Word: proof
(lookup in dictionary)
(lookup stats)
Dates: during 1990-1999
Sort By: most recent first
(reverse)
...such solutions exist only for squares. Raise the exponent to any number higher than 2 -- change the equation to x 7 + y 7 = z 7, for example, or x 12 + y 12 = z 12 -- said Fermat, and no combination of integers will work. "I have found a truly wonderful proof," wrote Fermat in the margin of a book, "which this margin is too small to contain." He lived until 1665 but never did write it down -- evidence, many believe, that he hadn't proved the proposition after...
...another math puzzle, known in the trade as the Taniyama Conjecture, which deals with the equations that describe mathematical objects known as elliptic curves. Just six years ago, Berkeley's Ribet demonstrated that proving this conjecture was tantamount to proving Fermat's Last Theorem. "What is amazing about Wiles' proof," says Boston, "is that while it built on previous attempts, Andrew realized how to put all these complicated pieces together...
There is always a chance that Wiles, too, has made a mistake. His proof runs more than 200 pages, and he could present only the highlights in the Cambridge lecture. The final test will come in a few months, when Wiles circulates a complete, written version of the proof to others for careful checking. That will not be easy. Says Ribet: "Wiles' arguments are based on the most advanced, most elaborate mathematics that exist in this field. The number of mathematicians who can really fully understand the arguments would fit into a conference room...
...Wiles' proof is historic, but the subfields of mathematics generated along the way by people working to solve Fermat's theorem are full of perplexing problems, and so are other areas of math. A proof of Fermat's famous theorem by no means brings any line of inquiry to an end. Still bedeviling mathematicians are the Poincare Conjecture, the Riemann Hypothesis, Goldbach's Conjecture, Kepler's sphere-packing problem and dozens of others. There are, in short, enough mind-bending challenges to keep mathematicians busy for at least the next 350 years...
...Eyewitnesses" who claimed to have seen or even touched the ark paraded in front of the camera. Unfortunately, the audience was told, an earthquake, attacks by terrorists, the Russian Revolution and other inopportune events had frustrated various attempts over the years to bring back clear pictures or other definitive proof of the ark's existence...