Evolution is the main theme of this issue. With Darwin's anniversary year not too far off, we find out how to reconstruct the tree of life and how to spot the fingerprint of natural selection. We report on the rapidly melting Arctic, bound to destroy much of evolution's achievements, and explore the maths used in ice and ocean models. And we have a look at cellular automata, simple
mathematical models that can evolve surprisingly complex behaviour. Plus you can learn how to best distribute money amongst your employees without evolving envy.
Apart from that you will find the usual Editorial, Outer space, puzzle and book and film reviews.
Bacon sandwiches, drinking while pregnant, obesity — health risks are a favourite with the media. But behind the simple numbers quoted in the headlines lies a huge and sophisticated body of statistical research. We talk to Professor Sheila Bird of the Biostatistics Unit in Cambridge about her work in public health and its impact on policy, and discuss bias in pharmaceutical studies, as
recently highlighted by the controversy around antidepressants.
Recent research suggests that generalists can thrive in society, even though most theories of evolution, and even Greek philosopher Plato, argue that individuals who perform specialist tasks are more likely to succeed.
Mathematics is the tool we use to solve our problems. But can maths uncover the
secrets behind love? Given that love is a game, and mathematical game theory can be used to find the best strategies to win at games, why not try and apply maths to love?
So here, on Valentines Day, are some Plus stories from society's most lucky in love, the mathematicians:
Love's a gamble — Delve into the application of game theory to love. Is it really in your best interests to buy an expensive present for the object of your affection, or will they merely find your show of ostentatiousness pretentious?
Maths, love and man's best friend — Finding your perfect partner, it seems, is simply a mathematical process. Dr Peter Todd, of the Max Planck Institute in Munich, says that by the time you have met 12 potential partners, you have enough information to make a good choice as to who should be your life-long love.
'Calculus' — Why sex is like mathematics? Because both can lead to productive results but that is not what we are thinking when we conduct it....
Symmetry, dance and sexual selection — There are not many concepts that are fundamental to both maths and sex, but symmetry is one of them. In maths the study of symmetry forms the basis of a vast field called group theory and can be exploited to understand the patterns inherent in nature and the abstract world. On the other hand, scientists have long suspected that
the symmetry of a person or animal's body is an indicator of health and strength and therefore desirability as a potential mate. Does it make us more attractive?
And finally, does the Golden Ratio really have anything to do with beauty?
From everyone here at Plus, have a great Valentines Day and we hope all your sexy mathematical dreams come true.
Lodovico Ferrari was an Italian mathematician famed for solving the quartic equation. Ferrari was born in 1522 in Bologna and at the age of 14 became the servant of Gerolamo Cardan, a celebrated Italian Renaissance mathematician, physician, astrologer and gambler.
Ferrari showed mathematical promise at a young age, and at the age of 20 became a public lecturer in geometry. He was also a player in a great mathematical controversy of the time - who should get credit for the development of solutions for the cubic and quartic equations.
Gerolamo Cardan, partner in controversy.
The controversy includes another notable mathematician of his day, Nicolo Fontana Tartaglia. Tartaglia was an Italian mathematician who was the first to apply mathematics to the investigation of the paths of cannonballs. He had developed his own solutions to the cubic equations, and when Cardan heard of this achievement,
nagged a reluctant Tartaglia to show him his work. He succeeded only when he challenged him to a debate and implied that through his influence he could arrange a potentially lucrative contact with the governor of Milan. Tartaglia agreed to tell Cardan his method if Cardan would swear never to reveal it and to only ever write it down in code so that even if he died, nobody would ever discover it.
Cardan agreed to this, and Tartaglia enigmatically handed over his formula in the form of a poem.
Several years later however, Cardan and Ferrari saw unpublished work by Scipione del Ferro who had independently devised the same solution as Tartaglia. This work was dated before the work of Tartaglia, and so they decided to break their promise and the include Tartaglia's solution in their published work. Based on Tartaglia's
formula, Cardan and Ferrari found proofs for all cases of the cubic and, more impressively, solved the quartic equation - this was reportedly largely due to the work of Ferrari.
Tartaglia then started a campaign of public abuse directed at Cardan and Ferrari, and whilst most of the insults washed off Cardan - who was now established as the world's leading mathematician - Ferrari wrote to Tartaglia challenging him to a public debate. Tartaglia however did not consider Ferrari as worthy of debate - it was Cardan he wanted. Ferrari and Tartaglia traded insults for over a
year until 1548 when Tartaglia received an offer of a lectureship in Brescia. To establish his credentials for the post, he was asked to take part in the debate with Ferrari.
Tartaglia was an experienced debater and expected to win. However, by the end of the first day, it was clear that things were not going his way and that Ferrari understood the cubic and quartic equations more thoroughly. Tartaglia decided to flee that night, with victory left to Ferrari. Ferrari's fame soared and he was inundated with offers of employment, including a request from the
Ferrari was appointed tax assessor to the governor of Milan, and after transferring to the service of the church, retired as a young (aged 42) and rich man. He moved back to his home town of Bologna and in with his widowed sister Maddalena. He died in 1565 of white arsenic poisoning, most likely administered by Maddalena. Maddalena did not grieve at his funeral and having inherited his
fortune, remarried two weeks later. Her new husband promptly left her with all her fortune and she died in poverty.
We talk to four researchers from UCL's centre for mathematics and physics in the life sciences and experimental biology (COMPLEX) about the role of maths in such fields as astrobiology, cancer modelling and biology.