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In fact, he proved a result viewed by specialists as deeper and more interesting than Fermat's last theorem itself; it demonstrated that a broader class of equations has, at most, a finite number of solutions. Paradox at the heart of mathematics makes physics problem unanswerable.

Fermat's last theorem earns Andrew Wiles the Abel Prize : Nature News & Comment

To narrow it to zero, Wiles took a different approach: he proved the Shimura-Taniyama conjecture, a s proposal that describes how two very different branches of mathematics, called elliptic curves and modular forms, are conceptually equivalent. The link between the Shimura—Taniyama conjecture and Fermat's theorum was first proposed in by number theorist Gerhard Frey, now at the University of Duisburg-Essen in Germany. He claimed that any counterexample to Fermat's last theorem would also lead to a counterexample to the Shimura—Taniyama conjecture.

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Kenneth Ribet, a mathematician at the University of California, Berkeley, soon proved that Frey was right, and therefore that anyone who proved the more recent conjecture would also bag Fermat's. Still, that did not seem to make the task any easier. Iranian is first woman to nab highest prize in maths.

Abel's Theorem in Problems and Solutions

Fermat's last theorem is also connected to another deep question in number theory called the abc conjecture, Rognes points out. Mathematician Shinichi Mochizuki of Kyoto University's Research Institute for Mathematical Sciences in Japan claimed to have proved that conjecture in , although his roughly page proof is still being vetted by his peers.

Some mathematicians say that Mochizuki's work could provide, as an extra perk, an alternative way of proving Fermat, although Wiles says that sees those hopes with scepticism. Wiles helped to arrange an Oxford workshop on Mochizuki's work last December, although his research interests are somewhat different. Lately, he has focused his efforts on another major, unsolved conjecture in number theory , which has been listed as one of seven Millennium Prize problems posed by the Clay Mathematics Institute in Oxford, UK.

He still works very hard and thinks about mathematics for most of his waking hours, including as he walks to the office in the morning. Wiles, A. Taylor, R. Davide joined Nature in December Previously he has been an editor at Scientific American and a physical sciences reporter at Science News.

He has degrees in mathematics and in science writing. For the best commenting experience, please login or register as a user and agree to our Community Guidelines. This gave Abel the imp etus to study the so-called elliptic integrals. Such integrals including other related integrals cannot be calculated in an elementary way; that is, one cannot express in terms of elementary functions a function whose derivative is the expression inside the integral sign.

Therefore, the values of such integrals can be computed only numerically. Abel had the idea to investigate the associated inverse function, whereby a particular arc length of the ellipse is related to the associated angle, thereby creating the theory of elliptic functions. Over the following two year s, he studied the French and German languages intensively and continued his work on mathematical problems. Because of his limited contact with the scientific world, Abel was unaware that Paolo Ruffini — had already, in , published a paper expounding similar ideas, although his proof was marred by several gaps.

Finally, in , he was granted the necessary funds for a journey.

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In the second of these papers, he gave a set of criteria for when an equation of higher degree could be solved in radicals. In the process of his research, he discovered the relationships that had to exist among the solutions arrangements whose order could be reversed, whence commutative groups are called abelian groups. However, he found there no suitable interlocutor.

Indeed, he was so busy with his own publications that he simply put the paper aside and lost track of it. Abel was disappointed, for he knew that a positive judgment from Cauchy would finally bring him the recognition that he sought.

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Discouraged, he travelled homeward. In Berlin, Crelle tried to convince Abel to stay. He offered to make him a coeditor of his journal; he also tried to obtain for him a position at the University of Berlin. There, he was able only to obtain a position as a substitute teacher; then he filled in for Hansteen, who was on a major expedition to Siberia, at the university.

In poor health, he continued to work on elliptic functions: between him and Carl Gustav Jacob Jacobi, who independently had discovered similar approaches, there developed a fruitful yet debilitating rivalry. At the end of the year , Abel became severely ill; he had contracted tuberculosis in Paris.

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He died on April 6 of the following year. Two days later, Crelle was informed by the University of Berlin that a teaching position would be offered to Abel. Your email address will not be published.

Differential Equation - 2nd Order (33 of 54) Abel's Theorem: Example

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