Tuscan travel in 2016

‘It all happened on Tuesday July 5th, barely 48 hours after I had arrived. Cowering from the afternoon heat in my small attic room I had attempted some maths, but then submitted to sleep, taking an overlong siesta before finally cooking dinner on the little gas hob; it was nearly 8pm by the time I ventured out for an evening passeggiata. The sweltering day had receded to sultry dusk, and I trotted from Santa Croce, along Borgo dei Greci, past San Firenze, and through to Piazza della Signoria.’


The year is spent. Growing up it was an unwritten tradition, on this day or near it, for my mother to ask me, “What was the best thing you did in the last twelve months?” My fading memory struggles to grasp my past replies with any certainty: yet I can be sure of one thing, that, on each occasion, I never had to think for very long, to plot the arc of my year, to consider its triumphs and its defeats, and to light upon my unwavering response. This New Year’s Eve feels markedly different. Perhaps the most obvious reason for this state is that, although still dancing to the familiar rhythm of the academic calendar, this has been the first of my university years to have been devoid of any obvious culmination or conclusion. I suffered exams every summer from the ages of 10 through 21, of varying degrees of significance; the summer of 2015 was my first without them, but even then I had begun the year still with the vertiginous sense of setting out on my research studies, and in November I had had the ‘Transfer of Status’ thesis to prepare, signifying at least, as Churchill might have put it, ‘the end of the beginning’ (of my third degree). In 2016, by contrast, I have been deep inside the long slow progression of the middle-portion of a mathematics DPhil. A bewildering array of things have happened, in my research and without, both good and ill, but though my mind teems with experiences, there is no grand unifying order, no natural aid to analytical reflection.

The brief summary, as it has been every day since the day I was born, is that I am outrageously fortunate in almost everything — to be paid to think all day and still to have the cheek to call it work. In exchange, what is there to offer but just to think really hard, and to be grateful? (Of course I teach too, do outreach with teenagers, interview for undergraduates, run the weekly maths department social, run and host a wide-ranging university podcast, give around 3 seminar talks and perform in around 10 musical concerts each year, but that’s not what my grant pays me to do). Yet, both of these laudable aims — strong work-ethic and humility — face competition from the self-absorption which begs to follow from having a day-job involving such long periods of introspection, voyaging though strange seas of thought, alone. This end-of-year note, of course, is really one vast ego-trip. I guess all you can do, if you allow yourself a temporary submission to the calls of narcissism, is to be narcissistic in an entertaining style.

One theme that has seemed to have typified 2016 has been the quantity and extent of my travel. Lucky accidents and an extremely understanding doctoral supervisor saw me in Mexico, France, Italy (for a month), and Austria, along with brief stays in Edinburgh and the Lake District. Only that final stay — on Esthwaite water, a skipping stone’s throw from Wordworth’s old school — was a traditional holiday. My 11 days in Mexico were spent on an astonishing choir tour with Schola Cantorum, centred around two concerts with the National Orchestra in the Palacio de Bellas Artes (a marvel of art-deco design, slowly sinking into Texcoco Lake, along with the rest of Mexico City); a conference saw a week of talks and discussion with most of France’s additive combinatorialists at the University of Bordeaux (I gave my first ‘grown-up’ research talk, and initiated a new collaboration); and then ELAZ 2016 happened, a meeting of elementary and analytic number theorists, which induced around 70 other mathematicians to take over a lakeside teacher-training complex in the Salzkammergut (the stunning region of lakes and mountains beloved by both Austro-Hungarian emperors and circle-method experts alike). In some peaceful future hour I hope to pen some pieces about each one of these trips. In fact one remarkable experience during the half-day break in the middle of the ELAZ conference, centred around my returning pilgrimage to the musical instrument museum in St. Gilgen, begs to be transformed into something approaching a short story. Another time.

