Plus Blog

April 22, 2008
Wednesday, April 23, 2008

A mathematician from the University of East Anglia has turned his gaze to the stars to try and answer one of humankind's oldest questions — are we alone in the Universe? And the unfortunate answer is, well, probably.

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posted by Plus @ 5:40 PM

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At 9:13 PM, Anonymous Anonymous said...

its true?

 
April 17, 2008
Friday, April 18, 2008

Edward Lorenz, American mathematician and meteorologist, died in his Cambridge Massachusetts home on April 16 aged 90. Lorenz was the "father of chaos theory" and discovered the Lorenz attractor that often occurs in chaotic systems.

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posted by westius @ 4:27 PM

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April 14, 2008
Tuesday, April 15, 2008

The Enigma machine was once considered unbreakable, and the cracking of the "unbreakable code" by the allies changed the course of World War 2. Plus talks to Nadia Baker from the Enigma Project about the history of codes and code-breaking, why the Enigma machine was considered unbreakable, the mathematics behind codes, and how it was finally cracked. The Enigma Project travels all over the United Kingdom and abroad, visiting over 100 schools and organisations, reaching over 12,000 people of all ages every year.

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posted by Plus @ 4:13 PM

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April 10, 2008
Friday, April 11, 2008

Sixty-three year-old Avraham Trakhtman has solved one of the current generation's toughest mathematical problems — the 38 year-old road colouring problem. The solution will shortly be published in the Israel Journal of Mathematics.

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posted by Plus @ 3:11 PM

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April 9, 2008
Thursday, April 10, 2008

Attacks on the foundations of calculus

George Berkeley

Born: 12 March 1685 in Kilkenny, County Kilkenny, Ireland

Died: 14 Jan 1753 in Oxford, England

George Berkeley was an Irish bishop and philosopher who is best known for his attacks on the logical foundations of the calculus as developed by Newton.

George Berkeley.

Berkeley started at Trinity College, Dublin at the tender age of 14 and graduated with a masters when only 18 years old. His attacks on the foundations of calculus were first aired in 1734 when he published The analyst: A discourse addressed to an infidel mathematician. The infidel mathematician is believed to have been either Edmond Halley or Isaac Newton. He argued that although the calculus led to true results, its foundations were no more secure than those that underpin religion. He stated that the calculus involved a logical fallacy and described derivatives thus:

"And what are these fluxions? The velocities of evanescent increments? And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities?"

In modern language, this could be read as:

"What are these 'instantaneous' rates of change? The ratios of vanishing increments? And what are these 'vanishing' increments? They are neither finite quantities nor 'infinitesimal' quantities, nor yet nothing. May we not call them the ghosts of departed quantities?"

His interesting theory as to why the calculus actually worked was that it was the result of two compensating errors.

As a consequence of the controversy surround Berkeley's publication, the foundations of calculus were rewritten in a much more formal and rigorous manner using limits. It was not until 1966, with the publication of Abraham Robinson's book Non-standard Analysis, that the concept of the infinitesimal was made rigorous. This gave an alternative way of overcoming the difficulties that Berkeley found in Newton's approach.

Berkeley's influence in mathematics is reflected by the fact that the University of California, Berkeley, and the city of Berkeley that grew up around it, are named after him. Berkeley died of a heart attack on 14 January 1753, sitting with his family listening to his wife reading. He died so peacefully that the event went unnoticed, his family thinking he had fallen asleep. He left instructions that he was not to be buried for at least five days and was buried at Christ Church, Oxford on 20 January.

For more information, see the MacTutor biography of Berkeley.

posted by westius @ 5:00 PM

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April 9, 2008
Thursday, April 10, 2008

I would do anything for maths, but I won't do that

One of the latest group emails that I have received concerns maths and music. Good to see that mathematics has embarked on viral marketing. See if you can pick the songs referenced in the pictures below.

posted by westius @ 5:02 PM

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At 8:33 PM, Blogger Tenon_Saw said...

I thought this was great! Thanks for posting it.

 
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