Professor Stewart’s Cabinet of Mathematical Curiosities – Ian Stewart

After a series of novels, time for something factual and an exercise for the brain. Ian Stewart was Professor of Mathematics at The University of Warwick when he wrote this book in 2008 and still holds that title although now Emeritus since he retired. He has written numerous books on mathematics, several of which I own so this was chosen as the first one I picked off the shelf, he was also the third person to write the recreational mathematics column for the periodical Scientific American, taking the reins from 1991 to 2001. This column was started by Martin Gardner back in 1956 and he wrote it until the mid 1980’s and this was the true start of my love of mathematics so it has been a pleasure over the years to have sat in a few bars with Ian and discuss maths and also to enjoy his very readable books.

This book, along with it’s sequels Professor Stewart’s Hoard of Mathematical Treasures’ from 2009 and ‘Professor Stewart’s Casebook of Mathematical Mysteries’ from 2014, are an interesting mix of puzzles and mathematical history and are partly built upon notebooks that Ian started whilst still at school and more snippets that he has gathered over his long career of anything that looked fun or interesting in the field of mathematics. I had come across roughly half of the puzzles before and it’s surprising it was so few as I have lots of maths puzzle books but the 249 pages of puzzles and essays plus 60 pages of solutions and/or further further discussions on points raised contained a lot that was new to me. Of the essays I particularly liked his short summary of Fermat’s Last Theorem and how Andrew Wiles finally came to solve it centuries later. Ian demonstrates his skill as a good teacher in these essays, not simplistic, after all anyone picking this book up will have an interest in mathematics but not too complex either. The solution relies on a whole new branch of mathematics so he doesn’t try to explain how the solution works but instead explains why it is important and hints at the complexity involved. There are also essays on fractals, chaos theory, various famous mathematicians and numerous important conjectures and theorems spread throughout the book.

It is in the puzzles though that Ian allows his wit to shine through, even if sometimes that is just a series of bad puns as in ‘The Shaggy Dog Story’ which is a fun rewriting of a really old puzzle that would be familiar to almost all readers of the book so he dresses it up to still make it fun and then in the solutions section introduces a variant of the puzzle which I hadn’t come across before. The puzzle involves the terms of a will where the eldest son is to have a half of his fathers dogs, the middle son a third and the youngest a ninth. Unfortunately when the father dies he has seventeen dogs so the division looks like it could be quite messy if the will is to be executed exactly. The solution is actually quite easy and I first saw this puzzle over forty years ago but I’d never seen the follow up question which can also be solved where the legacy of the first two sons remains the same but the third son gets a seventh of the dogs and the puzzle is reversed because you have to work out how many dogs the father had in order for there to be a solution with no dogs harmed. If you haven’t seen the original puzzle before I’ll put the answer at the end of this blog.

I’d recommend this book to anyone with an interest in maths, the essays are fascinating, the puzzles fun and you’re guaranteed to learn something new.

I also have both the subsequent books in this style and there is an interesting part to the introduction of the second book, I’ll reproduce it here.

Cabinet was published in 2008, and, as Christmas loomed it began to defy the law of gravity. Or perhaps to obey the law of levity. Anyway, by Boxing Day it had risen to number 16 in a well known national best seller list, and by late January it had peaked at number 6. A mathematics book was sharing company with Stephanie Meyer, Barack Obama, Jamie Oliver and Paul McKenna.

This was, of course, completely impossible, everyone knows that there aren’t that many people interested in mathematics.

Ian therefore unexpectedly received an email from the publisher wanting a sequel which did well, but not as well as the first hence the longer delay before the third book. The Casebook is easily the weakest of the three as too many puzzles are dressed up in cod Sherlock Holmes stories which frankly only serve to pad out the puzzle and it appears to have been remaindered as I didn’t know it existed until planning to write about the first two and got a brand new still shrink wrapped first edition copy for a third the original price seven years after it originally came out.

