The brilliance of Babylonian Mathematics

The achievements of Babylonian mathematics are still poorly recognised, but the people in ancient Iraq treated numbers in the abstract way we do today, rather than as lengths, areas or volumes. This began before 2000 BC, and enabled them to develop mathematical formulas in the modern sense. In particular they not only knew what we call Pythagoras’s theorem but had a formula for producing side lengths for right-angled triangles, something the Greeks could not do well over a millennium and a half later. See my article in Engelsberg Ideas.

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How modern Numbers came to Europe

Our modern representation of numbers is the result of a complex process that can be traced back to the ancient Near East, via India and the Arab world — see my article in Engelsberg Ideas.

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The Pythagoras Myth

Contrary to popular belief, Pythagoras was by no means the discoverer of his eponymous theorem – it had already been known for over a thousand years. In popular perception however he became the source of the famous theorem about right-angled triangles: The Square on the Hypotenuse is equal to the Sum of the Squares on the Other Two Sides, a great result – serious mathematics indeed. But it has little to do with Pythagoras — see my article in Engelsberg Ideas.

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Vandalism at the Coliseum: why we should not let the ENO die

Is the English National Opera dying? Or does it stand at the threshold of new developments? The argument for death is that it has difficulty filling the London Coliseum, a vast auditorium that accommodates an audience of about two and a half thousand. It cannot survive without a decent subsidy from the state. Can we afford it? As for the idea of moving the whole thing to Manchester, Arts Council England has certainly not evaluated the logistics nor the implications of its hasty decision. My essay in The Article.

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Reality check: mathematics is not racist

Engaging with students on the history of mathematics would do far more than pretending that the subject abounds with racism. My article in The Critic, 18 March 2021

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A new lease of life for Schrödinger’s Cat? Carlo Rovelli’s Helgoland

A review of Carlo Rovelli’s new book on quantum theory, dealing with the superposition of two states, and quantum entanglement. The Article, 4 March 2021.

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Just keep swimming

Those of us who partake in open air swimming should be allowed to return to this miraculous prophylactic, despite the semi-lockdown. The Critic, 12 November 2020.

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US Election History — a personal view

Recollections about elections from the post-Vietnam era when I first went to America, and their relevance today. The Article, 11 November 2020.

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The man behind the Monster

The man who first glimpsed the Monster has died. He came to this vision via very precise arguments, but later had to fight German students who wanted to cancel his branch of mathematics. We need his type again to fight the new battle against those who would turn mathematics from careful argument and precision to woolliness and confusion. The Critic 24 August 2020.

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Decolonise … maths?

If ‘decolonising maths’ means reassessing who did what, we need to put Greek geometry into perspective. Who invented algebra? And for modern arithmetic we have to thank the Sumerians, whose ethnicity and skin colour remains conveniently unknown. My article in The Critic, 7 July 2020

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Dark Matters

Academics in this country need to allow new ideas rather than orthodoxy and group-think. See my article in The Critic on 22 June 2020 about the dis-invitation of a physicist who was scheduled to give a technical talk.

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The mathematician and the Monster: a tribute to John Horton Conway

My tribute to the extraordinarily creative mathematician John Horton Conway. Originally from Liverpool, he died on 11 April, aged 82. Published in The Article, 16 April, 2020.

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Full Circle

The long history of why there are 360 degrees in a circle. The short answer is that it was due to the Babylonians. History Today, 23 March 2020.

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Eureka Moments in Syracuse

In a charming Sicilian museum you can test the theories of antiquity’s greatest mathematician. See my article in Standpoint magazine, July/ August 2019, p. 59

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Brotherly and sisterly love

André and Simone Weil were two sides of the same coin: impatient; determined; brilliant; attracted to ancient wisdom and ideas. Standpoint magazine, May 2019, pp. 61–2

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The English National Opera 2019/20 Season

The English National Opera needs to attract new audiences, so they must produce stagings that people want to see. Trying to be in the vanguard of bizarre reinterpretations won’t work, so what does the next season hold?

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Playing the numbers game

This review of David Spiegelhalter’s excellent new book The Art of Statistics shows that the methodology behind the numbers is hugely important, but the numbers themselves can still be misinterpreted. Standpoint magazine, April 2019, pp 61–2

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Brought to book

Some academic publishers abuse the system by producing fifth rate books with a good title and blurb, which American university libraries feel obliged to buy. Standpoint magazine, April 2019, p. 8.

