The two major events over the last couple of months have been the credit crunch and the US presidential election. We take a mathematical view of both of these, muse over the surprising effectiveness of maths when it comes to describing the world we live in, and scrutinise some mathematical philosophy. Plus the usual mix of news, reviews and podcasts.
Tonight sees a rare astronomical event: the Moon, Venus and Jupiter can all be seen close to each other in the same region of the night sky. In fact, Venus just passed behind the Moon! Over the next few nights, clouds permitting, you'll be able to see them slowly moving apart — get out your telescopes and look out for bright objects near the Moon!
What do the human brain, the Internet and climate change have in common? They're all hugely complex, and while they're very different, the tools used to grapple with this complexity are likely to be similar. We visited the Cambridge complex systems consortium, dedicated to building an over-arching science of complexity, and talked to neuroscientist Ed Bullmore, mathematician Frank Kelly
and climate scientist Hans Graf about their take on complexity. Listen to the podcast of the interviews.
The recent news of the great Indian batsman Sachin Tendulkar surpassing West Indian Brian Lara's record number of test runs has given maths-loving cricket geeks another opportunity to pull out their calculators and Excel spreadsheets. Marc West is openly one of these nuts and did just that.
It may come as a surprise that your average proof in an academic journal is riddled with holes. Authors gloss over details, appeal to pictures, even intuition, and take hidden leaps of logical faith that, philosophically speaking, aren't entirely justified. These days mathematics contains proofs so long and complex that few people are able to check and understand them in full, yet once a
result has made it through the peer review process and into a journal, its truth is taken as read.
All this is a far cry from the mathematical dream which started with Euclid over 2000 years ago: that every mathematical statement should be derived from the very axioms of mathematics in a sequence of verifiable logical steps. Proofs which do this are known as formal proofs, and they are the focus of a special issue of the Notices of the American Mathematics Society, which is
now freely available online.
Astronomers using NASA's Hubble Space Telescope have taken the first visible-light snapshot of a planet orbiting another star. Estimated to be no more than three times Jupiter's mass, the planet, called Fomalhaut b, orbits the bright southern star Fomalhaut, located 25 light-years away in the constellation Piscis Australis, or the "Southern Fish." An immense debris disc about
21.5 billion miles across surrounds the star. Fomalhaut b is orbiting 1.8 billion miles inside the disc's sharp inner edge, and is 1 billion times fainter than the star.
In a separate development, Canadian scientists have used ground-based telescopes in Hawaii and Chile to take infrared images of three giant planets they believe are orbiting a star about 130 light-years away in the Pegasus constellation.
These are not the first examples of exoplanets — planets orbiting stars outside our own solar system — but Formalhaut b is the first that can actually be observed in visible light wavelengths. All others have been detected indirectly, for example through the wobble their gravitational pull induces on their star.