Category Archives: Odds and Ends

Doctor, doctor give me the news…

Meghan Daum, who describes herself as a writer, started a Twitter shit storm by tweeting the following:

Seeing “Dr. Ford” trending reminds me anew of how much I hate when PhDs who are not medical doctors want to be addressed as “Dr.” It undermines authority rather than underscores it. That goes for you, too, Dr. Jill Biden.

Now this tweet is several degrees of bollocking stupid but unfortunately many of the negative responses to it were even more stupid, as they were by people propagating historical knowledge of the awarding of doctoral degrees that was, mildly put, total and utter crap. Before I give a quick historical sketch of university doctorates, I will first describe, what I surmise to be the origins of Ms[1] Daum’s more than somewhat dated take on the subject, which I suspect is largely motivated by wanting to take a swipe at Dr Jill Biden.


With thanks to Charlie Hurnemann

When I was growing up in the dim and distant past, in rural Essex, it was considered polite to address medical practitioners as Doctor irrespective of whether they possessed a MD or not. It was also considered bad etiquette to address non-medical holders of doctorates as Doctor, only the Germans do that sort of thing, if addressing them in writing they were Mr, or somewhat rarer Mrs, with their title appended to the end of their names in the form of the correct initials, D.D., M.D., D.Lit., PhD or whatever. Not being American I can’t be sure, but it is this bygone age that I think Ms Daum (see footnote) is appealing to.

When I moved to Germany, not quite so far in the dim and distant past, I discovered that it is de rigueur to address all holders of a doctoral degree as Doctor. However, medical practitioners, who do not possess an MD, are addressed as Herr or Frau. I don’t know whether this is still true, but the Austrians took it one stage further.  The wife of a man with a doctorate was referred to Frau Doctor, although she did not possess a doctorate. In the classical tradition of sexism the husband of a woman with a doctorate was not referred to as Herr Doctor, if he didn’t possess a doctorate.

However, times have changed and it is now considered correct in almost all countries to address somebody with a doctorate, irrespective of the academic discipline, as Doctor if they so wish it. If the wishes of the holder of the title are not known then etiquette demands the use of the title.

We now turn to the historical horrors on Twitter that have provoked this post. Numerous people claimed that the PhD was older than the medical degree and it was only in comparatively modern times that medical practitioners could even possess a doctorate. This is, I’m afraid to say, complete bollocks and I will now give a brief sketch of the history of the doctorate and its associated title.

As several people correctly pointed out the word doctor originally meant simply teacher, coming from the Latin verb docere meaning to teach. Interestingly the German word for a university lecturer, Docent, comes from the same root. As the European universities began to emerge in the eleventh century CE the term licentia docendi, licenced to teach was applied to somebody qualified in someway to teach at the university. With time a system of qualifications developed at the universities out of which the modern qualification developed over the centuries.

The fully developed medieval university had four faculties the lower or liberal arts faculty and three higher faculties, theology, law (with two divisions, canon and civil law) and medicine. A student started in the liberal arts faculty where he received a general education in the seven liberal arts, the trivium (grammar, logic and rhetoric) and the quadrivium (arithmetic, geometry, music and astronomy) this course of studies closed with the BA or baccalaureus atrium, modern Bachelor of Arts. Most students then left the university. Those that stayed continued their education in the same subjects advancing to the MA or Magister Artium, modern Master of Arts, which was now a licence to teach and qualified the holder to teach the undergraduate courses in the liberal arts faculty.

Some MAs were content to remain at this level but the majority enrolled in one of the three higher faculties to study theology, law or medicine. It was this course of studies that now closed with the degree of doctorate in the chosen faculty, qualifying the holder to now teach that subject. So the original three doctorates available at European universities all the way down to the eighteenth century were doctor of theology, doctor of law and doctor of medicine. This is of course a generalised, ideal model of the medieval university and many institutions deviated from it.

Turning to the doctor of medicine, those with a university degree were by no means the only medical practitioners in the Middle Ages and Early Modern Period with a wide range of others offering medical services, midwives, herbalists, apothecaries, surgeons etc. In fact most people would not have been able to afford the services of a university educated medical practitioner. Also someone with a doctorate in medicine would have been referred to as a medicus and not as a doctor. It was only in the late sixteenth century that people really began to generally refer to medical practitioners as doctors.