Dogs problem solution – You just need to borrow a dog from somebody else. This will mean you have 18 dogs, half of that is 9, a third is 6 and a ninth is 2. As 9 + 6 + 2 = 17 you can then give the borrowed dog back, Now try the follow up question…

Memoirs of Prince Alexy Haimatoff – Thomas Jefferson Hogg

This book is quite possibly unique in the annals of publishing in that the first review of it is far more famous than the book itself and that review has also been reprinted many more times than the book it was reviewing. This however is not difficult as following the first edition in 1813 (reprinted 1825) the next edition appears to be this one by The Folio Society in 1952 which has never been reprinted and apart from some modern ‘print on demand’ publishers offering it, as they offer most out of copyright works, that appears to be the sum total of published editions. So what about the review? Well that was written by Hogg’s friend Percy Bysshe Shelley and first appeared in The Critical Review in 1814. Hogg and Shelley had met at University College, Oxford where they were fellow undergraduates, one was destined to become a London barrister and the other one of the great romantic poets but if Hogg is remembered for anything nowadays it is his unfinished biography of Shelley which he was still working on when he died in 1862 forty years after the untimely death of his subject. The two nineteenth century printings of Memoirs of Prince Alexy Haimatoff are both extremely rare. Worldcat, the international library catalogue, lists one copy of each, both of which are in the British Library in London, there is also one copy of the 1825 reprint currently for sale in San Francisco. Regular readers of my blog will know that I sometimes include a link to out of copyright books at Project Gutenberg but I can’t do it for this book because it doesn’t even exist on that site.

Shelley’s review has however been reprinted many times either as a very short stand alone booklet or in collected editions of Shelley’s works, it is also included at the back of this Folio Society edition. It is 9½ pages long, which as it includes large chunks of the original book to illustrate his points is not very long at all but the real surprise is that The Critical Review published such a lengthy review by an unknown critic of a book that sold so badly that it has virtually vanished without trace.

But lets look at the book itself, the Folio Society edition is beautifully bound in quarter buckram with marbled boards and has eight wood engravings by well known Scottish artist Douglas Percy Bliss who was then Director of the Glasgow School of Art. It also has an interesting introduction written by Sidney Scott which looks not just at the novel but the friendship between Hogg and Shelley, they had collaborated a couple of times at university including on a pamphlet entitled ‘A Necessity of Atheism’ which, although published anonymously, was soon traced to the two friends who were both summarily rusticated, never to return to their studies. Hogg continued this idea of hiding the true author through to this book as the Memoirs were originally published as though it was a genuine translation from the original Latin by a mysterious John Brown and it was many years before Hogg was identified as the actual author.

Meeting the Sultana – Wood engraving by Douglas Percy Bliss

You may feel that I’m taking a long time to get to the novel itself. There is a very good reason for that and it is the same reason that the book is so rarely published and that is that it isn’t actually very good. The narrative is disjointed and whilst there are passages that are beautifully written these are soon let down by huge gaps where much has clearly happened but it is covered in just a line or two with no explanation as to how we have moved from one position to another. At one point after escaping from the clutches of the Sultana in Constantinople, who intends to poison him if he leaves her, he wishes to replace his desire for her by bizarrely buying a female slave that reminds him of the Sultana. We spend several pages at the slave dealer but then after getting her to Naples she bears him two sons before dying along with the children of smallpox within a few lines. This is not the only occasion where the treatment of women is reprehensible but serves as a good example of the whole. The extremely odd German cult that Haimatoff joins is just plain strange and it really isn’t clear why he would have committed himself to it which includes being locked in a room for three months with no human contact or any means of passing the time such as books or pen and paper. I have categorised this blog as a book tale not a review as the story of how the book appeared and disappeared is actually more interesting than the plot. The Folio Society edition is almost seventy years old now and I can’t imagine any publisher setting out to publish it again but it was interesting to read such a rare book, if you want to then the Folio edition is easily found secondhand online for just a few pounds. The 1825 copy I found in San Francisco is over £3000.

I will leave this with the final two paragraphs of Percy Byssche Shelley’s review which I think sums up the book quite well even if he was being overly generous to a friend.

In the delineation of the more evanescent feelings and uncommon instances of strong and delicate passion we conceive the author to have exhibited new and unparalleled powers. He has noticed some peculiarities of female character, with a delicacy and truth singularly exquisite. We think that the interesting subject of sexual relations requires for its successful development the application of a mind thus organised and endowed. Yet even here how great the deficiencies ; this mind must be pure from the fashionable superstitions of gallantry, must be exempt from the sordid feelings which with blind idolatry worship l the image and blaspheme the deity, reverence the type, and degrade the reality of which it is an emblem.

We do not hesitate to assert that the author of this volume is a man of ability. His great though indisciplinable energies and fervid rapidity of conception embodies scenes and situations, and of passions affording inexhaustible food for wonder and delight. The interest is deep and irresistible. A moral enchanter seems to have conjured up the shapes of all that is beautiful and strange to suspend the faculties in fascination and astonishment.

