Category Archives: Autobiographical

Robert Hunter (June 23 1941–September 23 2019)

If you don’t like the Grateful Dead then don’t read this. The Grateful Dead and especially the songs of Jerry Garcia and Robert Hunter have been the soundtrack of my life for the last fifty years. Those songs have given me hope when I was down and transported me to the stars when I was up. They have accompanied me through all the up and downs, along the twisting and turning highway that has been my life, the strange diversions and dead ends. They were always there a mental bedrock to which I could cling whatever happened.

Robert Hunter was one of the truly great lyricists of the rock era, with all of the literary and high art implications that lyricist rather than simple songwriter carries. The breadth and depth of emotional colours that his words could and do magic into existence are seemingly infinite. The music and words of Garcia and Hunter are attuned to my soul in a way no other music is, was or ever will be and I own and listen to a very wide spectrum of music. Robert Hunter’s lyrics melded perfectly with Jerry Garcia’s liquid gold guitar lines.

I listen to music when I write and about eighty per cent of the time it’s the Grateful Dead. Hundred Year Hall, to which Hunter wrote some very beautiful sleeve notes, is blasting out of the stereo system, as I write these inadequate words.

I cried when I heard that Jerry Garcia had died fourteen years ago, something that surprised more than a little but which I accepted. I’m crying now having heard of the passing of Robert Hunter. I, and I suspect many others, own him an unpayable debt for all of the joy, sustenance in dark times and peace of mind that he has given me through his wonderful songs.

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Chilli’s story

Sacha will always remain Honorary Editor in Chief in perpetuity but we now have a new Supervisory Editor here at the Renaissance Mathematicus, her name is Chilli and this is her story.

When Sascha died, having been a dog owner for nigh on thirty years, I started looking round for a new dog. Not a replacement, you can’t replace a dog, as each one has a unique personality. I failed to find the right one, as a dog becomes your life partner, especially if you live alone, it has to feel right and none of the dogs I considered did. I then figured that all three of my dogs had found me, so if I were destined to have a new dog, it would also find me. In the mean time I became a dog sitter. I looked after other peoples dogs in the times when they couldn’t, took them for walk, fed them, provided them with a home for weekends when their owners were away. This is how I came to know Chilli.


Chilli practicing being a rock

Chilli was a family dog living not very far away from me, who I already knew from walks with Sascha in the woods behind my flat. She lived together with a woman and her husband and their two kids. It was the kids I mostly met when walking in the woods. The couple got divorced and the kids grew up and got jobs and it came about that the mother, who worked full time, was left alone with Chilli. She would rush home during her lunch breaks to take Chilli out for a quick walk. One day, having learnt that I was a dog sitter, she asked me if I would take Chilli out at lunch times during the week; I work at home. I suggested instead that I pick Chilli up in the mornings, walk her, feed her, play with her and then return her home in the evenings. And so it came about that Chilli became my daytime, working week dog.


Chilli checking out the airfield at a local air show

After about nine months the daughter, who was living in Nürnberg, became pregnant and having stopped working decided to take Chilli to live with her and her new family. And so Chilli and I parted company. Fast-forward about fifteen months, the first baby is now a toddler and the daughter is pregnant for the second time. Chilli, who is now an old lady, does not like the high-speed toddler, who zooms around the family home and starts growling softly whenever said infant gets too close. The mother is justifiably worried that Chilli might snap at her child and injure it, so I got a telephone call from her mother for whom I had originally dog sat Chilli. She explained the situation and asked if I would, under the circumstances, be prepared to give Chilli a new home. After due consideration I agreed and so Chilli has now moved in with me. We are two old folks who just want a little bit of peace and quiet.