We now turn to the, in our day and age ubiquitous, PhD. The doctor of philosophy degree was first introduced in Germany in the late seventeenth century with 1652 being the earliest know award of the degree. The philosophy refers not to the discipline philosophy but to a much wider range of subjects, philosophy being used as a synonym for the liberal arts. By the nineteenth century this had become a research-based degree at German universities, the earlier medieval doctorates were entirely based on learning. These modern research doctorates PhD, DSc etc. slowly began to become accepted at American and British universities in the late nineteenth century. They still had the taint of something foreign and not quite wholesome when I was growing up in the 1950s and many university lecturers and even professors at British universities in this decade did not possess a doctorate.

Of course, nowadays in academia the doctoral degree in all faculties has become ubiquitous with universities churning out freshly backed doctors of everything under the sun at an alarming rate and if they desire to be addressed by their hard earned title as Doctor then please be so polite and have the decency to do so.

[1] It will come as no surprise to the reader that Ms Daum does not possess a doctorate


Filed under Odds and Ends, University History

Tis the season to be jolly

This is one of those very occasional blog posts that has nothing whatsoever to do with #histSTM, so if you come here just for that, you don’t need to read further.

We have entered that time of year with the winter solstice, Christmas, Hanukah, New Years and all the rest, when celebration in all its various forms is written big in most peoples calendars: office parties, department parties, club parties, private parties or just more trips to restaurants or the pub. It is a period when many people eat and drink to excess, which is their choice and not mine to comment on but I do want to say a few words for those, who don’t drink alcohol.


There are various reasons why people don’t, won’t or can’t drink alcohol. Not just Islam but other religious communities forbid the consumption, some, like myself, are alcoholics, addicted to alcohol, who no longer imbibe, others have medical conditions or take medicament that make it unwise or even possibly dangerous for them to consume alcohol, some sensible car drivers only sit behind the steering wheel with zero per mil, lastly there are those, who simply don’t like alcohol. Given this fact there are some points that anybody planning or hosting a party or other form of gathering with refreshments should take into consideration.

If you are going to a restaurant or bar then you don’t have to do anything, as they should have a range of non-alcoholic drinks on offer. However, I experienced, all too often, that especially restaurant have a very small range of mostly poor quality alcohol free drinks at extortionate prices.

The following is purely fictitious but I have experienced variations on the described scenario very often over the years that I have abstained from drinking alcohol. Your genial host, Mr Important (it’s always a man), explains that he drove thirty kilometres to this small private brewery to fetch a couple of barrels of their really special bitter or he knows this chap who does this deal on this super vintage Bordeaux from a little vineyard or your might not know this dry white but it’s a super drop from South Africa that’s equal to anything from Germany and half the price or he’s got Dave the barman from the luxury hotel down the road to mix cocktails for the evening, two of those will put you flat on your back. If you are lucky he remembered at the last moment that there might be some poor sods, who don’t drink alcohol, so he got a couple of plastic bottles of cheap fizzy sugar water from the discounter down the road. Not only is this totally inadequate it is totally insulting. Mr Important is keen to impress his boozing friend by going to a lot of trouble and expense to get them something of real quality to drink but he doesn’t give a shit about the teetotallers. Don’t be Mr Important.

If you are organising a gathering or party with refreshments, as well as getting an attractive range of alcoholic drinks, make sure that you have an equally attractive range of alcohol free ones, too. The abstemious car driver might enjoy an alcohol free beer or wine but not all non-drinkers do. A selection of good quality fruit juices and both fizzy and still mineral waters is a good place to start. Some of the traditional mixers, bitter lemon, ginger ale, etc. are also often enjoyed by people who don’t drink alcohol. I’m rather partial to a St Clement’s myself, bitter lemon and orange juice, fifty-fifty. These days there are good ranges of, often organic, fizzy drinks without too much sugar available, buy a selection. You can also offer both tea and coffee, which will probably also be appreciated by some of your alcohol drinking guest at the end of the evening.

