Dernier theoreme de Fermat

André Weil

Pierre de Fermat, le grand mathematicien du XVIIè siècle, a écrit à la fin de son cahier "x^n+y^n=z^n impossible si n>2. J'ai trouvé une solution merveilleuse, mais la place me manque ici pour la developper". Voilà l'enigme de 350 années est né. Ce n'est pas difficile de remarquer que pour n=2, il y a des solutions avec le theoreme de pythagore: 3^2+4^2=5^2.
Plusieurs mathématiciens se sont penchés comme Leonhard Euler,genie du XVIIème siècle,Sophie Germain sans grand succès. Ce sera la conjecture de Shimura-Taniyuma qui sera la clé de l'enigme: "toute courbe elliptique est modulaire". Une courbe elliptique verifie une équation de la forme y^2 + axy + by = x^3 + cx^2+ dx + e.

En effet, cette conjecture ne sera pas demontrée par Shimura et Taniyuma sachant que le premier se suicide. Mais quel est le lien entre le dernier théoreme de Fermat et cette conjecture? La reponse sera rapportée par Frey. Ce dernier va raisonner par absurde. En effet, il va supposer qu'il y a une solution pour l'équation de fermat, donc il existe N,A,B,C entiers tel que A^N+B^N =C^N. Il reussira à transformer cette équation sous forme d'une equation elliptique. Or la conjecture de Shimura et Taniyuma déclare que toute équation elliptique est modulaire et l'équation de Fred n'est pas modulaire (d'après Ken Ribet). Voilà la contradiction!! André Weil va donc démontrer la célèbre conjecture de Shimura-Taniyuma en 1995 donc resoudre le celèbre problème du milenium...Ouf!

Maintenant il ne reste plus aux admirateurs de Fermat à donner une demonstration plus simple que celle de Weil de 100 pages...Pour les curieux et les courageux, voici la demonstration en anglais:

http://math.stanford.edu/~lekheng/flt/wiles.pdf

Time changes, but mind not!!

A tremendous progress has made in science, particulary in genetic which prooves that race doesn't exist. How can we hope an abolition of racism when even the school which must teach this matter has faced to segregation?

Linda Brown, the first black American pupil was the origin of racial mix in school after fighting against board of education in 1951 and the supreme court struck down segregation. Almost six decades have elapsed, but "black and white children continue to learn in different worlds" Jefferson and Seattle' stricts has still maintained the racially integrate school system even if the Supreme Court threatened them. In Seattle, as the most famous high schools are scarce, the selection is based on race. Parents are the main reason for this integration separated, the white parents are mostly well-off, so they force administration to decide what they wish. They have to support racial mix instead of this system. However some districts propose a different alternative to improve the equality between black and white children,like the Wake county which subsidizes lunch for poor students. But blacks need more help because of their economic background.

Most of blacks come from low-income family. Vouchers advocates favour providing more money to this families to bridge the gap between rich and poor students. And others favour spending money on school and teaches' wage, to allow poor children to access a classroom attended by affluent ones and advantages brought by their parents. But many politiciens pay lip service to help disadvantaged pupils only to win support and others pander to middle-class people. Therefore the economic background of blacks doesn't improve much and may get worse.


As History shows (independence of women, abolition of slavery,etc.) that the men deny always that the equality is the first step for progress, thus they spend their time on increasing the inequality. The victims must fight against abusers to get rid of wretched conditions and the others should do similar against self-esteem.

source:

http://www.economist.com/research/articlesBySubject/displaystory.cfm?subjectid=526356&story_id=9079930

Tough conditions behind bars!!

The famous serial of nowadays, Prison Break has exposed life in jail. After seeing it, we should wonder about tough conditions behind bars.

We always think that the prison is a place for punishment. But Mr Hooks, jail's warden in Alabama considers it as rehabilitatation. "He tried to make prisons less horrible place to be locked up" He tried to provide education to inmates to make easier their life after the release, by building a library. The gouvernement doesn't want to pour into education for them because the needs of law-abiding folk come first and it argues that if conditions are improved , the prison wouldn't represent a fear for criminals, the prison is only a detterent. An study opposes the gouvernement: harsh conditions in cell would increase recidive's rate, in fact , these conditions brutalize prisoners. It's difficile whether unfair treatements raise crimes, increasing recidives, or reduce crimes, by acting as a detterent. To solve this problem, a private jail was built.

Correction cooperative of America (CCA) built a private jail near to Missisipi, in which more activities are provided to inmates (reading, sport,drug tratment, job training) . These prisons are cheap. And they respect Human Rights as public ones. The paradox is that they spend less money than the public ones. Thus the State signs a contrat with this society,CCA. Unfortunately, these prisons are scarce. It's really a good idea and an huge progress. It can also erase fear of murders to be locked up because they would feel comfortable in jail than their own home.

Anyway nobody was born criminal, it's the society, which changes a man into devil or angel. Therefore, it should repair its fault by helping him not by punishing.

source: http://www.economist.com/world/na/displaystory.cfm?story_id=9546217c