Tomorrow, it will be time for me to craft a fresh set of New Year’s Resolutions: today, I ponder at how last year’s went so badly awry. In anticipation of my inevitable future slackness, and with intimate knowledge of my inveterate laziness, on January 1st 2015 I made about ten resolutions, hoping that at least one of them might stick. There were plans for running, swimming, tightening up my daily administration routine, getting more sleep, having less screen-time in the evening, curtailing my YouTube binges, eating better, and so on. I made the great mistake of writing these down in a notebook which I have failed to lose. Thus, I can now examine in perfect detail the full extent of my failure.
Yet, although I won’t be winning a triathlon any time soon, a couple of my resolutions did stick, in particular my resolve to vastly increase the quantity and scope of my non-mathematical reading. Realising this, I thought that I would try my hand at an activity which, towards the end of last year, I saw take over the Facebook newsfeeds of my more literarily-minded friends. The idea is to write a list of all the books you have read throughout the calendar year, and, if you should so wish, to draw out a few reflective comments from the collection. I am sure that my list will seem feeble next to that of a true bookworm, but for a man who devotes a substantial amount of his time to thinking about prime number in a darkened room, I don’t think I’ve done too badly.
The adventures of Augie March, by Saul Bellow
I finished this long book on a train, travelling back to Oxford in early January. Martin Amis describes it as ‘the great American novel’, though he is rightly sceptical about the weird bit in the middle, when, suddenly, apropos of nothing, the book’s got an eagle in it. All told, the story is an extraordinarily vivid, endlessly imaginative coming-of-age tale, set in and around 1930s Chicago. My one qualm is that, despite encountering many obstacles of life, Bellow’s ‘everyman’ hero is always rather successful with women – hardly the abiding male experience.
Private Island, by James Meek
This collection of essays, many of which had previously appeared in the London Review of Books, is a concentrated attack on the last thirty years of state privatisation. The overall effect is savage, but the tone elegiac. Meek mourns the passing of the era of, “government intervention, of the belief that the state had the power, the right, and the duty to make a better world for its citizens.” He describes its replacement: “The market belief system holds that government is incompetent by default, that state taxation is oppressive, that desire of wealth is the right and principal motivator of achievement, and that virtually all human wants can be best met by competing private firms.” You will be horrified by Meek’s depiction of the current state of the nation, yet alas Meek does not succeed in his aim to proffer a coherent alternative programme – the chapter on social housing excepted. I could write about this book for days, in great praise, but for now just consider this particular morsel – an obvious idea that I should have noticed before: competition is the driver of capitalism’s success, but one should never imagine that competition is welcomed gladly by all of capitalism’s participators. It is often in a company’s self-interest to try to avoid it, and the company will do everything in its power – which is sometimes quite a lot – to do so.
The Language of Money, by John Lanchester
A humorous, though slightly superficial, glossary on finance-speak. About two years ago I toyed with the idea of writing something similar about mathematical language, and I found here, to my surprise, that some of the difficulties I perceived in the public understanding of mathematical vocabulary, which I had previously believed were unique to mathematics, arise also in the context of finance. These difficulties are eloquently explained by Lanchester; in particular, the difficulty when commonplace words undertake a new technical meaning, and then undergo further modification. The word ‘securitisation’ does not mean anything approximating the phrase ‘to make more secure’!
Lucky Jim, by Kingsley Amis
Lucky Jim was described by Clive James as the funniest book ever written. It does provide some excellent chortles – the madrigal scene, the terrifying lift in Professor Walsh’s car, lines such as, “He disliked this girl and her boyfriend so much that he couldn’t understand why they didn’t dislike each other.” I had expected the humour, but what surprised me most was how, in amongst all the slapstick, Amis manages to provide a myriad of calm, beautiful insights into the madness of individual existence, and the impossibility of ever being able to understand other people’s lives. To offer a non-trivial reservation, it must be said that, despite the existence of a heroine of sorts, the women don’t come out terribly well from the book – though the men do not fair that much better.
