The mathematical revolution behind ‘the greatest picture in the world’

Piero della Francesca, maths and masterpieces

19 April 2014

9:00 AM

19 April 2014

9:00 AM

It seems odd to enter a room dominated by what Aldous Huxley famously called ‘the greatest picture in the world’ to find not another soul there. Looking down from an end wall of the mediaeval civic hall in the quiet little Tuscan town of Borgo San Sepolcro, Piero della Francesca’s ‘Resurrection’ is an image of astonishing power, showing a stern-faced risen Christ stepping out of his tomb in the dawn light of the first Easter morning like an unstoppable force of nature, exuding supernatural authority as he turns the leaves on the trees behind him from wintry death to the new life of spring. This is a painting like no other in the history of art. But we can only still see it today thanks to the essay to which it inspired Huxley in 1925, ‘The Best Picture’.

When in 1964 H.V. Morton published A Traveller in Italy, he recalled a few years earlier meeting in Cape Town a second-hand bookseller, Anthony Clarke, who told him the remarkable story of how Huxley’s essay had prompted him to save this fresco from destruction. In 1944, as a British artillery captain, Clarke had been sent forward to the hills above San Sepolcro, supposedly full of Germans, with orders to blast the town to smithereens. Recalling its name from Huxley’s essay, in the nick of time he ordered his guns to stop firing. A young boy coming up the hill told them that the Germans had all left. Warily entering the town, Clarke, with huge relief, found Piero’s masterpiece untouched.

Last summer my family had two reasons for wanting to see all Piero’s paintings across Tuscany, by taking what is now known as ‘the Piero della Francesca trail’. One was that my son Nicholas had long shared my admiration for him as an artist like no other — the luminous nobility of his figures epitomising the Renaissance desire to portray humanity in its loftiest guise. His paintings are more subtly constructed than any others on mathematical lines: none more obviously than his ultimate puzzle picture, ‘The Flagellation’ in the Ducal Palace at Urbino: where three grave and exquisitely robed figures stand mysteriously in the foreground of a meticulously geometrical stage set, with Christ being flogged in the background.

Indeed, this was our second reason for wanting to take what Nick called ‘the PDF trail’, because Piero was in his day known not just as a painter but as a mathematician, playing a central part in that revolution which followed from the introduction to Europe of ‘Arabic’ numerals, which in fact originated from India. Nick is writing a book on India’s immense hidden contributions to western civilisation. One of the most important of these was the transformation brought about in European mathematics when the cumbersome old Roman numerals came to be replaced in the Middle Ages by the single-digit numerals from 0 to 10, adapted by the Arabs from Hindi originals.

The man who more than anyone codified these numerals, inventing the use of zero and the concept of negative numbers, was Brahma-gupta, a Rajasthani mathematician of the early 7th century. In 773, the second Abbasid caliph of Baghdad, Al-Mansur, summoned an international conference of astronomers and mathematicians, one of whom, Kankah, brought from India Brahmagupta’s chief treatise. Such an impact did this make on the assembled scholars that the caliph ordered it to be translated into Arabic, thus spreading use of the new numerals right across the Muslim world. It was from Algeria that, around 1200, the young Pisan mathematician Fibonacci brought them back to Italy (the famous ‘Fibonacci sequence’ he took directly from Brahmagupta).

However, it was not until the 15th century that the new numerals really caught on, in particular inspiring that interlinked group of multi-talented geniuses whose use of them to work out the scientific rules of perspective finally launched the Renaissance into overdrive. In Florence last summer we admired the architecture of Brunelleschi and Alberti and the frescoes of Masaccio, based on the eye-opening possibilities opened up by the ‘new maths’. But no one took them further than Piero, who became so preoccupied with the science of perspective and Euclidian geometry that his three treatises on mathematics made him as famous in his lifetime as his skill at painting.

This had come so to obsess him that, in the last 20 years of his long life, the imaginative fire of his art faded away, as he abandoned painting to concentrate on his mathematical researches. But their influence lived on, ironically, through one of his pupils in San Sepolcro, Friar Luca Pacioli, whose own most influential book, summarising the mathematical knowledge of his day, was shamelessly plagiarised from one by his master Piero. Because this, inter alia, set out all the principles of modern accounting, such as double-entry book-keeping, Pacioli has become known as ‘the father of accountancy’. But without Piero, or those Indian numerals, he couldn’t have done it, any more than he could have used the same principles to influence his friend Leonardo da Vinci in Milan in constructing what came to be looked on as one of the Renaissance’s supreme masterpieces, Leonardo’s ‘Last Supper’. It was not this, however, which Huxley hailed as the greatest picture in the world.

Got something to add? Join the discussion and comment below.

Christopher Booker was one of the founders of Private Eye, and writes a column for the Sunday Telegraph.