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First woman to win the prestigious Abel mathematics prize

My ex-colleague Karen Uhlenbeck has just won the Abel Prize, mathematicians’ answer to the Nobel Prize, which has no category for mathematics. Bravo to her and to the Norwegian Academy of Science and Letters for instituting this prize named after the brilliant young Norwegian mathematician Niels Henrik Abel. My summary in The Article.

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Civilisation made concrete

The great ‘Hanging Garden’ was built by the ancient Assyrians, who were pioneering builders and engineers, Standpoint magazine, February 2019, p.70.

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Is this the real life or just fantasy?

It may not be possible to know if we are living in a simulation — but perhaps we don’t need certainty. Standpoint magazine, Dec 2018, p.78.

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Wagner’s Ring and the European Union have a lot in common

A comparison of the Ring itself with the Euro, and Valhalla with the EU. The Article, 16 November 2018.

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Escaping the Moscow ghetto

Now a professor at UC Berkeley, Edward Frenkel was once a brilliant Russian teenager rejected by Moscow State University simply because he was classed as Jewish. Standpoint magazine, Oct 2018, p.55.

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Opera’s summer in the country

My take on summer opera festivals at Glyndebourne, Grange Park Opera, The Grange Festival, Longborough, Nevill Holt, Holland Park and Buxton. Standpoint magazine, September 2018, p. 57

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Isabeau, Opera Holland Park review: a faultless production of a minor work

Italian composer Pietro Mascagni never repeated the huge success of Cavalleria Rusticana, his first opera written at age 26, but he had a jolly good try. Daily Telegraph, 15 July 2018.

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The heroes who came up with zero

Zero — part of the ‘place-value’ system for writing numbers — came to Europe from India via the Arabic world. But the ancient Sumerians invented it! Standpoint magazine, July/August 2018, p. 68

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An Italian take on time and space

My review of The Order of Time by Carlo Rovelli. Standpoint magazine, June 2018, p. 56

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Numbers Game (contd.)

How the Monty Hall problem exposes a human tendency to stick with difficult decisions. Standpoint magazine, March 2018, p. 6.

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March is the cruellest month

At one time the New Year started in March, in China it’s February 16 this year, and the British tax year starts on April 6. Why the differences? Standpoint magazine, February 2018, p. 57.

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Acting the goat with the Greeks

Innumeracy at the top of European politics beggared Greece and may now vitiate Brexit negotiations, Standpoint magazine, December 2017, p. 69

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Indiana Jones and the table of Babel

An ancient mathematical tablet from about 1800 BC shows Babylonian trigonometrists had long anticipated the Greeks, Standpoint magazine, November 2017, p. 59.

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Coming to Terms with History

How Barrie Kosky’s new Meistersinger at Bayreuth is helping the Wagner Festival to come to terms with the past. Standpoint magazine, September 2017, p. 54.

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The Great Expedition

In the mid-eighteenth century a Danish-German expedition sought to discover the roots of the Hebrew Bible in Arabia and Mesopotamia. History Today, June 2017, pp. 72–77.

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Berlin Magic

Superb performances of Richard Strauss’s Die Frau ohne Schatten and Wagner’s Parsifal by the Berlin Staatsoper under the batons of Zubin Mehta and Daniel Barenboim, Standpoint magazine, June 2017, p.8

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Dating Dilemmas

The problem of dating Easter and its relationship to Passover. Standpoint magazine, April 2017, p. 51

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Country cousins show how to do it

Private festivals avoid the absurd interpretations of classic operas that shame the subsidised sector. Standpoint magazine, October 2016, p. 71.

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New Parsifal at Bayreuth — a triumph

A vision of Christians, Jews and Muslims living in harmony in the Middle East is the redemptive message of this new production from the opening night of the 2016 festival, Daily Telegraph, 27 July 2016.

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A marvellous lost Hamlet opera, rediscovered

A review of the opening night production of Franco Faccio’s Hamlet at the Bregenz Festival. Daily Telegraph, 21 July 2016.

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The One-Eyed Maths Monster

Leonard Euler became the presiding genius at the Academy of St Petersburg founded by Peter the Great, then in Berlin under Frederick the Great, before returning to St Petersburg under Empress Catherine the Great. Standpoint magazine, July/August 2016, p. 85.

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It wasn’t Pi in the sky after all

This article about young mathematical genius Ramanujan (1887–1920) coincides with the release of  The Man Who Knew Infinity, a new movie about his life. Standpoint magazine, April 2016, p. 70

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Standing the test of spacetime

Einstein’s General Relativity, inspired by a thought experiment, celebrates its centenary this month, Standpoint magazine, November 2015, p. 75.