Filed under Autobiographical


Sometimes the lights are shinning on me

Other times I can barely see

Lately it occurs to me

What a long strange trip it’s been


That we regard tenth or hundredth anniversaries as being special is actually just an accident of evolution. Because we have ten fingers, we based our most commonly used counting system on the number ten. If we had twelve fingers we would celebrate twelfth and one hundred and forty-fourth anniversaries instead; can’t see many people getting a telegram from the Queen on that system. If like the Simpsons we only had three fingers on each hand, we could make whoopee every six years with an extra big party every thirty-six years.


Today the Renaissance Mathematicus turns ten–time to blow up the balloons, hang out the bunting and bake a cake. I am in somewhat of a state of denial and disbelief that I have apparently managed to keep producing almost coherent scribblings on a fairly regular basis for all of ten years. As I have oft repeated in the past, when I started I wouldn’t have given this blog more than a ten per cent chance of surviving ten weeks let alone ten years. I also wouldn’t have seriously expected to gain more than ten readers. Instead of which we have the following, I think, mind boggling set of statistics for what is, after all, more than somewhat of a niche product in the grand scheme of all things Internet.

This is the 875th post on the Renaissance Mathematicus, there have been 1,318,488 views of those posts from 629,179 visitors, who have made 8.8 thousand comments. The Renaissance Mathematicus has 5,692 followers.

I’ve never counted but a rough guestimate is that in the last ten years I’ve written something north of half a million words! That 500,000! And I still claim I couldn’t write a book!

I don’t usually look at my blog statistics, as I see them as a sort of trap. Oh my god, so many readers, am I writing the right things to satisfy them? What, so few readers I must write something more popular/attractive/controversial or whatever to make my blog more attractive. No thanks! I just write what I want to write, ignore the statistics and if somebody reads what I write, fine. If not, also fine. In other words the only reason I trotted the statistics out today is because it’s my tenth boggiversary. If you want to see the statistics again come back in another ten years, assuming I’m still going or even still alive!

When I first started writing this blog I don’t really know what my aim/motivation/purpose was in writing it. I just felt that there were some things that I had collected in the back of my brain over the decades that I might possibly unload and a blog seemed like a good way to do so. Later I began to maybe regard the blog as a sort of substitute for the career I might have had, as a historian of science but for a number of complex reasons didn’t. I can’t say exactly when but somewhere down the line I realised that The Renaissance Mathematicus is not a substitute for anything, it’s me, it’s my calling, it’s what I do. In a different age I might have become a columnist or essayist in a newspaper or journal churning out weekly vignettes and reviews on a diverse range of history of science topics. It seems that is my strength and it’s what I feel comfortable with.

One of the things that became clear to me over the years is that I operate best just being me. I managed the history of science monthly blog carnival On Giants’ Shoulders for five years and complied and collated the online, weekly history of science journal Whewell’s Gazette for three years. These activities meant that I probably read more history of sciences blogs than anybody else in the whole Internet. There were and still are some very, very good history of science writers out there. I used to think I wish I could write as well as or express myself as cleverly as a whole lot of people that I regard as my superiors and betters. Somewhere down the line I stopped comparing, they do their thing I do mine. I now accept that I am who I am and other people do it differently.

In my teens I had already become a convinced atheist, something that has over the years never changed. I find it amusing when I write pieces defending or even praising a religious scientist and self-proclaimed radical atheists accuse me of being an apologist for the Church or Christianity in general, but I digress.  In my youth I was what in England during the religious wars in the seventeenth century was called a Seeker, someone, who doesn’t acknowledge any particular group but is looking for answers. You might say I was looking for a lebensphilosophie or a moral compass or the meaning of life or just somewhere to belong, I don’t really know myself.

I read quite a lot of Western philosophy, a lot of anthropology, a lot of Buddhist and Daoist literature, a lot of esoteric literature especially on the I Ching, the novels of Hermann Hesse, Ken Kessey and Robert Heinlein, and the LSD preachings of Timothy Leary amongst many other diverse things. I also took an awful lot of drugs. I was looking for something but I don’t think I ever truly knew what it was that I was seeking. For what it’s worth my personal lebensphilosophie is a bastard mixture of Buddhism, Daoism, the Ranters[1]and sex and drugs and rock’n’roll (in my case mostly West Coast rock especially the Grateful Dead). If I had a god it would be Shiva, the god of sex, drugs, rock’n’roll and death!

