Wiles' proof of Fermat's Last Theorem was scrutinized by mathematical experts. Wiles was interviewed for an episode of the BBC documentary series "Horizon" that focused on Fermat's Last Theorem. This was renamed "The Proof". It was made an episode of the Public Broadcasting Service's science television series "Nova".
Richard Taylor (mathematician)
Richard Lawrence Taylor (born 19 May 1962) is a British mathematician. He works in number theory. He was a former research student of Andrew Wiles. He returned to Princeton to help Wiles complete the proof of Fermat's last theorem.
Taylor received the 2007 Shaw Prize in Mathematical Sciences. This for his work on the Langlands program. He did this work with Robert Langlands.
Taylor received his B.A. from Clare College, Cambridge. He received his Ph.D. from Princeton University in 1988. From 1995 to 1996 he held the Savilian Chair of Geometry at Oxford University. He was also a Fellow of New College, Oxford. Currently, he is the Herchel Smith Professor of Mathematics at Harvard University.
He received the Whitehead Prize in 1990, the Fermat Prize and the Ostrowski Prize in 2001. He also got the Cole Prize of the American Mathematical Society in 2002, and the Shaw Prize for Mathematics in 2007. He was also elected a Fellow of the Royal Society in 1995.
There are two papers which have the complete proof of Fermat's Last Theorem. One of them was written by Taylor with Andrew Wiles.
In his later work, Taylor (along with Michael Harris) proved the local Langlands conjectures. A simpler proof was suggested almost at the same time by Guy Henniart.
Later, together with Christophe Breuil, Brian Conrad, and Fred Diamond, he completed proving the Taniyama–Shimura conjecture, by performing very difficult computations.
Recently, Taylor, following the ideas of Michael Harris, developed on his work with Laurent Clozel, Michael Harris, and Nick Shepherd-Barron. He has announced that he proved the Sato–Tate conjecture, for elliptic curves with non-integral j-invariant. This partial proof of the Sato–Tate conjecture uses a theorem of Wiles.
Taylor is married to Christine Taylor . She is a mathematical biologist. They have two children: Jeremy and Chloe. He is also the son of British physicist, John C. Taylor.
Yi Bok-nam
Yi Bok-nam ( Hanja: ; born June 28 1555 in Gangneung - died August 16 1597 Namwon, Lee Bok-nam) was an army general and politician of the Joseon Dynasty of Korea. He was one of Korea's generals in the Imjin War.
Algebraic equation
In mathematics, an algebraic equation, also called polynomial equation over a given field is an equation of the form
where "P" and "Q" are polynomials over that field, and have one (univariate) or more than one (multivariate) variables. For example:
is an algebraic equation over the rational numbers.
Two equations are called equivalent if they have the same set of solutions. This means that all solutions of the second equation must also be solutions of the first one and vice versa. The equation formula_1 is equivalent with formula_4. So the study of algebraic equations is equivalent to the study of polynomials.
If an algebraic equation is over the rationals, it can always be converted to an equivalent one, where all the coefficients are integers. For example, in the equation given above, we multiply by 42 = 2·3·7 and group the terms in the first member. The equation is converted to
The solutions of an equation are the values of the variables for which the equation is true. But for algebraic equations there are also called roots. When solving an equation, we need to say in which set the solutions are allowed. For example, for an equation over the rationals, one can find solutions in the integers. Then, the equation is a diophantine equation. One may also look for solutions in the field of complex numbers. One can also look for solutions in real numbers.
Ancient mathematicians wanted the solutions of univariate equations (that is, equations with one variable) in the form of radical expressions, like formula_6 for the positive solution of formula_7. The ancient Egyptians knew how to solve equations of degree 2 (that is equations in which the highest power of the variable is 2) in this manner. During the Renaissance, Gerolamo Cardano solved the equation of degree 3 and Lodovico Ferrari solved the equation of degree 4. Finally Niels Henrik Abel proved in 1824 that the equation of degree 5 and the equations of higher degree cannot always be solved by using radicals. Galois theory, named after Évariste Galois, were introduced to give criteria deciding if an equation is solvable using radicals.
Algebraic solution
An algebraic solution is an algebraic expression which is the solution of an algebraic equation in terms of the coefficients of the variables. It is found only by addition, subtraction, multiplication, division, and the extraction of roots (square roots, cube roots, etc.).
The most well-known example is the solution of the general quadratic equation.
(where "a" ≠ 0).
There is a more complicated solution for the general cubic equation and quartic equation. The Abel-Ruffini theorem states that the general quintic equation does not have an algebraic solution. This means that the general polynomial equation of degree "n", for "n" ≥ 5, cannot be solved by using algebra. However, under certain conditions, we can get algebraic solutions; for example, the equation formula_3 can be solved as formula_4
Sylvie Faucheux
Sylvie Faucheux (b. 29 May 1960 in the 20th arrondissement of Paris) is a French professor and politician. She specialized in the fields of economy of the natural environment and sustainable development. She was President of the "Université de Versailles Saint-Quentin-en-Yvelines" from 2002 till the 12 April 2012.
Faucheux graduated from the Paris 1 Pantheon-Sorbonne University which she founded in 1995. She managed the Center for economics and ethics environment and sustainable development, which, in 2002, became a joint research unit between UVSQ and the "Institut de recherche pour le développement" (IRD) (Institute of Development Research).
Faucheux is a politician as well as an educator. She was a SP candidate at the parliamentary elections for the first district of Yvelines in June 2007.
In December 2002, she was named President of the "Université de Versailles Saint-Quentin-en-Yvelines". She was president until 12 April 2012, when Jean-Luc Vayssière was made president. She is the current head of "Université du grand ouest parisien". Faucheux is a member of the Board of Research and Higher Education in France. She has been a member since 2002. She is responsible for the working group on sustainable development.
Sylvie Faucheux is Chevalier of the "Ordre des Palmes Académiques" (14 July 2004 promotion), Chevalier of the "Ordre national du Mérite" (14 November 2005 Decret), Chevalier of the Legion of Honour and owner of the "Marianne d'Or" 2009 for her actions in favor of the sustainable development.
Derivative (finance)
In finance, a derivative is a special type of contract. In it, the two parties agree to sell (or to buy) certain goods, at a given price, on a given date. Derivatives can be used in two ways. The first is called speculation: One party hopes that the "market price" differs from the "price agreed upon in the contract", so that he can make the difference between the two. The second is called hedging: One party wants to make sure that the market price doesn't go in a direction that would hurt his profits, so he make sure that the price is agreed upon a long time before the transaction takes place. For a seller, hedging means that he can be certain to receive the agreed upon price, and for the buyer hedging means that he can be certain not to pay more than the agreed upon price. From a moral point of view, speculation is considered a negative activity.