Sunday, July 06, 2003

Mathematics: Does the Proof Stack Up? by George Szpiro 03 Jul 03 Just under five years ago, Thomas Hales made a startling claim. In an e-mail he sent to dozens of mathematicians, Hales declared that he had used a series of computers to prove an idea that has evaded certain confirmation for 400 years. The subject of his message was Kepler's conjecture, proposed by the German astronomer Johannes Kepler, which states that the densest arrangement of spheres is one in which they are stacked in a pyramid - much the same way as grocers arrange oranges. Soon after Hales made his announcement, reports of the breakthrough appeared on the front pages of newspapers around the world. But today, Hales's proof remains in limbo. It has been submitted to the prestigious Annals of Mathematics, but is yet to appear in print. Those charged with checking it say that they believe the proof is correct, but are so exhausted with the verification process that they cannot definitively rule out any errors. So when Hales's manuscript finally does appear in the Annals, probably during the next year, it will carry an unusual editorial note - a statement that parts of the paper have proved impossible to check. At the heart of this bizarre tale is the use of computers in mathematics, an issue that has split the field. [Nature] [Also see: Flyspeck Project, aka 'A Formal Proof of Kepler'] 9:03:28 AM  Google It!

Scientists Discover Planetary System Similar to Our Own The image shows an impression by David A. Hardy of a possible scene from a moon orbiting the extra-solar planet in orbit around the star HD70642. Photo Credit: David A. Hardy. Photo of Siding Spring Mountain and associated telescopes. Photo Credit: Paul Butler, Carnegie Institution of Washington. by Josh Camot 03 Jul 03 ARLINGTON, Va. An international team of scientists has discovered a planet and star that may share the same relationship as Jupiter and our Sun, the closest comparison that researchers have found since they began their search for extra-solar planets nearly a decade ago. By analyzing light spectra collected with the 3.9-meter Anglo-Australian Telescope in Siding Spring, Australia, scientists from the United States, Australia, and Britain made precision measurements of the star HD 70642. The telescope data reveal a wobble in the star's position, an artifact from the gravitational tug of a planet roughly twice the size of Jupiter. The star is similar in size and structure to our Sun. From the wobble of HD 70642, the team has learned that the orbit of its planet is similar to the orbit of Jupiter in both shape and distance. The planet, a gas giant, is right where it should be if the solar system evolved like ours, suggesting that other planets may be found nearby and that the system could potentially harbor life. The researchers, supported by the National Science Foundation (NSF), conduct the Anglo-Australian Planet Search (AAPS), one of the leading extra-solar planet searches in the world. [National Science Foundation] 4:10:45 AM  Google It!