If you do employ Dave the barman to mix cocktails, make sure that he also has ingredients and recipes for a range of mocktails, that’s cocktails without alcohol if you didn’t know. If you offer your guests a welcoming drink, a glass of sparkling wine for example, or an aperitif then make sure you have an attractive alcohol free alternative on offer as well.

My final point is perhaps the most important if you wish to be a good and conscientious host. If you offer somebody an alcoholic drink and they decline, do not under any circumstances try to persuade them to change their mind. Simply accept their choice and offer them something alcohol free instead.

I hope you all enjoy your seasonal festivities and that if you are throwing a party that you make it possible for the non-drinkers to also enjoy theirs. All of this, of course, applies when you are organising a party at other times of the year.



Filed under Autobiographical, Odds and Ends

Christmas at the Renaissance Mathematicus – A guide for new readers


Being new to the Renaissance Mathematicus one might be excused if one assumed that the blogging activities were wound down over the Christmas period. However, exactly the opposite is true with the Renaissance Mathematicus going into hyper-drive posting its annual Christmas Trilogy, three blog posts in three days. Three of my favourite scientific figures have their birthday over Christmas–Isaac Newton 25thDecember, Charles Babbage 26thDecember and Johannes Kepler 27thDecember–and I write a blog post for each of them on their respective birthdays. Before somebody quibbles I am aware that the birthdays of Newton and Kepler are both old style, i.e. on the Julian Calendar, and Babbage new style, i.e. on the Gregorian Calendar but to be honest, in this case I don’t give a shit. So if you are looking for some #histSTM entertainment or possibly enlightenment over the holiday period the Renaissance Mathematicus is your number one address. In case the new trilogy is not enough for you:

The Trilogies of Christmas Past

Christmas Trilogy 2009 Post 1

Christmas Trilogy 2009 Post 2

Christmas Trilogy 2009 Post 3

Christmas Trilogy 2010 Post 1

Christmas Trilogy 2010 Post 2

Christmas Trilogy 2010 Post 3

Christmas Trilogy 2011 Post 1

Christmas Trilogy 2011 Post 2

Christmas Trilogy 2011 Post 3

Christmas Trilogy 2012 Post 1

Christmas Trilogy 2012 Post 2

Christmas Trilogy 2012 Post 3

Christmas Trilogy 2013 Post 1

Christmas Trilogy 2013 Post 2

Christmas Trilogy 2013 Post 3

Christmas Trilogy 2014 Post 1

Christmas Trilogy 2014 Post 2

Christmas Trilogy 2014 Post 3

Christmas Trilogy 2015 Post 1

Christmas Trilogy 2015 Post 2

Christmas Trilogy 2015 Post 3

Christmas Trilogy 2016 Post 1

Christmas Trilogy 2016 Post 2

Christmas Trilogy 2016 Post 3

Christmas Trilogy 2017 Post 1

Christmas Trilogy 2017 Post 2

Christmas Trilogy 2017 Post 3



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Filed under Odds and Ends, Uncategorized

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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Filed under Autobiographical, Odds and Ends, Uncategorized

Words matter

This morning, as usual, I caught the beginning of Thought for the Day on BBC Radio’s Today Programme (I know, I know), as I was preparing to leave my flat at 7:50 am. This morning the speaker, Bishop James Jones, took as his topic Yorkshire Day, the yearly celebration of God’s own county, as the natives like to call it. Bishop Jones, informed us that Yorkshire has 10% of the population of the UK (it’s actually nearer to 7% but who’s quibbling) and then went on to say, “Yorkshire is the most British region in the UK with over 40% of the population having Anglo-Saxon ancestry.

Now I’ve got nothing against Yorkshire, some of my best friends live there, but I fail to see how being of Anglo-Saxon descent makes somebody most British, in fact when I heard this my inner historian cringed. For those of my readers who are not up on the etymology of the terms of parts of the UK and its populations I will explain why this is fundamentally wrong. If the speaker had said most English I probably wouldn’t have reacted the way I did, as the words England and English are in fact derived from our Angle ancestors – England being Angle-Land. The problem is equating Britain or British with Anglo-Saxon.

