Plus Blog
November 25, 2008
Tuesday, November 25, 2008
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. Labels: Latest news posted by Plus @ 11:30 AM 0 Comments: |
November 25, 2008
Tuesday, November 25, 2008
Say cheese! First ever images of exoplanets.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. To find out more about the new discovery, and see more images and videos, visit the Hubble Site. There is more information on exoplanets in general on physicsworld.com and in the Plus article Brave young worlds. posted by Plus @ 11:25 AM 0 Comments: |
November 18, 2008
Tuesday, November 18, 2008
Who is to blame for the credit crunch? According to media reports there are two suspects in the dock: the rocket scientists' (a.k.a. the financial mathematicians) who provided the information behind the market's decisions, or the greedy bankers who only thought about quick profits and their end-of-year bonuses. In our latest podcast, we talk to David Hand, Chris Rogers and John Coates to find out who is guilty. This podcast accompanies the article Is maths to blame? Labels: podcast posted by Plus @ 4:26 PM 0 Comments: |
November 13, 2008
Thursday, November 13, 2008
What does zero and infinity mean to you?Zero, and infinity — more than just numbers, these two mathematical concepts have worried and inspired mathematicians for centuries. But they have also inspired philosophers and artists. What is zero? What is infinity? What do they look like: A black hole or a blank page? A spiral or the horizon? Mathematician Marcus du Sautoy, historian of mathematics Eleanor Robson, Science Museum curator Jane Wess and artist Paul Prudence will be discussing Zero to Infinity at the Dana Centre in London. You can hear their perspectives, take part in the discussion, and have a drink at the bar on Thursday 20 November at 7pm. For further information visit the Dana Centre website. And while you're waiting, you can read more about infinity on Plus. We'll see you there! posted by Plus @ 11:11 AM 0 Comments: |
November 12, 2008
Wednesday, November 12, 2008
Mathematical moments — Yutaka TaniyamaBorn on the 12th of November 1927 in Kisai, Japan Taniyama's name is associated with one of the most famous problems in mathematics: Fermat's last theorem. The theorem says that for any whole number n strictly greater than 2, there are no three non-zero whole numbers x, y and z such that x^{n} + y^{n} = z^{n}. Almost 400 years ago Fermat scribbled in the margin of a book that he had a proof for this assertion, which didn't fit in the margin. It wasn't until the 1990s that the theorem was finally proved by Andrew Wiles — and the proof definitely couldn't have been written in any margin! Andrew Wiles didn't actually prove Fermat's last theorem, but a conjecture which now carries Taniyama's name. In 1955 Taniyama, who was working in algebraic number theory, posed a problem concerning so-called elliptic curves — these are curves defined by points in the plane whose co-ordinates satisfy a particular type of equation. Goro Shimura and André Weil mused over the question and formulated a conjecture: that every elliptic curve should come with a modular form, a mathematical object that is symmetrical in an infinite number of ways. This is now known as the Taniyama-Shimura-Weil conjecture. The link to Fermat's last theorem was made around 30 years later, when the mathematician Ken Ribet realised that if Fermat's last theorem were false, then this would mean that a particular elliptic curve comes without a modular form. In other words, if Fermat's last theorem were false, then the Taniyama-Shimura-Weil conjecture would be false also. Reformulating this yet again, if the Taniyama-Shimura-Weil conjecture is true, then so is Fermat's last theorem. What Andrew Wiles proved is that the Taniyama-Shimura-Weil conjecture is indeed true for a class of examples that is sufficient to prove Fermat's last theorem. QED. In 1958, just days after his 31st birthday and not long before he was meant to get married, Taniyama committed suicide. His explanation was this: "Until yesterday I had no definite intention of killing myself. ... I don't quite understand it myself, but it is not the result of a particular incident, nor of a specific matter." To find out more about Fermat's last theorem and its proof, read the Plus articles Fermat's last theorem and Andrew Wiles and How maths can make you rich and famous. posted by Plus @ 4:58 PM |
November 12, 2008
Wednesday, November 12, 2008
Why are some people generous and others selfish? There's no doubt that both strategies pay off under certain circumstances, but research (as well as everyday experience) shows that we are not mere opportunists — some people simply are nicer than others. This raises a question which intrigues evolutionary psychologists: is there a selective force that works in favour of a wide range of personalities, preventing us from all evolving the same optimal character trait? A possible answer has recently been published by mathematicians from the universities of Bristol and Exeter. Labels: Latest news posted by Plus @ 11:44 AM |