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  • mikewaller

    The painting is OK, but I would swap a wall of them for one Wright of Derby.

    As for Christopher eulogising Brahmagupta et al for introducing the use of zero into mathematics, I cannot help but think that his praise may well be conditioned by it all having happened a long time ago. Given his modern antipathy to much of the great scientific enterprise, my inclination is to believe that were zero to be newly introduced now, he would be more likely to quote King Lear: “Nothing will come of nothing, speak again”. [:-)]

    • Dodgy Geezer

      Given his modern antipathy to much of the great scientific enterprise..

      Where does Booker say he doesn’t like science?

      • mikewaller

        I would make two points:

        1. In his chosen field of faux specialism, climatology, he likes the small number of pieces that fit his prejudices. The much bigger balance is termed mendacious rubbish.

        2. Neither he nor other deniers have risen to the challenge of explaining why, if climate science has managed to pull the wool over the eyes of so many, nutritional scientists been so spectacularly unsuccessful in changing public policy with regard to sugar? Given the massive harm this pernicious substance does to so many in the Western World and the outright confidence trick pulled with regard to “low fat” food, how has the big food and drink lobby managed to fight off simple steps such as putting VAT on fizzy drinks? Surely, if Booker at al are right, a quick seminar with the Merlins of climatology would teach them all the “tricks” they would need to bring politicians and food and drink manufacturers to heel.

        • Dodgy Geezer

          I’m afraid you would be surprised at how little real science is being done in the medical world, and how even that little swamps the infinitesimal work being done in climate science.

          I suspect that you only read journalists’ reports. May I encourage you to make the acquaintance of ‘Retraction Watch’, a web site which tracks retracted scientific papers, and come to your own conclusions?

          To start you off, here are some useful introductory papers:


          This last is J. P. A. Ioannidis’ famous paper – one you should certainly read before making pronouncements on dietary issues…

          • mikewaller

            With the now massive levels of obesity in this country and even higher levels in the USA, the quality of the science has very little to do with it. My grandmother who died about fifty years ago could have told you what is wrong with the Western diet. Too much food in general of which far to big a proportion is processed.

            I look at most things from an evolutionary perspective and it seems to me obvious that what in times past would have been comparatively rare opportunities to gorge on high carbohydrate foodstuffs, has now been industrialized to the extent that they have become dietary staples. Unfortunately, as is very well known, industrial processing makes them seriously damaging to both our cardiovascular system and our digestive tract. Shamefully, in spite of this already being well understood, this process went into overdrive when, in the 1980s, fast-food suppliers came to realise that the low marginal cost of the food was such that they could massively increase demand and profits by offering supersize everything.

            One outcome of that has been the creation of a very “sizeable” element of our younger citizens who, in the terrible event of our having to fight another total war, simply could not make an active contribution.

            Incidentally, before mocking “journalist” contributions, make sure that you see “The men who made us fat” a TV series fairly recently shown on BBC about this. One of its final stories was of a quite serious movement within the European Parliament directed towards legislation that would in some way have limited the efforts of soft drink companies to relentlessly increase sales. It was killed stone-dead by a threat by the makers to inform the workers in every soft drink plant across Europe that their MEP was trying to destroy their job.

            So again I ask, why cannot those involved in seeking encourage healthy eating use the same magic that you reckon has suborned both high and low into a false belief about global warming?

          • Dodgy Geezer

            I see that you have been unable, for whatever reason, to read my references. Why, then, do you think you are competent to continue asserting these rumours as fact?

            ..make sure that you see “The men who made us fat” a TV series fairly recently shown on BBC..

            Alas, there is no TV at this end. I find that it damages the brain, and only provides entertainment for morons.

          • mikewaller

            “Rumours as fact”!!!!!!!!!!!!!!!!!!!!! Go stand on the High Street and see just how many seriously overweight folks waddle past you. A 90 year old friend of mine who has, in effect, to do this because he now has to sit in the car whilst his wife shops tells me he could weep at the sight of what a once reasonably sized nation has morphed into. From my experience, if he went to the States he would have a nervous breakdown.

            Can’t help thinking that your internal standards regarding what constitutes a reliable fact have led to your total detachment from reality. As to TV damaging your brain, that may be your self-delusion, but I can’t help feeling that the real risk to you would be the challenging of the fantasy world your have created.

        • Eric Cartman

          The demonizing of sugar is very anti-science. There is no calorie difference between pop and fruit juices, yet pop is “bad”?
          The starch we eat in huge quantity converts to glucose (sugar) within hours. Why not just make all food expensive?

          • mikewaller

            You seem to understand the facts so why not engage your brain? I have already mentioned the “low-fat” scam, and another is the fruit-juice industry doing all it can to maintain the false belief that fruit juice is an unalloyed good. At its worse with the “Sunny Delight” scandal where that artificial concoction was so aggressively marketed that one (very foolish) mother managed to turn her child orange, it still continues with the routine claim that a small glass of a fruit-juice can be one of your 5-a-day. What the industry is busting a gut to avoid is saying anything about the simple fact that beyond that point – as you suggest – the stuff is positively harmful.