The first mention of the origin of word Britain turns up in the reports of the Greek geographer explorer Pytheas of Massalia who voyaged around the British Isles in about 300 BCE and referred to them as the Prettanikē or something similar (Pytheas’ original writings are lost and we only have later secondary accounts of his report). This evolves to Britannia in the writings of Latin scholars. Now Pytheas undertook his voyages about four hundred years before Tacitus makes the first know reference to the Anglii, then still firmly on the continent, in his Germania and at least eight hundred years before the Angles invaded North East England.

Possible locations of the Angles, Saxons and Jutes before their migration to Britain. Source: Wikimedia Commons

Possible locations of the Angles, Saxons and Jutes before their migration to Britain.
Source: Wikimedia Commons

Viewed historically, the term British references the pre-Germanic pre-Roman, Celtic, population of the British Isles in contrast to the term English, which references the Germanic post Roman invaders. Etymologically the phrase of Anglo-Saxon descent would at best indicate most English and definitely not most but rather least British.

Angles, Saxons and Jutes throughout England Source: Wikimedia Commons

Angles, Saxons and Jutes throughout England
Source: Wikimedia Commons



Filed under Odds and Ends

The Renaissance Road Show – November 2014

If you happen to be in Nürnberg tomorrow evening (Wed 12 Nov) I shall be babbling on about Christoph Clavius in the Nicolaus Copernicus Planetarium (in German) at 7:00pm MET. This is an updated version of the lecture I held five years ago in Bamberg, a summary of which forms the first substantive post on this blog. You are welcome to come along and throw peanuts or whatever and if you’re nice to me I’ll even let you buy me a coffee.

For those who miss the blogging activity around here, you can rest assured that normal posting will resume next week, the Norns willing. For those waiting patiently or maybe not so patiently for reviews of their books, and there are a couple, all review obligations will be fulfilled before the end of the year. (But which year? – Just kidding).




Filed under Odds and Ends


Crunch, Crunch, Crunch, Crunch, Crunch,…

That’s the sound of me banging my head against a concrete wall to relieve the pain I suffered on reading the latest pearl of wisdom that world famous astrophysicist and science communicator Neil deGrasse Tyson imparted to his 1, 228, 112 adoring acolytes on Twitter.

Not that anybody asked, but the symbol “lb” for pound comes from an abbreviation of the constellation Libra, the scales. Neil deGrasse Tyson (@neiltyson)

This is the sort of comment, which if made by one of his students, my twitter friend @grummpyhistorian tweets with a hash tag such as #epicetymologicalfail.

The Latin word libra has two meanings it is both the Roman standard unit of weight (approx. 327g) as well as a balance or set of scales. It is the former that is the origin of the abbreviation lb for pound, the standard unit of weight in the imperial system, and the latter, which supplied the name of the constellation. It is of course also the former that is the origin of the £ symbol for the pound unit of money, originally a pound or libra of some precious metal. This, if my memory serves me correctly, however comes into English via the French word for pound, livre. Instead of lb we might have had pf as abbreviation for the pound from the German word Pfund.

As to the asterism it would appear that it was the Babylonian who first called it a balance as explained here by Ian Ridpath in his excellent book Star Tales:

Now there has been a lot of deriding and decrying of the humanities and their usefulness or lack there of in recent times but if Neil deGrasse Tyson had paid a little more attention to the humanities in his education he might not have put his foot straight into his mouth when he opened it. He could have saved me a lot of mental pain if he had a) learnt some Latin or b) read an etymological dictionary or c) consulted the much-maligned Wikipedia anyone of which would have prevented him from exposing himself as an ignoramus, a Latin term meaning, “we do not know”.


Filed under Myths of Science, Odds and Ends

Carnivalesque #93 Pre-Modern History with Added Cats

Hello I’m the Renaissance Mathematicus and actually I’m a historian of science and this blog is normally mostly about the history of the mathematical sciences mostly in the Early Modern Period. However as far as I’m concerned a historian of science is also just a historian, a point of view not shared by some historians of science, and so just for a change I’m hosting Carnivalesque the blog carnival for pre-modern history.

Now I’m a trained archaeologist and spent several happy years digging up various bits of Britain and I’m also the son of a pre-historian so for me archaeology and pre-history are also pre-modern history. With this in mind I’ve been collecting blog post that I found interesting since Sharon hosted Carnivalesque #92 in January and the list has got somewhat gargantuan and completely unmanageable, so I didn’t even try.