1984, by George Orwell
I should have read this long ago. If you too haven’t got round to it yet, I can report that the book is as brilliant and as devastating as you’ve been told, and worryingly easy to read. It made a substantial contribution to the pall that hung over my February, but I’m glad to have experienced its full visceral power. For me, Orwell’s key genius is in creating a dystopia that is both utterly terrifying and completely believable – neither of which Huxley quite manages. He was helped, perhaps, by the fact that the future he was predicting for England already existed as the USSR’s present.
Stoner, by John Williams
Stoner is a short novella – I read it over the course of 36 hours – giving a whistle-stop rendering of the life story of an English Lecturer at the University of Missouri in the early twentieth century. It was Julian Barnes’ book of the year in 2013, though published 50 years before – a rediscovered masterpiece. The contrast with ‘Augie March’ – the other ‘life story’ I had recently read – could not have been greater. From a book in which every minutiae of existence is pored over in detail, I’d gone to one which eschews all but the most critical components of life and, in doing so, encourages you to consider what these truly are. The writing is so economical, so plaintive, on every page raising paragraphs of prose to great poetic heights. It is a beautiful, beautiful book.
Rosencrantz and Guildenstern, by Tom Stoppard
I had an enjoyable evening’s saunter through this great ‘modern’ play – though I guess now it is not so modern. The humour and depth of the constant metaphysical bantering is so good that the moments when one of the titular characters launches into a genuine soliloquy seem rather stodgy, overly philosophical. But maybe these passages just require different skills of the actor, and I must admit to never having seen this play performed. So please forgive this minor quibble of mine with an otherwise deeply moving work, which I will now think about every time I toss a coin, and every time I brim with wanderlust: “It’s still the same sky.”
Birth of a Theorem, by Cédric Villani
I bought a signed copy of this book as a birthday present for my father, but couldn’t resist giving it a quick look before wrapping it up. It is a peculiar book, in almost every sense of that word. It takes exactly the opposite view to that of Stephen Hawking’s publisher – who famously claimed that every equation included in ‘A Brief History of Time’ would halve the readership – by including page after page of LaTeX equations. Villani quipped that, if the publisher’s theory were right, he might only have a few molecules of reader left. But the book has been very successful. The intention behind the approach, the author claims, is not for the readers to understand the equations – such understanding is impossible, even for a trained mathematician such as myself – but to follow Poincaré’s lead and attempt to give a genuine insight into the real life of a working mathematician, rather than shying away, using some tame anodyne replacement. Though the result of this process is slightly odd, Villani has succeeded, and his book has a rare verisimilitude which is lacking from almost all other popular maths books.
Cultural Amnesia, by Clive James
How can I hope to summarise this vast sprawling tome in a short paragraph? Over nine-hundred pages long – only a small indicator of its true vastness – it was given to me by Richard Moxham, the recently retired headmaster of Dover Grammar School for Boys and a childhood friend of my dad. For nearly two years it has been my ongoing project to finish it, and finish it I finally have. The book is a collection of essays about James’ various intellectual obsessions, through which he attempts to sketch an impression of twentieth century humanism. His obsession with fin de siècle Vienna, say, has introduced me to a wealth of humanist accomplishment to which hitherto I had been blind, but really this is just one of the many facets of this, “starburst of wild brilliance,” as Simon Schama puts it. Most of the hundred essays are a humorously vicious skewering of those thinkers who have had the misfortune of rubbing the author up the wrong way. Take Sartre. James doesn’t like Sartre, to put it mildly, and towards the climax of his ritual disembowelling of one of the most preeminent thinkers of the twentieth century, we’re brought to the line, “In Sartre’s style of argument, German metaphysics met French sophistry in a kind of European Coal and Steel Community producing nothing but rhetorical gas.” From James, I have learnt that, in the game of cultural reference, anything goes! Alluding to both the Death Star and Dante in the same sentence may not be classical style, but that needn’t stop you doing it, a lot.
