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
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Pompeii, Capri & the Bay of Naples
Seven Cities of Italy
Burgundy, the River Rhone & Provence
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Lake Garda
Minoan Crete and Santorini
Prices correct as of 15 May 2015
Why the cost of parenting has become so expensive

Why the cost of parenting has become so expensive

Today's pre-school child costs £35,000, according to Aviva. And that's but the tip of an iceberg, says DJ Taylor
Fifa corruption: The 161-page dossier that exposes the organisation's dark heart

The 161-page dossier that exposes Fifa's dark heart

How did a group of corrupt officials turn football’s governing body into what was, in essence, a criminal enterprise? Chris Green and David Connett reveal all
Mediterranean migrant crisis: 'If Europe thinks bombing boats will stop smuggling, it will not. We will defend ourselves,' says Tripoli PM

Exclusive interview with Tripoli PM Khalifa al-Ghweil

'If Europe thinks bombing boats will stop smuggling, it will not. We will defend ourselves'
Raymond Chandler's Los Angeles: How the author foretold the Californian water crisis

Raymond Chandler's Los Angeles

How the author foretold the Californian water crisis
Chinese artist who posted funny image of President Xi Jinping facing five years in prison as authorities crackdown on dissent in the arts

Art attack

Chinese artist who posted funny image of President Xi Jinping facing five years in prison
Marc Jacobs is putting Cher in the limelight as the face of his latest campaign

Cher is the new face of Marc Jacobs

Alexander Fury explains why designers are turning to august stars to front their lines
Parents of six-year-old who beat leukaemia plan to climb Ben Nevis for cancer charity

'I'm climbing Ben Nevis for my daughter'

Karen Attwood's young daughter Yasmin beat cancer. Now her family is about to take on a new challenge - scaling Ben Nevis to help other children
10 best wedding gift ideas

It's that time of year again... 10 best wedding gift ideas

Forget that fancy toaster, we've gone off-list to find memorable gifts that will last a lifetime
Paul Scholes column: With the Premier League over for another year, here are my end of season awards

Paul Scholes column

With the Premier League over for another year, here are my end of season awards
Heysel disaster 30th anniversary: Liverpool have seen too much tragedy to forget fateful day in Belgium

Liverpool have seen too much tragedy to forget Heysel

Thirty years ago, 39 fans waiting to watch a European Cup final died as a result of a fatal cocktail of circumstances. Ian Herbert looks at how a club dealt with this tragedy
Amir Khan vs Chris Algieri: Khan’s audition for Floyd Mayweather may turn into a no-win situation, says Frank Warren

Khan’s audition for Mayweather may turn into a no-win situation

The Bolton fighter could be damned if he dazzles and damned if he doesn’t against Algieri, the man last seen being decked six times by Pacquiao, says Frank Warren
Blundering Tony Blair quits as Middle East peace envoy – only Israel will miss him

Blundering Blair quits as Middle East peace envoy – only Israel will miss him

For Arabs – and for Britons who lost their loved ones in his shambolic war in Iraq – his appointment was an insult, says Robert Fisk
Fifa corruption arrests: All hail the Feds for riding to football's rescue

Fifa corruption arrests

All hail the Feds for riding to football's rescue, says Ian Herbert
Isis in Syria: The Kurdish enclave still resisting the tyranny of President Assad and militant fighters

The Kurdish enclave still resisting the tyranny of Assad and Isis

In Syrian Kurdish cantons along the Turkish border, the progressive aims of the 2011 uprising are being enacted despite the war. Patrick Cockburn returns to Amuda
How I survived Cambodia's Killing Fields: Acclaimed surgeon SreyRam Kuy celebrates her mother's determination to escape the US

How I survived Cambodia's Killing Fields

Acclaimed surgeon SreyRam Kuy celebrates her mother's determination to escape to the US