Look through the list and if a blog post title catches your imagination then click and read! You won’t be disappointed they’re all good!

Now as all denizens of the Intertubes know they real secret of cyberspace success is cats. If your blog post has cats then it’s a guaranteed runner. With this in mind Carnivalesque #93 has added cats! For those who only read cat posts the feline section closes out the list and at the request of co-host Sascha who says, “dogs are much better than cats” begins with medieval dogs.

Carnivalesque #94 will be hosted by the many-headed monster in April. Nominations can be made either direct to the host of through the nominations form here.

Pompeii “Wall Posts” Reveal Ancient Social Networks

Christine de Pizan in her Study

Toothy Tumor Found in 1,600-Year-Old Roman Corpse …

Medieval warfare had well-organised ‘ransom market’

‘Weird’ remedies and the problem of ‘folklore’

A French-Peruvian-Spanish team discovers a chamber in Machu Picchu

Review: Emotion and Cognitive Life in Medieval and Early Modern Philosophy

Fishbourne Roman Palace pottery ‘was toilet paper’

Technology and autonomous mechanisms in the mediterranean from Ancient Greece to Byzantium

The Art of Swimming

The Royal Amour Workshops at Greenwich

The Recipe Collection of the Last Medici Princess

Mourning Coffee

The Mystery of Curry

Margaret Stewart of Scotland, Dauphine of France

It is Richard III: ‘beyond reasonable doubt’

Archaic Native Americans built massive Louisiana mound in less than 90 days

35 Ancient Pyramids Discovered in Sudan Necropolis

Alexander the Great and the Rain of Burning Sand

Ice Age Art: Arrival of the Modern Mind

The Regular Canons and the Use of Food c. 1200 – 1350

Listening to the Book: Medieval Music Manuscripts

Virtual Autopsy: explore a natural mummy from early Egypt

Late surviving pterosaur

My first year on Twitter: How I became @erik_kwakkel

The European No. 3 Johann Gutenberg

On Pins and Needles: Stylist Turns Ancient Hairdo Debate on its Head

Silent Voices in History: The Searchers of the Dead

The Last Time a Pope Resigned Mass Media was Called…Mass

Eat Your Heart Out

The Little French Renaissance Book of Love

Syphilis, Misogyny, and Witchcraft in 16th Century Europe

Romeo and the Apothecary

Beowulf Online

A 13th Century Tally Stick

An Environmental History of the Middle Ages: The Crucible of Nature

Mystery of Henry IV’s missing head divides France

Elizabeth Tanfield Cary 1598 manuscript published

Why Yes

Merlin: International man of mystery

What was the Investiture Controversy a Controversy About?

Ignorance and Experience: An Illuminator’s Trajectory

Israel Antiquities Authority: An ancient industrial installation was revealed beneath the asphalt in Yafo

The History of Libraries Through the Ages

Goose Quills and Iron Gall Ink

For Valentine’s Day: The 17th Century Method for Knowing When Your Heart is Broken

Behold, the Kindle of the 16th Century

Byzantine wine press discovered in Jaffa

Oranges and Lemons

How to see naked people in Renaissance Italy

Time and Motion Studies

Myths and Mandrakes

Mussolini looks at Jan Hus and the Bohemian Reformation

Gamma ray burst hit earth in 8th century

150 Mexican Skulls that reveal the largest mass sacrifice in the region’s bloody history

Animals in Medieval Sports, Entertainment and Menageries

When Taking Multiple Husbands Make Sense

Carved medieval head in Wexford

Famed Warrior Medici Died from Gangrene

Ice Age Art

The Dumb Proctor of Lochwinnoch

Briton finds 500 year old arrest warrant for Machiavelli

Roman Bones in Istanbul

The Ice-age flute can play The Star-Spangled Banner

Memeing the Early Modern: Danse Harlem Shake Macabre #WoodcutWednesday

From the wtf department a rotating book server designed during the renaissance recreated and mis-built by architecture students destroyed by terrorists

So, what did the Romans do for us?