Percy Byssche Shelly in The Critical Review 1814

There is an extremely badly formatted version of Shelley’s review available online here. If anyone knows of a better version I would love to hear of it so I can replace this link.

A Room with a View – E M Forster

Originally published in 1908 this Edwardian romance and comedy of manners is nowadays regarded as one of the classics in English literature although probably not rated as highly as two of Forster’s other novels ‘Howards End’ and ‘A Passage to India’. I know I have read it before, probably around 1985 when the Merchant Ivory film adaptation came out, but to my genuine surprise I realised that I had completely forgotten the story line when I started reading it again this week. I chose this over the other two, that I also have on my shelves as a good friend of mine in Barcelona has just started reading a brand new Catalan translation along with two friends so I thought it would be fun to join in with the English original.

The novel is in two parts, the first of which is set entirely in Florence, Italy whilst the second part mainly takes place in England. We start with twenty year old Lucy Honeychurch and her much older cousin Charlotte Bartlett, who is acting as her chaperone, newly arrived at the Pensione Bertolini in Florence and bemoaning the fact that neither of them had been allocated a room with a view despite being assured when booking that they would each have a good view of the square and the river. We are then rapidly introduced to the other guests at the hotel as they discuss the situation leading up to Mr Emerson and his son George offering to swap rooms as they do have good views

“What I mean,” he continued, “is that you can have our rooms, and we’ll have yours. We’ll change.”

The better class of tourist was shocked at this, and sympathised with the new-comers. Miss Bartlett, in reply, opened her mouth as little as possible, and said “Thank you very much indeed; that is out of the question.”

“Why?” said the old man, with both fists on the table.

“Because it is quite out of the question, thank you.”

“You see, we don’t like to take—” began Lucy. Her cousin again repressed her.

“But why?” he persisted. “Women like looking at a view; men don’t.” And he thumped with his fists like a naughty child, and turned to his son, saying, “George, persuade them!”

And so within the first couple of pages we hit on the class difference between the Emerson’s and the other guests at the hotel as Lucy and Charlotte were shocked by the suggestion as it would leave the two women under a perceived obligation to two strange men, something that never occurs to either of the Emerson’s. It is this perceived total social unsuitability of these men to the rest of the group that provides the dynamic through the remainder of the book as various characters keep meeting them and recoil regarding their ‘common ways’. In fact a clergyman, Mr Beebe intercedes and convinces Charlotte that the exchange of rooms can be done without obligation so they both end up with a room with a view by the end of the first chapter. I don’t want to give away the plot but suffice to say that Lucy finds herself accidentally alone with George on more than one occasion whilst in Florence to the considerable embarrassment of her and the pleasure of him.

Part two has a sudden shift in location and time, clearly many weeks, if not months have passed and a new character is introduced, Cecil Vyse. We are also at the home of Mrs Honeychurch, Lucy’s mother in the fictional village of Summer Street in Surrey. Slowly various characters that made up the guests at the Pensione Bertolini also appear in the village either accidentally or deliberately and the tensions between the group are reproduced only this time with the added complication of Cecil who has become Lucy’s fiance or her ‘fiasco’ according to her brother Freddy and never a truer word was said in jest. The problems caused by various unseemly, at least to the mores of the time, acts or words by the assorted people and again unfortunate meetings and misunderstandings carry us through a thoroughly satisfying final chapter. I greatly enjoyed the book and the interplay between the characters and although many of the things they regard as shocking or unsuitable would not be so nowadays the fact that Forster is gently poking fun at them is always clear.

The edition that I currently own is from a set of six Penguin Classics designed in 2008 by Bill Amberg, the London based leather work studio, each book comes in a sturdy box with a belly band indicating which book is inside. The book itself is fully bound in a soft brown leather with a hole punched right through the cover and all the pages in the top left corner where a leather book mark is attached with the titles and author embossed in it. The only thing marking the cover itself is the Penguin Books logo at the base of the spine. It is also incredibly difficult to photograph accurately, the photos below are as close as I could get, with the bookmark being the closest to the actual colour of the leather. The leather cover overlaps the pages by a significant amount making it a yapp binding where over time and repeated reading the leather will fold over to totally encase the book. Each book was published in a limited edition of 1000 and priced at £50 per volume.

