and Hypothesis is a classic text in history and philosophy of science. Widely popular since its original publication in 1902, this first new translation of the work in over a century features unpublished material missing from earlier editions. Addressing errors introduced by Greenstreet and Halsted in their early 20th-century translations, it incorporates all the changes, corrections and additions Poincare made over the years. Taking care to update the writing for a modern audience, Poincare's ideas and arguments on the role of hypotheses in mathematics and in science become clearer and closer to his original meaning, while David J. Stump's introduction gives fresh insights into Poincare's philosophy of science. By approaching Science and Hypothesis from a contemporary perspective, it presents a better understanding of Poincare's hierarchy of the sciences, with arithmetic as the foundation, geometry as the science of space, then mechanics and the rest of physics. For philosophers of science and scientists working on problems of space, time and relativity, this is a much needed translation of a ground-breaking work which demonstrates why Poincare is still relevant today.