Travels with Epicurus, by Daniel Klein
This is a tiny book, which had been a birthday present from my father to my mother on the occasion of her 62nd birthday: it is about growing old. Beautifully non-prescriptive, Klein builds an admirably down-to-earth philosophy out of his own personal experience, returning to the Greek island he knew as a young man. Unfortunately, if one is looking in the book for an answer to the conundrum of life, the conclusion is clear. If you can retire to a Greek island, you might be alright: otherwise, you’re stuffed.
Travelling to Infinity, by Jane Hawking
Both these next entries have a delightful shared provenance. I was heading back to Oxford after my brief Easter break when I found myself with an unexpectedly long wait at Banbury station. Wondering whether my train had in fact been built yet, I bought an outrageously expensive bacon sandwich from the station cafe and slumped down in a drab metal chair. Looking across again at the cafe, it appeared that they were also selling a small collection of paperback books. In my limited experience the literary offerings from such establishments are rather trashy, yet, most unexpectedly, they were selling two books which I had been meaning to read for a while. I snaffled them up, and the wait passed quickly.
By a strange twist of fate I have a personal connection with Jane Hawking, arising from my singing in her second husband’s choir for several years, and I’d always been curious to read about her life with Stephen, in her own words. Although I found a particular recurring trope – the building up of dramatic tension in the final paragraph of each chapter – to wear a little thin, the tale is fascinating, beautifully told, and it has raised my already great admiration of both Jane and Jonathan to loftier heights still.
The Establishment, by Owen Jones
This second book by Owen Jones is an unashamed polemic against ‘the powers that be’, both institutions and individuals. It is not as lyrically written as the aforementioned James Meek, but it is nonetheless extremely lucid, and brimming with remarkable research. One of the main thrusts of the book is the following question: how there can be any notion of independence of the press and media, given the happy flow of personnel between political advisers, the BBC, think-tanks, and newspaper editors? How can it be that the institutions set to benefit hugely from certain government actions, such as tax regulations, are also the institutions advising the government about those actions? Poachers, turned gamekeepers, turned poachers again. Searching online one can discover that The Telegraph review misses all of the book’s nuances, unsurprisingly. Yet the review is right to point out that Jones’ proposed solutions seem rather unconvincing.
Now time for a maths diversion…
In Hilary Term 2015 – I still catch myself calling it Lent – I ended up doing rather too much teaching. The situation was entirely my own fault, being just a boy who can’t say no, but the upshot was that I had not had quite as much time for research as I would have liked, but had at least managed to earn a fair amount of pocket money. Thus, to ameliorate my condition and clear my conscience, I spent almost all my money on maths books. Combining these with my existing collection I now have a small but rather various additive combinatorics/ analytic number theory-themed library, from which I will now select a few choice items for your delectation.
Opera de Cribro, by John Friedlander and Henryk Iwaniec
The title translates as ‘Sieve Works’. This 500+ page book is the authors’ magnum opus on sieve theory, the mathematical sub-discipline which studies prime numbers as the residue remaining after sieving out by arithmetic progressions. Its commitment to generality and depth can make certain sections difficult to digest on a first reading: yet on more than one occasion, after struggling through seas of silent thought to some small personal sieve theory insight, I have later found the same idea waiting for me in Opera de Cribro, having hidden itself there all along.
Ten Lectures on the Interface between Harmonic Analysis and Analytic Number Theory, by Hugh Montgomery
Purchased on the recommendation of my supervisor, this is a really fabulous book. I had not heard of it beforehand, as it is not perhaps in the ‘Davenport: Multiplicative Number Theory’-class of fame – though it does crop up rather often in the bibliographies of fine papers. Montgomery picks a rather tiny area of mathematical analysis – the subtitle ‘Applications of the Fejér kernel’ would not be too ungenerous – but by showing a huge variety of applications he has helped me to reach a more connected view of my entire subject. I have come across a slightly embarrassing oversight in chapter 2 – in which Montgomery claims that every positive real trigonometric polynomial is the square of a trigonometric polynomial of half the degree – but, such an error notwithstanding, the clarity of exposition and the range of topics covered is exemplary. I used several chapters as the basis for the informal seminar series I gave at the end of last term.