Amongst the things I read were the books of Carlos Castaneda supposedly about a Native Middle American shaman Don Juan, the first of which was The Teachings of Don Juan: A Yaqui Way of Knowledge. I say supposedly because although Castaneda claimed they were factual accounts, modern scholars think they are fiction. Sometimes when you read a sentence sticks in your mind and becomes part of your personal store of knowledge. For example, somewhere in his writings Leary wrote, based on his interpretation of Vedantic philosophy, “Life is a farce, death is a farce, suicide is the ultimate farce,” a phrase that has literally saved my live a couple of times during the worst periods of my mental illness. The part of Castaneda’s writings that has remained with me and I paraphrase: Don Juan said that there are many different paths through life, it doesn’t matter which path you choose as long as it’s a path with a heart. The Renaissance Mathematicus is my path with a heart, it took me a long time to find it, but it’s never too late.

What about the future? Above I casually mentioned the next ten years but who knows? I do know that I’m not planning on quitting yet. I have enough ideas for blog posts, in petto, to keep going for at least another ten weeks.

Above I mentioned my claim that I wouldn’t be able to write a book, good for sprints but not for marathons. In fact I’m currently contemplating writing not one but two books! Some time ago a reader of my blog who is a very successful science writer offered to help me find a publisher and an editor for a printed-paper version of the blog. I suggested the way I wanted it to be done and he said that the editor would decide how to present the blog in book form. In my life I have taken a lot of left turns and even more detours but I have always decided what to do with my life and have stood by my mistakes and by god I’ve made more than a few. The blog is my baby, it is one hundred per cent my own creation and if it is going to become a book then it will be my book and not that of some editor or other. I am seriously contemplating self-publishing, my concept is to do groups of posts on related subjects–history of cartography, early Dutch science, Renaissance Nürnberg, the Renaissance mathematicus, women in science, and so on–slightly rewritten for book form with a new general introduction for each section. Working title: “The Renaissance Mathematicus Garage Sale!” One of my readers, has successfully self-published and I’m hoping that he’ll give me some tips down the line. Another reader has already offered to help me set the final text for printing, he used to do this for a living, so maybe at some point I shall be running a GoFundMe to help launch the printed version of The Renaissance Mathematicus.

It should have become fairly obvious that the current series of posts, “The emergence of modern astronomy – a complex mosaic,” is actually the abstract/sketch/backbone for a potential book. When I finish the blog post series, if I like what I have, I will rewrite, refine, improve, expand the whole thing into a book and maybe try to find a publisher, maybe self-publish. All of this is of course future dreams but as Oscar Hammerstein II once wrote, “You’ve gotta have a dream. If you don’t have a dream, how you gonna have a dream come true?”

[1]If you don’t know who the Ranters were, they were a seventeenth century religious sect, who basically preached amoralism.


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An open letter to an author

Dear Yuval,

if I may? Sometime around the publication in English of your trendy mega bestseller, Sapiens, I read something from you, I can’t remember if it was an essay or an extract from the book, on the Scientific Revolution, as part of the extensive sales campaign for your publication. To say the least, I was, to put it mildly, totally underwhelmed and decided that I really didn’t need to read your book. Since then whenever the subject of your book came up in conversations or on the Internet I made disparaging comments about your abilities as a historian of Early Modern science. Recently it occurred to me that I might be being somewhat unfair, my comments being based on a half remembered short piece of writing and that maybe I ought to give you a second chance. Eventually I ordered your book through interlibrary loan, my university library apparently doesn’t have a copy. When it arrived I sat down to read the Fourth Section of the book entitled The Scientific Revolution. You must excuse me but I have so much that I want to read that I don’t really have time to read your whole book.