            What we really need is a government with the guts to force the traffic light system down the industry’s throats and a VAT system which only exempts really healthy food and drink. Either directing the VAT thus raised to the NHS or using it to subsidise the good stuff are both worth considering.

    • mikewaller

      My initial response to this was quite lighthearted but I have just read the appalling bilge Booker has had published in today’s Telegraph. There are three elements. The first is the usual dreary attack on the BBC, in this instance comparing it unfavourably with what is on offer in the USA. I go to the States quite often and, contra his views, am usually deeply depressed by what is available there. Yes, there is some very good stuff, but that is usually behind a very significant pay-wall that denies it to the poor. Much of what is freely available ranges from fairly good, to mediocre, to absolutely dire; and to make it all so much worse, most of it is cut in pieces by advertisements which are longer, more frequent and even more awful than ours. As to the discussion programmes he venerates, give me the BBC anytime. And remember, under the current arrangements the BBC provides its massive range of radio and TV services for about £3 per week per household, significantly less than we now pay for our largely ineffectual Police and Crime Commissioner.

      His second element is straight into Farage territory telling us that the situation in the Ukraine is all the fault of the EU. There is no specific mention of the bully-boy Putin but the inference seems to be that what he has done is perfectly reasonable given that he was goaded beyond endurance. Surely, the really big story about the Ukraine is that for all the nonsense about the new world order, we have in Putin a throw-back to the great dictators of the 20th century (several of whom were elected into office) to whom military force is very far from the final option. Telling him that it wasn’t his fault anyway is about as smart as telling Hitler that his “need” to invade and incorporate the Sudetenland was all down to the silly old Treaty of Versailles.

      His final piece is a very good expose of a horrible miscarriage of justice which he rightly brings to our attention. I think it would be a better world were he to stick to this kind of stuff.

      • transponder

        You seem to know all about bilge, old boy. Keep sticking up for those that put us all down, eh?

    • Jambo25

      I much prefer Stanley Spencer’s paintings of Cookham resurrection and the Sandham Memorial Chapel Resurrection. Far more moving than the Della Francesca.

      • Full Name

        Tbh I like some of the original authentic aboriginal “paintings” before it became an industry. The ideas I think being expressed were the Song Lines (Bruce Chatwin’s books is interesting on that) in these somewhat psychedelic looking spot creations! Possibly it’s the simpleness and order that simulates a color representation of the feeling of our subconscious dreams? Unfortunately it’s become an industry and they churn them out now: Song Lines or otherwise.

        • Jambo25

          I quite like some of the more stylised elements of naïve or primitive art but I must admit I’m more at home with 17th century Dutch painting, Turner, Constable, Manet and the Impressionists.

    • transponder

      That’s just a slur. Grrrrrr…..

  • Clarke’s Bookshop was (and under current owners still is) a legend in Cape Town where I live. I spent many hours browsing the groaning shelves in the upper rooms where all sorts of arcane literature could be found.

    He was a quiet, intelligent gentleman (in the real sense) and it’s wonderful to read that he was instrumental in saving this artwork.

  • Full Name

    That was interesting. The more I learn the more I begin to think I should have persevered with mathematics (I did up to A-Level at least) as much as I have with words each day…

    Alex’s Adventure’s in Numberland by Alex Bellos is a good book to inspire about mathematics if anyone is taken in by this interesting story and connection between art and mathematics (usually music hogs the numbers!). He’s also just released a new one too.

    I know I start to enjoy art paintings more when I understand their cultural inheritance – I have friends who are elderly married couple who paint wonderful works (their house is stacked with paintings) of countryside vistas in a stylized bright or at least making the colours the subjects of the work and the sensibility of these people and their world view in the British Isles I can see the connection I think in their work. Usually art and music are closed books to me. Banksy surprisingly seems to get it even if that is an odd artist to bring up in an article about some of the Italian greats.

    So sometimes wonder what makes a painting great apart from the subjective perceptions: Certainly it’s place in history and tradition is a good measure! Stephen Pinker brings up art in his book The Blank Slate and I tend to agree with some of the contributions to the subject he eloquently raises. “Beauty is in the eye of the beholder” could become “Beauty is in the genes of the eyes of the beholder”. Thought the way the construction of reality echoes in fractals and ratios that mathematics describes so well perhaps the truth is in there somewhere. /end ramblings.

  • Sam Sung

    Those of the liberty school understand that voluntary associations of free people are capable of far more than detached central planners.

  • DennisHorne

    Really interesting story. Shows how good Booker is when he doesn’t write on science. Climate change he doesn’t understand.