# What are the Weil conjectures?

## What are the Weil conjectures?

In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). Weil conjectured that such zeta functions for smooth varieties are rational functions, satisfy a certain functional equation, and have their zeros in restricted places.

## What did Pierre Deligne win the 1974 Fields Medal the highest Honour in mathematics for?

Pierre Deligne is a Belgian mathematician who won a Fields Medal for his work on algebraic number theory.

What is Pierre Deligne known for?

Pierre René, Viscount Deligne (French: [dəliɲ]; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.

### Is Hodge conjecture solved?

In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties.

### What is the answer to the Hodge conjecture?

The current version of the Hodge Conjecture says: every Hodge class is algebraic. In other words, we can take any Hodge class, no matter how weird, and deform it into an honest subvariety.

When was the Poincare Conjecture solved?

On August 22, 2006, the ICM awarded Perelman the Fields Medal for his work on the conjecture, but Perelman refused the medal. John Morgan spoke at the ICM on the Poincaré conjecture on August 24, 2006, declaring that “in 2003, Perelman solved the Poincaré Conjecture.”

## How was the Poincare Conjecture solved?

In 1982 Michael Freedman proved the Poincaré conjecture in four dimensions. Freedman’s work left open the possibility that there is a smooth four-manifold homeomorphic to the four-sphere which is not diffeomorphic to the four-sphere.

Has the Poincaré conjecture been proven?

As of October 17, 2021, the Poincaré conjecture is the only solved Millennium problem. On December 22, 2006, the journal Science honored Perelman’s proof of the Poincaré conjecture as the scientific “Breakthrough of the Year”, the first time this honor was bestowed in the area of mathematics.

### Who solved the Poincaré conjecture?

Grigori “Grisha” Perelman
Russian mathematician Grigori “Grisha” Perelman was awarded the Prize on March 18 last year for solving one of the problems, the Poincaré conjecture – as yet the only one that’s been solved. Famously, he turned down the \$1,000,000 Millennium Prize.

### Who Solved Millennium Problems?

To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved in 2003 by the Russian mathematician Grigori Perelman.