The first page of waffle about time travelling peasants and battleships didn’t really impress me but then on the second page I stumbled across the following:

In 1500, few cities had more than 100,000 inhabitants. Most buildings were constructed of mud, wood and straw; a three-story building was a skyscraper. The streets were rutted dirt tracks, dusty in summer and muddy in winter, plied by pedestrians, horses, goats, chickens and a few carts. The most common urban noises were human and animal voices, along with the occasional hammer and saw. At sunset, the cityscape went black, with only an occasional candle or torch flickering in the gloom.

The evocative picture that you paint with your words in this paragraph reminds me of the Hollywood B-movie visions of medieval hovels and unwashed peasants that informed my childhood and in my opinion has about as much truth content as those movies of yore.

I am a historian of Renaissance science, hence the name of this blog, and I live just up the road from the German, Renaissance city of Nürnberg, where, belonging as I do the an active group of local historians, I conduct on a fairly regular basis guided tours of the history of astronomy of that city most, but not all, of which revolves around the year 1500, plus or minus 50 years. For your edification and education I would now like to take you on part of that tour to show what a Middle European city really looked like in 1500.

Before I start I will grant that few European cities had more than 100,000 inhabitants; Nürnberg, then the second biggest German city, only had a population of 40,000. Of course there were much bigger cities in other parts of the world, Middle East, India, China but as the entire world population has been estimated to lay between 400 and 500 million in 1500, it is not surprising that the major cities were much smaller than those of today. Scaling up proportionally a city of 40,000 in 1500 with a world population of 500 million is equivalent to a city of more than 500,000 in today’s world of 7,000 million inhabitants, slightly less than Nürnberg’s current population.

I always start my tour with this sundial, which was created in 1502.


Lorenzkirche Sundial Source: Astronomie in Nürnberg

As you can see it is a quite sophisticated sundial and if you know how, you can read the time on it in three different ways, from sunrise, from midday and according to the Great Nürnberger clock: a system between the medieval local time system and our equinoctial hours: A bit beyond the primitive culture that you sketch. I hear you muttering but what about clocks. We’ll get to one of those a bit later.

The sundial is on the side of the Lorenzkirche, one of Nürnberg’s two parish churches started in 1250 and finished in 1477.

Nürnberg St. Lorenz Türme von Westen

Source: Wikimedia Commons

As you can see it’s a rather impressive sandstone building with a slate roof, as were most of the city buildings in 1500. By the way, the streets were also paved. No dirt tracks here.

Our next station is the Heilige-Geist-Spital built in 1399 as an old peoples residence, a function it still fulfils today.


Heilige-Geist-Spital Source: Wikimedia Commons

Moving on, we come to the Market Place and the Frauenkirche built between 1352-1362.


Frauenkirche Source: Wikimedia Commons

The mechanical clock on the facade was built in 1509.


Source: Wikimedia Commons

The ball above the clock shows the phases of the moon, still accurate today. At twelve-noon everyday there is a complex mechanical display with fanfares by the trumpeters, drum rolls and bell ringing. This is followed by the seven Electors circling the Emperor in the middle, three times. Tourists from all over the world come to Nürnberg to witness this spectacle.

I like this 19th-century picture showing the Schöner Brunnen (Beautiful Fountain), also on the Market Place, which was built between 1385-1396.


Here it is in all its glory, today.


Schöner Brunnen. In the backgrounfd you can see the towers of the other parish church St. Sebald (14th century) Source: Wikimedia Commons

You might like this house, it was the home of a local artisan, Albrecht Dürer (1471–1525), you might have heard of him?


