Henri poincare mathematician biography rubrica 2

Mathematicians can use the methods of logic to check a proof, but they must use intuition to create a proof, he believed. Although all geometries are about physical space, a choice of one geometry over others is a matter of economy and simplicity, not a matter of finding the true one among the false ones. Although every scientific theory has its own language or syntax, which is chosen by convention, it is not a matter of convention whether scientific predictions agree with the facts.

Some mathematicians, Poincaré among them, already dealt success- fully with infinite systems, but they considered algebraic infinite systems in particular and.

Rather, the scientist declares the law to be some interpolated curve that is more or less smooth and so will miss some of those points. Thus a scientific theory is not directly falsifiable by the data of experience; instead, the falsification process is more indirect. His sister Aline married the spiritualist philosopher Emile Boutroux.

Beginning in , he taught at the University of Paris. He not only faced the question of determining the integral of such equations, but also was the first person to study the general geometric properties of these functions. He clearly saw that this method was useful in the solution of problems such as the stability of the solar system, in which the question is about the qualitative properties of planetary orbits for example, are orbits regular or chaotic?

His research on the stability of the solar system opened the door to the study of chaotic deterministic systems; and the methods he used gave rise to algebraic topology.

Biography.

He formulated the principle of relativity, according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest, and he derived the Lorentz transformation. He argued for conventionalism and against both formalism and logicism. He wrote several articles on the philosophical interpretation of mathematical logic.

During his life, he published three books on the philosophy of science and mathematics. A fourth book was published posthumously in Given the law of gravity and the initial positions and velocities of the only three bodies in all of space, the subsequent positions and velocities are fixed—so the three-body system is deterministic.