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Meistersinger, Staatsoper Berlin, review: ‘marvellous’

The new season opened on the twenty-fifth anniversary of Reunification Day with Acts 1 and 2 of Meistersinger, Act 3 following next day. Daily Telegraph, 5 Oct 2015.

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Adriano in Siria, by Pergolesi, Cadogan Hall, review

In this remarkable 1734 opera, soprano Erica Eloff showed marvellous expressiveness and musical embellishments, Daily Telegraph, 17 Sept 2015.

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Glorious Summer

Compares the success of Britain’s privately funded opera festivals, with the ready acceptance of failure at publicly funded Covent Garden, Standpoint magazine, September 2015, p. 6.

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Tristan und Isolde, Bayreuth Festival, review: ‘hugely moving’

Will a Wagnerian triumph keep Bayreuth in the family? Daily Telegraph, 27 July 2015, p. B15

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Fiddler and the proof

A connection between the Yiddish world of Fiddler on the Roof and one of the great quests in modern mathematics. Standpoint Magazine, July/Aug 2015, p. 89.

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The Rise and Fall of Nimrud

The wanton destruction of this once great city in ancient Assyria leaves a hole in history. History Today, June 2015, p. 7.

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Revenge not redemption is message of new Parsifal in Berlin

Wagner’s Parsifal is about redemption and renewal, but this new production by Russian director Dmitri Tcherniakov adds a jarring note — revenge. Telegraph, 29 March 2015.

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The ultimate space explorer

The brilliantly creative Alexander Grothendieck died recently after reshaping mathematics and then withdrawing from society. Standpoint Magazine, Jan/Feb 2015, p. 89

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Music of Resignation

Turbulence, trauma and transformation in the life of composer Richard Strauss. History Today, January 2015, pp. 4, 5.

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The prime numbers have it

New mathematics prizes show the public that the subject is constantly renewing itself with new ideas.  Standpoint Magazine, September 2014, p. 79

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The Fields Medal is the greatest prize in maths

The Fields Medal is awarded every four years, and the 2014 winners are announced today. This is the mathematics equivalent to the Nobel Prize. Daily Telegraph, 13 August 2014, p. 18

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Reconstructing Baroque Opera

This year marks an intriguing step forward in the revival of baroque opera — a realistic performance space in the new candle-lit Sam Wanamaker Theatre. History Today, 1 July 2014

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High pressure

David Haig’s riveting new play Pressure about the weather forecasting for D-Day opened at Chichester and should move to the West End. Standpoint Magazine, July/Aug 2014, p. 14

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Antediluvian Ark

Irving Finkel’s new book The Ark Before Noah:Decoding the Story of the Flood, analyses an ancient cuneiform tablet describing a circular Ark. What was its purpose? Standpoint Magazine, April 2014, p.73

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What is it that makes mathematics beautiful?

A UCL study on brain imaging points to mathematical beauty in the mind of the beholder, and this brief essay gives examples. The Independent, 13 Feb 2014.

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Underrated: Tycho Brahe

Tycho Brahe — the greatest observational astronomer before the advent of the telescope. Standpoint Magazine, Jan/Feb 2014, p. 95.

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Overrated: Claudius Ptolemy

Did the author of Ptolemy’s famous Almagest make his own observations, or make them up? Standpoint Magazine, Jan/Feb 2014, p.94.

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Wagner: A Long-Running Cycle of Triumph and Despair

A brief history of the Bayreuth Festival, and discussion of the new 2013 Ring production for Wagner’s bicentenary, History Today, December 2013, pp.3,4

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Donizetti’s Three Queens at Welsh National Opera

A review of Anna Bolena, Maria Stuarda, and Roberto Devereux in new productions at the WNO, New Statesman, 1–7 November 2013, pp.58,59.

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One Ring to rule them all

Compares four Wagner Rings from this bicentenary year: concert performances at the BBC Proms, and staged performances at Longborough Festival Opera, Staatsoper Berlin, and Bayreuth. New Statesman 4–10 October 2013, pp.52,53.

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Wotan’s trolley

In Berlin to review Wagner’s Ring, my request to pay for a shopping trolley was refused. Can the Eurozone survive even stronger differences, and does the Ring hold a warning for us? Standpoint Magazine, May 2013, p. 12.