Source: Wikimedia Commons

In 1500, Nürnberg was a major industrial city, producing a very wide range of metal products, as well as being a leading European trading centre. In fact it was one of the biggest centres in Europe for the production of everything that could be made out of metal. For example, the Nürnberg craftsmen received an order from the Emperor, Charles V (1500–1558), for five thousand suits of armour, so we can assume that there was quite a lot of noise on the streets on the city. Nürnberg traded on a large scale with much of Europe. It was not unusual for the traders to attend the Frankfurter Fair with a waggon train of five hundred waggons

You can get a good overall impression of the city from this illustration out of the Schedelsche Weltchronik (known in English as the Nuremberg Chronicle), the world’s first printed encyclopaedia, printed and published in Nürnberg in 1493.


Nürnberg as depicted in the Nuremberg Chronicles 1493

By now I hope you will realise that the real historical Nürnberg in 1500 was radically different from your fairy tale description of a city in 1500. Having recovered from having read the paragraph reproduced above, I tried to persevere with your book but having come across several more equally dubious paragraphs in the next few pages, I must honestly say that I can’t be bothered. I have better things to do with my time. I can’t claim that this is a review of your book but I certainly won’t be recommending it to anybody, anytime soon.

No hard feelings











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It’s Solstice Time Again!

We are deep in what is commonly called the holiday season. For personal reasons I don’t celebrate Christmas and as I explained in this post starting the New Year on 1 January on the Gregorian Calendar is/was a purely arbitrary decision. I wrote there that I consider the winter solstice to be the best choice to celebrate the end and beginning of a solar cycle in the northern hemisphere.


Stonehenge Winter Solstice

Today at 22:23 UTC the sun will turn at the Tropic of Capricorn and begin its journey northwards to the Tropic of Cancer and the summer solstice.  Tropic comes from the Latin tropicus “pertaining to a turn,” from Greek tropikos “of or pertaining to a turn or change.”

I wish all of my readers a happy solstice and may the next 365 days, 5 hours, 48 minutes and 45 seconds bring you much light, joy, peace and wisdom. We can only hope that they will be better than the last 365 days, 5 hours, 48 minutes and 45 seconds (length of the mean tropical or solar year).

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Don’t criticise what you don’t understand!

I was pleasantly surprised by the level of positive support my latest anti-Ada polemic received on Twitter, I had expected much more negative reaction to be honest. But I did receive two attacks that I would like to comment on more fully here. The first came from a certain Yael Moussaieff (@sachaieff) and reads as follows:


It still blows my mind how convinced mediocre men are that they’re not mediocre and that their opinions are in fact urgent and needed.

I’m not really sure in what sense here I am supposedly mediocre: my intelligence, my expertise, my abilities, all three, in all aspects of my existence? And how does Ms Moussaieff (I assume she is a she) know this, never having met me, on the basis of one, what I consider to be a fairly reasonably argued, blog post on the evaluation of the contributions of one Victorian woman to computer science. If she had brought some counter arguments to demonstrate the mediocrity of my thought processes or the mediocrity of my understanding of the historical period or the mediocrity of my abilities as a historian of computing (and I am one, see the reply to the next comment) then perhaps I could understand the intension or meaning of her criticism but for the moment I remain perplexed. Maybe my inability to comprehend is, in itself, a sign of my mediocrity.

Peter Robinson (@PeterRobinson76) chose a different line of attack:

We also love to put down anyone that dares to have popularity. Even long dead women.

To which I spontaneously responded:

There is a difference between a put down and a reasoned argument based on facts. I formally studied and researched both Babbage and Lovelace long before the current Lovelace hagiography started, as a professional historian of logic and computing. What are your qualifications?

For his benefit I would like to elucidate and explain my claim to professionalism in this matter. Some or even most of what I am now going to relate ought to be already known to those who have been reading this blog for a number of years for newer readers it might prove instructive.