My stay in Italy was of an altogether different nature, not least because of its much greater length — if one neglects a brief return to the UK in order to attend an old school friend’s wedding, I was there from July 3rd until August 7th, by quite some margin the longest foreign excursion of my life (never having done the canonical teenage European inter-railing). For the final 6 days I was in Rome — the eternal city, another ten personal tales to tell — but the majority of the time was spent in Florence, spending the afternoons battling the Inverse Large Sieve problem in the reading room of the Biblioteca Nazionale and the mornings learning Italian at the British Institute. I’ve had a dilettante’s fascination with Italy and the Italian language for a fair while, and serendipitously now find myself surrounded both by Italians in the Oxford maths department and by Italian itself in my tentative forays into classical baritone singing. On this justification and more, I was fortunate enough to receive one of the three tuition-fee-funded exchange places from Magdalen to study at the British Institute for a month. So, at the start of July, I packed my bags, said goodbye to the circus, boarded with a married couple of professional pianists on Via dei Benci, and began my stay at culture’s cradle.

Florence in summer is a strange place, populated almost entirely by tourists. Indeed, I barely saw my hosts, as they spent most of the month down at the cost by Isola d’Elba. What’s more, the language which fills ones ears during a morning stroll — my commute cut right across the centre of town, from Santa Croce to Piazza della Signoria to Piazza della Republica — is not Italian, but English, such is the concentration of visitors from the US and the UK and the linguistic accommodation of those wishing to sell the town to them. Passive language assimilation is therefore rather difficult, and though I studied hard I didn’t leave as fluent as I had hoped. But, though I won’t be able to woo you with Petrarch, I will at least be able to buy your groceries; in Rome I could potter around town without needing recourse to English, performing all the little administrative tasks that were required of me, and even being able natter briefly with any curious locals as to my views on the recent Brexit vote. But a trip to the enoteca shattered any grand notions of personal competency: there is still much work to be done.

Though these days my musical affinity with Italy stems largely from my burning life-ambition to play Marcello in a production of La Boheme, the city of Florence is also the subject of what for a decade or more has been one of my favourite musicals, ‘The Light in the Piazza’, with lyrics and music by Adam Guettel. (A rather interesting character — though Richard Rodger’s grandson, his music descends more from Sondheim and Ravel). The basis for the plot is simple enough, though depth later emerges quite unexpectedly: a mother and daughter from South Carolina travel to Florence, Rome, then Florence again, and meet some handsome Italians. The admirable opening number is itself called ‘Firenze’ (the best song is the mother’s 11 o’clock heart-wrencher, ‘Fable’). Florence is, “a city of statues and stories,” so Guettel tells us, and regarding said statues I can confirm that the original of Michelangelo’s David, now housed in the Galleria dell’Accademia in pristine conditions after having been moved from the Piazza della Signoria 100 years ago, is worth all the hype and more. For a contrast, the Arnolfo di Cambio ‘Madonna of the glass eyes’, striking in its medieval simplicity and directness, is my off-beat recommendation. My favourite sculptures of all however, also rather curious, were the Andrea Pisano stone relief series labelled, “The beginning of…” which used to adorn the campanile but now are to be found in the refurbished Museo dell’Opera del Duomo. There are around 20 hexagonal pieces, each utterly charming, witty, technically intricate — ‘The beginning of navigation’, with three wily seafarers paddling furiously off towards stage-left, and the beginning of farming, with even the shepherd himself surprised at the how the gossamer lightness of his tent has been conveyed in stone, are the best.

Regarding the stories, there are already so many soaked into the stone that, on the one hand, it seems wholly unnecessary to add my own. My conversation with Roberto at the Mercato San. Ambrogio, as he sold me a pair of shorts for 2 Euros; being taught the finer points of muscle toning when happening to end up watching Andy Murray win the Wimbledon final with two professional sports physiotherapists; accidentally spending ten minutes in Venice after taking a wrong train; finding Fermi’s grave alongside Michelangelo’s and Machiavelli’s; singing ‘Vecchia zimarra, senti’ in a 16th century palazzo; hearing a Haydn string quartet in the courtyard of the house where Michelangelo was apprenticed; the day in San Gimignano; Peter’s hilarious poem about the future tense; Suzanna’s teaching. But, already taxing your patience, I will restrict myself to just one, already begun.