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Wagner’s Ring, Staatsoper Berlin, review

After tenor Lance Ryan failed to turn up for Act 1 of Siegfried, the hero of this performance of Wagner’s Ring cycle was conductor Daniel Barenboim, Daily Telegraph, 12 April 2013.

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The genius who beat Einstein to it

An essay on Henri Poincaré, inspired by Jeremy Gray’s new scientific biography, Standpoint Magazine, March 2013, p. 75.

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The Puzzle of Proto-Elamite

Describes new efforts at the Ashmolean Museum, Oxford to decode the world’s oldest undeciphered language, History Today, January 2013, p. 6.

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The Olympian and his Thunderbolt

A review of Ray Monk’s new biography of Robert Oppenheimer, Standpoint Magazine, December 2012, p. 67.

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It’s not elementary, my dear Watson

Compares the ancient belief in four elements to the modern belief in four elementary forces, Standpoint Magazine, October 2012, p. 68.

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Flying Dutchman, Bayreuth Festival, review

In this new production at the 2012 Bayreuth Festival, conductor Christian Thielemann gave the music of the Flying Dutchman huge excitement. Daily Telegraph, 27 July 2012

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Accelerating the debate on motion

Compares Einstein’s depth of thought with the lower level sophistication in modern finance, Standpoint Magazine, July/August 2012, p. 83.

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Eurodämmerung

As the Eurozone countries wrestle with the fate of the single currency, we examine parallels in Wagner’s Ring cycle. History Today, July 2012, p. 5.

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A light shining from Babylon

Compares the search for the Higgs boson to the Babylonian discovery of how to predict eclipses, Standpoint Magazine, May 2012, p 72.

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Perishing Publishers

Describes publication practices in academia, and mathematicians’ recent boycott of Elsevier, Standpoint Magazine, April 2012, p. 11.

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The Mathematician’s Tale

In The New Millennium Tales by Kevin Lavery and Reg Starkey, November 2011.

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Removing The Neutrino Anomaly

Discusses the apparent speed of neutrinos being faster than light, Standpoint Magazine, November 2011, p. 68.

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Euro soap opera

Describes the new Bayreuth production of Tannhäuser in relation to the Euro Crisis, Standpoint Magazine, September 2011, p. 13.

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Tannhäuser, Bayreuth Festival, review

Wagner’s Tannhäuser was greeted by boos on the opening night of this year’s Bayreuth Festival. Daily Telegraph, 27 July 2011.

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The genius of geometry

Places the mystery of Euclid’s life in a modern context, Standpoint Magazine, July/August 2011, p. 83.

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Lighting Design for Ballet

Essay in Focus, The Journal for the Association of Lighting Designers, April/May 2011, p. 28–32.

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University Challenged

On the stifling bureaucracy in universities, Standpoint Magazine, January/February 2011, p. 12.

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Die Walküre, La Scala, Milan, review

This was opera magic where Daniel Barenboim brought out the full depth and passion of Wagner’s music. Daily Telegraph, 21 December 2010

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On Her Majesty’s Secret Service

Describes the move from war-time code breaking at Bletchley to modern methods of encryption and GCHQ, Standpoint Magazine, September 2010, p. 64.

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Never too Old

Applauds the value of learning ancient Greek, Standpoint Magazine, May 2010, p. 13.

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Maths Class

On the sensible way to teach arithmetic and elementary algebra, Standpoint Magazine, April 2010, p. 13.

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Experts and Axioms

Describes how experts have been wrong in mathematics, and could be wrong on the global warming debate, Standpoint Magazine, January/February 2010, p. 13.

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Unsound Science

Criticises the government’s recent misguided proposal to evaluate the social and economic impact of scientific research, Standpoint Magazine, December 2009, p. 10–11.

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Maths Moves in Mysterious Ways

Describes the ability of mathematics to explain nature’s patterns, and outlines its development from the Greek world to the Arabic world, and later to Europe and America, Standpoint Magazine, October 2009, p. 89.

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Facing the Music

A review of Ronald Harwood’s plays Collaboration and Taking Sides, which deal with music and the Nazis, Standpoint Magazine, June 2009, p. 83.

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Taking research for granted

Suggests better ways to fund scientific creativity in universities, Standpoint Magazine, April 2009, p. 82.

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Ditch the new maths for good old Euclid

On the sad loss of Euclidean geometry as a foundation for logical reasoning, Standpoint Magazine, November 2008, p. 54.

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