Throughout the 1980s and the early 1990s I studied as a mature student at the Friedrich-Alexander University of Erlangen & Nürnberg. The first two and a half years I studied mathematics with philosophy as my subsidiary. I then changed to philosophy with English philology and history as my subsidiaries. The emphasis of my studies was always on the history and philosophy of science. During this time I worked for ten years as a paid research assistant in a major research project into the history of formal/symbolic/mathematical logic under the supervision of one of the world’s leading logic historians. This means that somebody, who is considered knowledgeable in these things, thought me competent enough to appoint me to this position. The fact that I was still there ten years later shows that he still believed in my competence. Possibly because I was the only English native speaker in the research team, my main area of research was nineteenth century British algebraic logics, which means I was researching Boole, Jevons, De Morgan, Venn, Cayley, McColl and others including the Americans working together with Peirce. Because algebraic logic was just a small part of the much wider field of abstract algebras emerging in the nineteenth century, I also researched Peacock, John Herschel, Babbage, Cayley, Sylvester, William Rowan Hamilton and various others. Calculating machines was also a part of our remit so Babbage and his computers along with the good Countess Lovelace came in for extensive study on my part.

Now ten plus years might seem a rather long time to study as a student but as I said I was a mature student without grant or parental support, which meant I had to earn money to do silly things like pay the rent or even on occasions eat and the pittance paid to research assistants in those days did not cover my daily living costs, so I also worked outside of the university. I had virtually finished my studies with just my master thesis to complete and my final exams to write–not a very big deal, as there was in those days a strong emphasis on continual assessment–when I crashed out with serious mental health problems. You can only burn the candle at both ends for a limited period of time until the two flames meet in the middle. Coming out of the loony bin I chucked my studies because being a qualified historian of science was never going to pay those pesky bills.

When I quit I had completed the entire research for both my master’s thesis and my doctoral thesis. I had written about 50–70% of my master’s thesis and a complete, highly detailed outline for my doctoral thesis. Now it might seem strange that I was writing both theses at the same time but my original master’s thesis, a wide-ranging study of the entire English speaking nineteenth century algebraic logic community, had grown far too big to be a master’s thesis, so I had cut out one section, on the life and work of Hugh McColl, to be my master’s thesis and turned the main project into a potential doctoral thesis. I recently, whilst clearing out some old cartons, came across all the material for that doctoral thesis. I was stunned at how far I had got with it, having in the intervening years forgotten most of the work I had invested. I sat and stared at it for three days then threw it all away.

So you see, if I say that I have researched and studied Babbage and Lovelace in a professional capacity it is simply the truth. I should point out that if I write about either of them now, I don’t rely on my memory of work done long ago but go back and read the original sources that I sorted out and studied then, modifying if necessary my views, as my knowledge has grown over the intervening years. In more recent years I have been paid by reputable, educational institutions to hold public lectures on Mr Babbage and his computing engines, so yes through preparing those lectures my knowledge has grown.

Let us return to my critics. Over the years battling the Ada hagiography I have come to the conclusion that the majority of her acolytes don’t actually bother to look at the sources at all. It seems some of them have read a blog post or an article in a non-academic Internet magazine, highly biased and based on dubious secondary sources rather than primary ones (and yes I am aware of the irony of writing that on a blog post). The rest have only ever read a short précis of those blog posts/articles posted on one or other of the Internet’s social media, which parrot the inaccurate accounts of their sources. This majority continue to parrot this ‘fake news’ without bothering to check whether it is historical accurate. The result is that we now have a major Ada myth industry.

If I had the chance to discuss with Yael, Peter or any of the acolytes who have criticised and attacked me over the years I would ask them the following questions:

Which Ada biography have you read?

 I have read five of which I have what I regard as the two best ones standing on my bookshelf.

What about Babbage? Have you read his autobiography?

It’s actually a fascinating piece of literature covering much more than the computing engines for which Babbage is famous.

Maybe you have instead read the more modern and objective biography contained in Laura Snyder’s “The Philosophical Breakfast Club”?

A wonderful book, as I wrote in my review of it for the journal Endeavour

Have you read his 9thBridgewater Treatise, in which Babbage discusses religion and expands on his theory that one could explain miracles by unexpected changes in computer programmes?