‘The piazza was busy, one side brightly illuminated by the powerful spotlights mounted on the far buildings. In the corner by the outdoor copy of Michelangelo’s David a crowd had begun to gather, but the shadowy sides were still populated by a Florentine peculiarity — the fluorescent sycamores. These remarkable devices have two floppy glowing plastic wings, and, when the ensemble is catapulted at speed into the air using a hand-held elastic sling, these wings fold back and create a streamlined shape which can achieve astonishing heights, nearly level with the buildings surrounding the piazza, if not the tower of the Palazzo Vecchio itself — a good 30 metres or more. Yet the true ingenuity of the design is that, when gravity eventually obeys Galileo’s call, the wings are pulled out in such a way that the object is moved to rotate extremely rapidly — like a sycamore seed — winging its way slowly down to earth. Every night, including this one, about ten young men of the town, intent both on proving their own virility and on selling these marvels to the goggle-eyed children passing through, would gather in the open spaces and fire their wares high up into the silent sky, for hours on end.

Leaving these behind, I turned around Neptune’s fountain to discover that the throng of spectators, by now numbering around 300, were watching what could only be a big band, in the final stages of setting up. The players, dressed in immaculate black, were going to be performing on a temporarily constructed platform, which had been erected to David’s right — between him and (the copy of) Donatello’s lion. They were carrying a rhythm guitar, rather than a keyboard player — a small dagger, me having spent the Monday evenings of my adolescence practising the rarified art of the big band jazz pianist — but other than that they seemed to be the real deal. Announcements, in Italian, followed quickly; my two-day-old nascent Italian ear found these utterly incomprehensible, save for some reference to Glen Miller, but then the language lesson ceased, and ‘String of Pearls’ began to waft gently over the air. How unendingly curious, this world, in which a tune which I had played not a week previously, filling in at the rehearsal of my father’s big band, in an Egbaston Quaker Meeting House, could now be heard again in such different surroundings.

The next tune was ‘American Patrol’, which I had first played almost exactly 10 years previously, preparing for the tour of The Netherlands as part of the Birmingham Schools’ Jazz Ensemble. From the slightly faltering nature of the improvised solos I concluded that the band was probably amateur rather than professional — no doubt this had been clarified during the unknown introductory spiel — but they were as tight as could be. David smiled down, the fountain trickled — all was well.

I left the Piazza, and continued my walk up Via dei Calzaiuoli, the wide promenade, lined from top to bottom with the shops of luxury Italian brands, connecting the Piazza della Signoria with the Piazza del Duomo. This is prime passeggiata location, and I would return several more times before July was through, taking the sweet, delectably humid air whilst wondering if I would be propositioned by some fiery Tuscan damsel. Apparently this is the sort of thing that should happen on a passeggiata (it never did). The music faded as I approached the green brilliance of the Duomo itself — back with the sycamores — and I did a circuit of the baptistery before returning south the way I had come. It is worth mentioning that, as the historic centre is build roughly on a grid pattern, one quickly develops a compass sense in Florence. The position of the sun at different times of day greatly affects which directions of travel will be afforded some shade: crossing east to west in the morning or evening, particularly along any of the Lungarno streets, is a recipe for blindness and sunburn, but attempting a north-south traversal during the middle of the day, on Via dei Calzaiuoli or any of the other wide avenues, is even worse. Melanoma in a moment.

Anyway, the sun had long set, and it was rather a thrill to be able to freely walk this path without oozing factor 50 from every pore. But this thrill faded, and, whether overtired from the acclimatisation to the new location and new heat, or touched by a deeper malaise, an unease then began to dwell upon me, as the music swelled anew.

By the time I returned to the square, observed the standing crowd beginning to take partners and dance, the Loggia dei Lanzi carpeted with beaming faces, the very sculptures themselves appearing to turn to the shining trumpet-brass — even the severed Medusa’s head of Cellini’s bronze looked to be enjoying herself — I was struggling to hold back a tear. “Why this rush of self-indulgent sentiment?” I wondered to myself, self-indulgently. It struck me that I was seeing, strewn across my present gaze, a vision of some of the greatest works of visual art which had ever been made, frozen in time, kept as they once had been, preserved through solemn care: not preserved through a living tradition. The piazza was a time-lock, miraculous, beautiful, but dying — dead already, perhaps. How many of those happy revellers had the skill, the talent, the desire to make sculptures as beautiful as those which had been made four centuries before their births, the sculptures about which they blithely danced? How many would notice the lack, even, notice the poverty of humanity’s current aesthetic ambition, that no-one cares to sculpt like Giambologna anymore? Is this to be the grand summation of our creative worth: a single, unchanging square, trapped amongst the tourist tat? Such thoughts for the grim fate for the classical arts crowded upon my fevered brain.

