Life and Style

Johanes Kepler, who was born on 27 December 1771, was born near Stuttgart and made his foray into astronomy after he worked as a maths teacher in Graz, Austria - where he became an associate of Prince Hans Ulrich von Eggenberg.

Mandelbrot, father of fractals, dies at 85

Benoit Mandelbrot, the Polish-born mathematician who played a central role in Chaos theory, has died at his home in Cambridge, Massachusetts, aged 85, of cancer.

Maths prodigy Arran Fernandez is the youngest Cambridge fresher since 1773

Boy, 15, follows trail blazed by Pitt the Younger – but dad will take him to lectures

Boffinology, By Justin Pollard

After encountering the weird odds and ends in this book of scientific quirks – the "Halifax gibbet", invented for the dispatch of Yorkshire miscreants, was a predecessor of the guillotine; heroin, invented by the Bayer company, takes its name from heroisch because it made one user feel heroic; an Indiana mathematician persuaded his state to grant him a patent for pi at the incorrect value of 3.2 – the reader may recall a TV programme that specialises in unlikely revelations.

God didn't create universe, says Hawking

The universe was not created by God, scientist Stephen Hawking has said in his new book.

Official: just 20 moves needed to solve a Rubik's Cube

To be precise: there are 43,252,003,274,489,856,000 different possible configurations of the coloured squares on any Rubik's Cube. Yet now researchers have calculated that you're never more than 20 moves away from solving the famous puzzle.

Russian mathematician rejects $1m prize

A Russian mathematician has rejected a $1m (£700,000) prize for solving one of the most challenging problems because he considers it unfair.

Colombia set to elect the world's first Green leader

A former philosopher with some unusual policy ideas looks certain to take the country's presidency

Book mixing math and crochet wins UK 'odd' prize

A book charting the frontier between handicrafts and geometry on Friday won Britain's quirkiest literary award, the Diagram Prize for year's oddest book title.

Shy maths genius leaves million dollar prize money on the table

Russian recluse holed up in apartment urged to give unclaimed reward to charity

Keynes, By Peter Clarke

Shares in John Maynard Keynes are rising, and Peter Clarke's elegant, succinct biography could not be more timely. The first half is a chronological account of Keynes's life, reminding us what a polymath the man was. As well as the most influential economist of the 20th century, he was a mathematician and philosopher whose first published work was a treatise on probability, an essayist and journalist, an adviser to governments, and friend of most of the leading intellectuals of his day. (Bertrand Russell described him as the cleverest man he ever knew, and said that every time he argued with Keynes he felt as though he was taking his life in his hands.)

Last Night's Television: Vampires: Why They Bite, BBC3<br />Horizon, BBC2

My relationship with Horizon has been a bit rocky of late. We were pretty much inseparable back in the Eighties, but recently it's been nothing but bickering and rows. I've often thought about cutting my losses entirely and going for a clean break, perhaps even dating other science strands less obsessed with cosmetics and celebrities. The only problem is that there aren't any out there, and certainly none that can match the memories I have with Horizon. Also, every now and then, something clicks and I remember what made me fall in love in the first place. It happened last night, with Stephen Cooter's "To Infinity and Beyond", a dizzyingly enjoyably attempt to net the ineffable. It won't, I think, have been one for the real puritans, those for whom a Seventies Open University physics module remains the apogee of science broadcasting. But I thought it was close to exemplary in its quiet wit and patience and relish for paradox.

Seeing Further, Edited by Bill Bryson

This year the Royal Society celebrates its 350th birthday. The "Royal Society of London for Improving Natural Knowledge" was founded on 28 November 1660, when a dozen "ingenious and curious gentlemen" met at Gresham College, London, after a lecture by Christopher Wren, the 28-year-old Professor of Astronomy, and decided to found "a Colledge for the Promoting of Physico-Mathematicall Experimentall Learning." Among the signatories of that historic memorandum were Wren, chemist Robert Boyle, clergyman and polymath John Wilkins, Sir Robert Moray, and mathematician William, Viscount Brouncker.

The core of truth behind Sir Isaac Newton's apple

The manuscript that gave rise to one of science's best-known anecdotes is now online.

The schizophrenic genius whose worst fears came true

Walter Sartory made a fortune in the markets, but it never made him happy and was the motive for his murder, writes Guy Adams
Alex Salmond said he accepted 'the democratic verdict of the people'
newsSNP leader says Scotland must move forward as 'one nation'
Arts and Entertainment
Friends is celebrating its 20th anniversary this year
tvSeries celebrates 20th anniversary
Yaya Touré (left) and Bayern Munich’s Spanish defender Juan Bernat
footballToure's lack of defensive work is big problem for City
voicesApple continually kill off smaller app developers, and that's no good for anyone
Arts and Entertainment
Liam Neeson said he wouldn't

Liam Neeson's Downton dreams

Wembley Stadium
footballNews follows deal with Germany
Arts and Entertainment
A spell in the sun: Emma Stone and Colin Firth star in ‘Magic in the Moonlight’
filmReview: Magic In The Moonlight
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Languedoc Roussillon
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The Jura Mountains
Dubrovnik & the Dalmatian Coast
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Mystery of the Ground Zero wedding photo

A shot in the dark

Mystery of the wedding photo from Ground Zero
His life, the universe and everything

His life, the universe and everything

New biography sheds light on comic genius of Douglas Adams
Save us from small screen superheroes

Save us from small screen superheroes

Shows like Agents of S.H.I.E.L.D are little more than marketing tools
Reach for the skies

Reach for the skies

From pools to football pitches, rooftop living is looking up
These are the 12 best hotel spas in the UK

12 best hotel spas in the UK

Some hotels go all out on facilities; others stand out for the sheer quality of treatments
These Iranian-controlled Shia militias used to specialise in killing American soldiers. Now they are fighting Isis, backed up by US airstrikes

Widespread fear of Isis is producing strange bedfellows

Iranian-controlled Shia militias that used to kill American soldiers are now fighting Isis, helped by US airstrikes
Topshop goes part Athena poster, part last spring Prada

Topshop goes part Athena poster, part last spring Prada

Shoppers don't come to Topshop for the unique
How to make a Lego masterpiece

How to make a Lego masterpiece

Toy breaks out of the nursery and heads for the gallery
Meet the ‘Endies’ – city dwellers who are too poor to have fun

Meet the ‘Endies’ – city dwellers who are too poor to have fun

Urbanites are cursed with an acronym pointing to Employed but No Disposable Income or Savings
Paisley’s decision to make peace with IRA enemies might remind the Arabs of Sadat

Ian Paisley’s decision to make peace with his IRA enemies

His Save Ulster from Sodomy campaign would surely have been supported by many a Sunni imam
'She was a singer, a superstar, an addict, but to me, her mother, she is simply Amy'

'She was a singer, a superstar, an addict, but to me, her mother, she is simply Amy'

Exclusive extract from Janis Winehouse's poignant new memoir
Is this the role to win Cumberbatch an Oscar?

Is this the role to win Cumberbatch an Oscar?

The Imitation Game, film review
England and Roy Hodgson take a joint step towards redemption in Basel

England and Hodgson take a joint step towards redemption

Welbeck double puts England on the road to Euro 2016
Relatives fight over Vivian Maier’s rare photos

Relatives fight over Vivian Maier’s rare photos

Pictures removed from public view as courts decide ownership
‘Fashion has to be fun. It’s a big business, not a cure for cancer’

‘Fashion has to be fun. It’s a big business, not a cure for cancer’

Donatella Versace at New York Fashion Week