Introduction to Analytic and Probabilistic Number Theory, by Gérald Tenenbaum
Oh Tenenbaum, oh Tenenbaum… This is a recently published third edition of the mid-nineties classic, in which the material is expanded, rearranged and, most importantly, completely re-typeset. Reading both editions has made me acutely aware of how important typesetting is in the overall comprehensibility of a mathematical text: the previous edition was an impenetrable mire, this a model of limpidity. Like the sort of undergraduate student I never was, I’ve actually been going through some exercises. As with ‘Hartshorne’, the famous algebraic geometry textbook, I am getting the sense that the exercises comprise a substantial proportion of the book’s educational worth. This book is the only reference I know of for the Selberg-Delange method, the fruits of which play an important role in my first research paper.
Additive Combinatorics, by Terence Tao and Van Vu.
Written in 2006, this book remains the only vaguely comprehensive tract on Additive Combinatorics. It suffers from being written about a fast moving field, and so a lot of its material – on sum-product theorems, Roth’s theorem, Freiman’s theorem, and the Erdȍs distance problem – has since been greatly improved upon, and in certain cases completely revolutionised. The typesetting is also disastrous, as is also commented upon by Ben Green’s AMS review — not CUP’s finest hour. Yet, rather like Opera de Cribro, it is a veritable mine of information. This year I’ve used it to finally get my head around viewing energy increment arguments in terms of conditional expectations, and to aid my nascent understanding of restriction theory.
The Probabilistic Method, by Noga Alon and Joel Spencer
A classic, and, like all Wiley Classics, really expensive! But there’s nothing like having the book in your hands, and I should have laid my hands on this book long ago. It turns out that I had become familiar with most of the material already, what with the Combinatorics Summer School I attended in Lisbon a few years ago and Prof. Bollobás’ course during my Masters year, but the authors’ exposition is marvellous, and the range of applications discussed is dramatic. The slick proof of the Erdȍs-Kac theorem is my personal highlight.
Leaving mathematics to one side…
The Shakespeare Project
The week beginning Monday May 11th was the unhappiest in my life that I can care to remember. Worse things have happened to me, but never have I been unlucky enough to experience such an accumulation of irksome occurrences. To try to cheer things up, I treated myself to a book. A big book: the RSC Complete Works of Shakespeare edition, to be precise. The thought struck me that, preparing as I was for a monastic summer of mathematical study, it might be a good time for a serious reading side-project, to return to in the evenings after a hard day at mill. One surely cannot claim to be an educated Englishman without an intimate knowledge of the Shakespearean canon and, though there are a couple of plays that – through the quirk of unexpected multiple viewings – I know rather well, beyond these I was completely ignorant, save for the small amount of metadata I conned for University Challenge.
I know that there are many who feel that Shakespeare can be appreciated only in performance, not on paper. Yet though I love seeing the plays in the flesh after having read them, as happened twice this summer, I find that without prior study I lose the full majesty of the remarkable language; the verses torrent by too fast for my untrained ears, and it’s all I can do to keep up with the plot. Shakespeare’s hallmark is the outrageous quality of his by-writing, and it would be such a shame to miss it.
I decided to read the plays in First Folio order, with the exception of ‘The Merry Wives of Windsor’, which it seemed sensible to read only after having finished both parts of Henry IV. The project is still ongoing, though I am about 65% of the way through, but already I have found it to be a life enhancing experience of rare intensity. I have spent New Year at my parents’ house, and alas my RSC edition, in which I have made marginal notes and been a precocious ‘underliner’, languishes in my Oxford room. Because of this fact I will refrain from offering such comments as I have on individual plays until I am reunited with my notes. Let me give you a list of plays I have read so far, and present a couple of anecdotes from my Shakespearian summer.