Yet more, the juxtaposition of expressive forms made me begin to fear the same end for my treasured jazz. The 40s big band and David, side by side; not equivalent or even comparable creations, true enough, but here, in this place, weren’t they performing the same function? Beguiling reminders of a lost yesteryear, of a lost people who could write such songs and work such stone: of lost art? The band were playing ‘Lil’ Darlin’ ‘ now, impeccably beautifully. But is this all that we will have in the age to come? Expert regurgitations? Why isn’t every budding Michelangelo champing at the bit to try to write a chart as sublime as ‘Lil’ Darlin”? To those few of us who fell in love with these sounds and styles in childhood years, are we doomed to live out our days as witnesses to the creeping death of our beloved music, its condemnation to the same open-air museum?

The last time I was in Florence, I was not dancing alone. If on this occasion I had been able to join the jiving couples, perhaps I would have been distracted from this existential pang: as it was, my despair was absolute.

But then, a new announcement, as incomprehensible as all the others, but for a single verb — ‘telefonare’. “They’re about to play Pennsylvania 6500!” I thought (the ditty about a lover’s excitement and desire to dial his sweetheart in New York City, arranged by Glenn Miller for big band, curiously expunged of all lyrics save for the titular telephone dial itself). And sure enough, the loping saxophone line ambled out, followed by the entire band shouting, as I have done myself many times, “Pennsylvania 6, 5, Oh Oh Oh!”. But this was an Italian band, and Italians don’t really do diphthongs, their ‘Oh’ vowel crystal bright, cardinal — it sounded a little ridiculous! The smile returned to my face, if through tears, and I retreated back around the square, through the frolicking couples, stopping on one of the two benches placed by the main entrance to the Palazzo Vecchio. I had been carrying around some mathematics notes in my rucksack. So, settling myself down to consider whether Chebyschev’s inequality would yield any non-trivial bound in my toy function-field large sieve problem, I passed the evening.

Several scribbled pages later, after I had convinced myself that the error-free nature of the Chinese Remainder Theorem application meant that — for rather dull reasons — Chebyschev’s inequality was applicable, my meditation was broken by the interests of an Italian family at the other end of the bench. Somebody parking themselves down in the centre of Florence and filling pages with unfamiliar symbols was an object of some curiosity, it seemed. Through a disarming directness and charm, the man closest to me initiated conversation. He was visiting his brother, who worked on a vineyard in Chianti, about 20 kilometres south of Florence — I received that brother’s ‘biglietto da vista’. In stumbling reply, I managed to convey that I was a graduate student from Oxford, studying mathematics, but that I was also studying Italian for this month. They seemed very impressed with my conversation given that I’d only been learning for two days: I didn’t have the heart, or the linguistic ability, to explain that I’d been studying grammar and vocabulary in isolation, on-and-off, for nearly a year. Rather pleased with myself for having made some new Italian friends, without any need of English — the language spoken by, “the Gods of my cradle,” to quote the mathematician Hermann Weyl — I was expecting polite parting and a return to my work.

But this is not the Italian way. It quickly became apparent that they were really interested to know more precisely what I had been thinking about — what manner of abstract witchcraft could occupy the mind so fully? The brother was a trained mechanical engineer, with substantial mathematical literacy. Now, explaining what I study, in English, with slides, and lots of preparation time, is tricky enough — this past Michaelmas I just about managed to do it in 6 minutes, with slides that had taken me the best part of a day to prepare. On the spot, at 10 o’clock at night, on a bench in the middle of the Piazza della Signoria, in a language I don’t really speak, whilst already feeling over-emotional… I nearly ran straight for Fiesole. Yet powers of paraphrase swelled within, and vigorous gesticulation — combined with a fair splattering of that golden phrase ‘studio i numeri primi’ — sated my companions’ curiosity.

The performance over, me glowing with nervous pride, they had to be on their way, and, after a respectful pause, I too retreated home, forever changed. The following week, I would successfully explain in Italian, to the rest of my distinctly non-mathematical language class, why there were an infinitude of primes. I never saw the brothers again.’



A single evening, from happiness to despair to hope, through mathematics and jazz, in broken Italian. If that isn’t a microcosm of my year, I don’t know what is. Happy 2017.


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