In Praise of Small Data

It’s the Manuscript Stupid

Thinking Big About Medieval Data

Eighteenth-century DIY

Have some ginger dear

Pilau eighteenth-century style

REED all about it III: Some musings on music and the micro-politics of Sabbath-breaking in Jacobethan Lancashire

Next Pope what happens now?

Diadems are forever

I blame Gerald of Wales

Sealed with a Roman Kiss

Vile-Hearted Renaissance Peckerhead oft he Month: January

Baby Bones Were Trash to Romans

PTSD in Antiquity

Concussion and PTSD in the Ancient World

The Tale of the Leather Asses: Numa Pompilius and Leather Coinage

The History of Menstruation


Nothin’ but a Hound Dog

Lolcats in the Middle Ages

1 Kitty, 2 Empires, 2000 Years: World History Told through a Brick

A Rocket Cat? Early Modern Explosives Treatises at Penn.

Of Cats and Manuscripts

Grumpy Cat Responds to the Medieval Cat–Print Manuscript


Filed under Odds and Ends

It’s just a question of words

I wrote this piece sometime ago but for some reason never got round to posting it, possibly because I think it really needs expanding. However the years I have spent studying both the philosophy of mathematics and the philosophy of science have convinced me that an expanded version of this answer would become a fairly substantial book; a book I have no real desire to write. I have chosen to post this piece now because the Irish student of philosophy Cathy who inhabits my twitter stream as @Cathyby recently posed the question dealt with here, so Cathy my answer to your query.

I want to turn my attention to a question that has bothered me whenever I have met it in one form or another in the intertubes, “is mathematics a science?” Usually one meets the question in the form of a denial, “but that’s mathematics and that’s not a science”. I have deliberately not chosen this question as title for this post because I don’t think it’s actually a legitimate question as it’s based on a mistaken idea of what science is.

The question that I shall be considering here cannot be asked in German or rather it would be rather strange. In German each academic discipline is a Wissenschaft. Wissen is the German for knowledge and the suffix “shaft” is equivalent to the English suffix “hood” as in neighbourhood or brotherhood and functions as a collective for everything that falls under the concept, so Wissenschaft is everything that falls under the concept knowledge. It is interesting in this context to remind ourselves that both the Latin word scientia and the Greek word mathema also originally meant knowledge. German differentiates between the different types of knowledge so the closest it gets to the common English understanding of the word science is Naturwissenschaft, which however can be translated as the natural sciences and this brings us to what I consider to be the crux of the problem.

All those who vehemently deny the status of science to mathematics have a very limited concept or view of what constitutes science. They believe there is one thing called science that employs something called “the” scientific method. What they actually mean is physics or the physical sciences. Contrary to what these people think there is no monolithic scientific method but rather a fairly large set of related and similar methods that are employed in different branches of the sciences. What constitutes a test for a hypothesis in biology is not necessarily the same as that which constitutes a test for a hypothesis in physics. This is actually tacitly recognised in that we group the sciences according to the subject matter that they investigate and the methodology that they use. We differentiate between the physical sciences, the life sciences, the earth sciences, the social sciences and so on and so forth. Each group delivers its own form of knowledge conform to the subject matter of its investigations.

Mathematics belongs together with informatics (computer science) and formal or symbolic logic to the formal sciences or in German die Formalwissenschaften. These sciences are distinguished by the fact that their true statements are true as a result of their form and not their content, in all three we talk about well-formed statements. Like physics or biology mathematics delivers knowledge and as such is without question a science but it is a different type of science to physics or biology, which in turn also differ from one another.


Filed under Odds and Ends

The Renaissance Mathematicus Roadshow

Next week the Renaissance Mathematicus will be undertaking a mini-tour of Berlin to hold two semi-popular public lectures, in German. Actually it’s the same lecture on the history of the calendar and the calendar reform held twice. On Tuesday I shall be entertaining the good folks at the Urania Berlin e.V. at 17:30 and on Wednesday those at the Wilhelm-Foerster-Sternwarte mit Planetarium am Insulaner Berlin at 20:00.

If you are in Berlin and should you wish to experience The Renaissance Mathematicus in real live Technicolor, living, breathing and even talking then please come along. If you would like to meet up for a chat, coffee or whatever then leave a comment below and I’ll get in touch.


Filed under Autobiographical, Odds and Ends