For the Penguin Classics leather binding I have chosen a vegetable tanned, buffalo calf. I should stress that all the skins were taken from ‘fallen animals’ – i.e. they died from natural causes – and were sourced from India’s premium calf tannery. They use traditional methods in a totally ecological process, where the water used is recycled after filtering through reed beds. This creates leather that improves with every use, the grain and sheen brightening continually over time.

Bill Amberg

Leaflet included with the book

Chekhov: A Life in Letters – edited by Gordon McVay

Rather than produce a standard biography, Gordon McVay has translated and edited a selection of letters from Anton Chekhov which give a wide view of his interests and career development from starting medical school in Moscow in 1879 through to his final letter in June 1904 written the day of his heart attack which would ultimately prove fatal four days later. There are extensive notes that put the letters into context and this has proved to be an excellent use of the material as Chekhov is a lively letter writer and travelled extensively so his correspondence is full of detailed descriptions of his experiences both good and bad. My copy is the Folio Society 1994 edition bound in black buckram and embossed with Chekhov’s signature across both covers. The book is currently available as a Penguin Classics edition. To give a feel for the letters I’ll selected a few extracts and will add them between paragraphs in this blog.

23 December 1888

That this represents just a tiny fraction of Chekhov’s letters is proven by the regular mention in the notes of a thirty volume Soviet edition and even that is not complete because it can only include those letters that were kept by the recipients. The Soviet edition is also censored to remove things they didn’t feel appropriate, such as his dalliance with a Japanese woman on his trip to Sakhalin, and anything judged not politically sound. The edition I have has 365 pages dedicated to the letters along with a useful 22 page introduction and an excellent index which made going back to find things I wanted to refer to very easy. That the Soviet edition is censored is actually quite appropriate as Chekhov complains many times about what the censors in his own time had done to his stories and plays, some of which he regarded as particularly badly damaged so that the sense of the play is lost.

In Siberia on his way to the island of Sakhalin 1890

In 1890 Chekhov travelled to the penal colony of Sakhalin to survey the conditions and interview prisoners for what he explains in various letters is a payback to medicine. It eventually took him three years to write up his findings to appear in ten parts in one of the serious journals and then more work to produce a somewhat longer book. Presumably he wrote letters from his months on Sakhalin but none of them are included in this collection however there are quite a few describing his massive journey by horse drawn carriages and river boats right across Russia as Sakhalin is as far east as it is possible to go and he started in Moscow. The extract above highlights that even then Siberia was a place of exile for people that had offended the state in someway but his observation that now they can say what they like as where else would they be sent is to the point. On Sakhalin he was only allowed to interview a small number of the political prisoners but he still produced a comprehensive report and oddly his health, which was never very good appeared to improve during his time away from Moscow and St Petersburg. Although he was a doctor he seemed to have a blind spot regarding his own tuberculosis which he suffered from for decades, describing many occasions of ‘blood spitting’ although he was never formally diagnosed until 1897.

4 July 1888

The letters are also often quite humorous which lightens the tone overall against some of the more serious pieces or times when things are just plain going wrong like his descriptions of the disastrous first performance of The Seagull in 1896 or when his health issues cause significant problems which was quite often. One of the more interesting features is the continuation of his career as a doctor even as his fame as a playwright and story writer grew dramatically. As can be seen below this devotion to medicine had serious implications in his ability to write of travel to oversee productions of plays and talk to his various publishers. By the early 1890’s he had purchased an estate in Melikhovo and become the local doctor in preference to renting a home in Moscow which he had done since arriving there to study as a doctor.

16 July 1892

By the mid 1890’s however he had started travelling extensively in Europe and correspondence from various Italian, French and German cities amongst other countries he passed through bring a different outlook to the letters, some places he loved others he was glad to see the back of. There is also a lot of letters to women throughout the book some of which he probably came close to marrying but in fact he was a confirmed bachelor until just three years before he died when he finally married an actress he had come to know from her performances in his plays. Oddly his letters to women, even the ones he was particularly close to, are rarely romantic and quite often have some slight barb to them. The ones to his future wife, Olga, are mainly about her performances rather than anything else even though they actually lived almost 1000 miles apart most of their married lives as she was in Moscow and he was in Yalta to get a better climate for his tuberculosis. Chekhov was much happier on his own, hence his long time avoidance of marriage and indeed living apart suited him well.

13 June 1890

The letters are great fun to read and show much more of Chekhov’s character than would be found in a biography. I don’t think I could cope with the full thirty volumes, even assuming they were available in English, but this selection made an excellent way to pass a few evenings this week.