An interesting if slightly bizarre  argument.

Or perhaps, you have read his On the Economy of Machinery Manufactures, the result of his extensive research into automation?

Babbage’s interest in automation drove much of his studies including his work on computing and computers. His On the Economy was a highly influential book in the nineteenth century.

Maybe you have read his unpublished writings on abstract algebra, now in the British Library, that are thought to have inspired George Peacock’s “Treatise on Algebra”?

 I will admit that I haven’t but it’s on my bucket list. I have however read Peacock’s book, fascinating and an important milestone in the history of mathematics,

Maybe you’ve read up on the Analytical Society, the student group Babbage and Herschel created in Cambridge to convince the university to introduce continental methods of analysis to replace Newton?

I stumbled across this intriguing piece of maths history during my research; it shows the dynamic that drove Babbage even from an early age.

This might seem like an intellectual pissing contest but if you wish to criticise me and maybe show me that I have erred, that I am mistaken or that I’m just plain wrong then I expect you to at least do the leg work. I actually like being shown that I am wrong because it means that I have learnt something new and I love to learn, to improve and to expand my knowledge of a subject. It is what I live for. I am a historian of science with a good international reputation that I have worked very hard to earn. I also work very hard to get my facts right. If you criticise me and hold a different opinion on some topic that I have written about but treat me with respect then I will treat you with respect even if I know that you are wrong. If, however, you just gratuitously insult me, as, in my opinion, Yael and Peter have done then I will treat you with disdain and if the mood suits me with a generous portion of sarcasm.





Filed under Autobiographical, History of Computing, Uncategorized

A Newtonian Refugee

Erlangen, the Franconian university town, where I (almost) live and where I went to university is known in German as ‘Die Hugenottenstadt’, in English the Huguenot town. This name reflects the religious conflicts within Europe in the 17thcentury. The Huguenots were Calvinists living in a strongly and predominantly Catholic France. Much persecuted their suffering reached a low point in 1572 with the St Bartholomew’s Day massacre, which started in the night of 23-24 August. It is not know how many Huguenots were murdered, estimates vary between five and thirty thousand. Amongst the more prominent victims was Pierre de la Ramée the highly influential Humanist logician and educationalist. The ascent of Henry IV to the French Throne saw an easing of the situation for the Huguenots, when he issued the Edict of Nantes confirming Catholicism as the state religion but giving Protestants equal rights with the Catholics. However the seventeenth century saw much tension and conflict between the two communities. In 1643 Louis XIV gained the throne and began systematic persecution of the Huguenots. In 1685 he issued the Edict of Fontainebleau revoking the Edict of Nantes and declaring Protestantism illegal. This led to a mass exodus of Huguenots out of France into other European countries.

Franconia had suffered intensely like the rest of Middle Europe during the Thirty Years War (1618-1648) in which somewhere between one third and two thirds of the population of this area died, most of them through famine and disease. The Margrave of Brandenburg-Bayreuth, Christian Ernst invited Huguenot refugees to come to Erlangen to replace the depleted inhabitants. The first six Huguenots reached Erlangen on 17 May 1686 and about fifteen hundred more followed in waves. Due to the comparatively large numbers the Margrave decided to establish a new town south of the old town of Erlangen and so “Die Hugenottenstadt” came into being.


The earliest known plan of New Erlangen (1686) Attributed to Johann Moritz Richter Source: Wikimedia Commons

In 1698 one thousand Huguenots and three hundred and seventeen Germans lived in Erlangen. Many of the Huguenot refugees also fled to Protestant England establish settlements in many towns such as Canterbury, Norwich and London.


