What is Poincare Conjecture answer?

Poincaré conjecture, in topology, conjecture—now proven to be a true theorem—that every simply connected, closed, three-dimensional manifold is topologically equivalent to S3, which is a generalization of the ordinary sphere to a higher dimension (in particular, the set of points in four-dimensional space that are …

What was the first scientific achievement of Henri Poincare?

In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible).

What was Henri Poincare famous for?

Henri Poincaré was a mathematician, theoretical physicist and a philosopher of science famous for discoveries in several fields and referred to as the last polymath, one who could make significant contributions in multiple areas of mathematics and the physical sciences.

Who discovered the conjecture?

greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin.

Where did Henri Poincare live?

France
Henri Poincaré/Places lived
Henri Poincaré, in full Jules Henri Poincaré, (born April 29, 1854, Nancy, France—died July 17, 1912, Paris), French mathematician, one of the greatest mathematicians and mathematical physicists at the end of 19th century.

What did Henri Poincare contribution to mathematics?

Henri Poincaré was the first to introduce four-vectors, the Lorentz group and its invariants (including the space-time metric), “Poincaré stresses,” as well as making other valuable contributions to relativity theory.

Which are the method of conjecture?

A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases.

Is the Poincaré conjecture essentially true in dimension 4?

The Poincaré conjecture was essentially true in both dimension four and all higher dimensions for substantially different reasons. In dimension three, the conjecture had an uncertain reputation until the geometrization conjecture put it into a framework governing all 3-manifolds.

What is the significance of Poincaré’s work in physics?

In the field of differential equations Poincaré has given many results that are critical for the qualitative theory of differential equations, for example the Poincaré sphere and the Poincaré map. Published an influential paper providing a novel mathematical argument in support of quantum mechanics.

What is the Poincaré group used for?

The Poincaré group used in physics and mathematics was named after him. Early in the 20th century he formulated the Poincaré conjecture that became over time one of the famous unsolved problems in mathematics until it was solved in 2002–2003 by Grigori Perelman .

What did Poincare de Poincaré discover?

Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell’s equations, an important step in the formulation of the theory of special relativity.