The Tempest
Two Gentlemen of Verona
Measure for Measure
A Midsummer Night’s Dream
Love’s Labour’s Lost
The Winter’s Tale
Much Ado About Nothing
All’s Well That End’s Well
Twelfth Night
As You Like It
The Merchant of Venice
Comedy of Errors
Taming of the Shrew
King John
Richard II
Henry IV Part i
Henry IV Part ii
Henry V
Troilus and Cressida
Coriolanus
I saw a Globe touring production of Much Ado About Nothing in the Bodleian quadrangle. The portrayal of Dogberry struck me as frightfully familiar, and I suddenly realised that he was the doppelganger of the man who had tried to sell me an iPad that morning: same beard, same accent, same irrepressible self-confidence.
A friend of mine was playing Jacques in an outdoor production of As You Like It in the courtyard of Oxford Castle. My friend was suitably melancholy, and Touchstone a revelation, but my abiding memory will be the incongruous full-cast dance to ‘Uptown Funk’, which the director had decided to insert just before the famous, “All the world’s a stage,” speech. An odd choice.
On June 18th, having spent the entire day reading Love’s Labour’s Lost, I trotted over to St. Giles church for a choral concert given by a few friends. One of their musical items was a series of George Shearing settings of various Shakespeare songs, including the one that I had read only a few hours previously, the song with which Love’s Labour’s Lost finishes. I started in my seat when I began to recognise the text!
The Murder of Roger Ackroyd, by Agatha Christie
I read this on a rainy day in Worthing, in a very strange flat which my parents had rented for the week (me joining for the Bank Holiday weekend). The flat was decked out with multitudinous art deco regalia, and possessed a formidable Agatha Christie collection. My father and I were entranced.
Four Parts, no waiting, by Gage Averill.
My father gave me this book for Christmas several years ago, but at the time I lacked the academic maturity to stick it through. The book is an extended musicological essay on the place of Barbershop music in American culture, in particular its relationship with race and with institutionalised nostalgia, through the Barbershop revival movement. The style was for the most part rather ponderous, and I would have liked much more discussion of gender, but an interesting read nonetheless and a source of rich insight into the early era of musical recording.
The Pilgrim’s Progress, by John Bunyan
I came to read this after singing Vaughan-Williams’ ‘Valiant for Truth’ in the Schola Cantorum UK tour, after which I developed an interest in understanding where the mesmerising text to that particular work fits in the overall novel. It turns out to come from the second book, concerning the progress of Christian’s wife and children, and alas it represents somewhat of an outlier of literary quality in the book, which is less a novel, more an acute case of liturgical reference diarrhoea. Nevertheless, the section in Vanity Fair is quite remarkable: in trying to describe the worst den of iniquity he could imagine, Bunyan outputs a rather tame description of21st century consumerism.
Godel, Escher, Bach, by Douglas Hofstadter
I’ve written a whole other blog post about this one. Vast, weird, unique.
The Chinese: Portrait of a People, by John Fraser
I’ve not quite finished this yet, having saved it from a charity shop box as it left my parents’ house, who, at my last reckoning, have upwards of 2000 books in a moderately sized semi-detached. The book is a very classily written account of the author’s two-year stint as a journalist in Peking in the late 1970s, and how he found himself caught up in the democracy demonstrations which occurred around the Xidan wall in the winter of 1978.
What are my literary plans for next year? Well, given that we seem to be entering the Wars of Religion, a quick perusal of the King James and the Qu’ran seems in order. There’s a lot of Shakespeare still to finish. As for another big project, I am frequently embarrassed by how little Dickens I have actually read, but also by the fact that only one female author appears on the above list. Perhaps I’ll mix some Dickens with some Mary Ann Evans (aka George Eliot).
Plenty to be getting on with.
Aled Walker 