Town plan of Erlangen 1721 Johann Christoph Homann Source: Wikimedia Commons

In the early eighteenth century Isaac Newton, now well established in London at the Royal Mint, would hold court in the London coffee houses surrounded by a group of enthusiastic mathematical scholars, the first Newtonian, eager to absorb the wisdom of Europe’s most famous mathematician and to read the unpublished mathematical manuscripts than he passed around for their enlightenment. One of those coffee house acolytes was the Huguenot refugee, Abraham de Moivre (1667–1754).


Abraham de Moivre artist unknown

Abraham de Moivre the son of a surgeon was born in Vitry-le-François on 26 May 1667. Although a Huguenot, he was initially educated at the Christian Brothers’ Catholic school. At the age of eleven he moved to Protestant Academy at Sedan, where he studied Greek. As a result of the increasing religious tension the Protestant Academy was suppressed in 1682 and de Moivre moved to Saumur to study logic. By this time he was teaching himself mathematics using amongst others Jean Prestet’s Elémens desmathématiques and Christiaan Huygens’ De Rationciniis in Ludo Aleae, a small book on games of chance. In 1684 he moved to Paris to study physics and received for the first time formal teaching in mathematics from Jacques Ozanam a respected and successful journeyman mathematician.

Although it is not known for sure why de Moivre left France it is a reasonable assumption that it was Edict of Fontainebleau that motivated this move. Accounts vary as to when he arrived in London with some saying he was already there in 1686, others that he first arrived a year later, whilst a different account has him imprisoned in France in 1688. Suffering the fate of many a refugee de Moivre was unable to find employment and was forced to learn his living as a private maths tutor and through holding lectures on mathematics in the London coffee houses, the so-called Penny Universities.

Shortly after his arrival in England, de Moivre first encountered Newton’s Principia, which impressed him greatly. Due to the pressure of having to earn a living he had very little time to study, so according to his own account he tore pages out of the book and studied them whilst walking between his tutoring appointments. In the 1690s he had already become friends with Edmund Halley and acquainted with Newton himself. In 1695 Halley communicated de Moivre’s first paper Methods of Fluxions to the Royal Society of which he was elected a member in 1697.


Edmund Halley portrait by Thomas Murray Source: Wikipedia Commons

In 1710 de Moivre, now an established member of Newton’s inner circle, was appointed to the Royal Society Commission set up to determine whether Newton or Leibniz should be considered the inventor of the calculus. Not surprisingly this Commission found in favour of Newton, the Society’s President.

De Moivre produced papers in many areas of mathematics but he is best remembered for his contributions to probability theory. He published the first edition of The Doctrine of Chances: A method of calculating the probabilities of events in playin 1718 (175 pages).


Title page of he Doctrine of Chances: A method of calculating the probabilities of events in playin 1718

An earlier Latin version of his thesis was published in the Philosophical Transactions of the Royal Society in 1711. Although there were earlier works on probability, most notably Cardano’s Liber de ludo aleae (published posthumously 1663), Huygens’De Rationciniis in Ludo Aleae and the correspondence on the subject between Pascal and Fermat, De Moivre’s book along with Jacob Bernoulli’s Ars Conjectandi (published posthumously in 1713) laid the foundations of modern mathematical probability theory. There were new expanded editions of The Doctrine of Chances in 1738 (258 pages) and posthumously in 1756 (348 pages).

De Moivre is most well known for the so-called De Moivre’s formula, which he first

(cos θ + i sin θ)n = cos n θ + i sin n θ

published in a paper in 1722 but which follows from a formula he published in 1707. In his Miscellanea Analytica from 1730 he published what is now falsely known as Stirling’s formula, although de Moivre credits James Stirling (1692–1770) with having improved his original version.

Although a well known mathematician, with a Europa wide reputation, producing much original mathematics de Moivre, the refugee (he became a naturalised British citizen in 1705), never succeeded in obtaining a university appointment and remained a private tutor all of his life, dying in poverty on 27 November 1754. It is claimed that he accurately predicted the date of his own death.








Filed under Autobiographical, History of Mathematics, Newton, Uncategorized