More Mathematicians & Miscellaneous Math Stuff

During my travels I gathered information and took pictures of anything and everything I came across that was related to mathematics, mathematicians and the history of mathematics. Most of these images found their way into full-length posts on the many individual mathematicians I've written about, but in some instances I don't have enough material to support a full post on a specific topic or person.  I don't want these extra images and visits to go unused, however, so in this post I present additional images relating to mathematicians, the history of mathematics and mathematical objects, hoping that my students may find them to be interesting and to be helpful resources - and that others might simply enjoy the images taken of places and objects in the USA, the UK, France and Germany.

Rene Descartes

The great Rene Descartes (1596-1650) - a towering figure in philosophy as well as in mathematics - is one of the mathematicians for whom I was not able to get to a large number of relevant sites.  I did get to visit the church where he is buried, St. Germain de Pres in Paris, and I also happened across a Parisian University named for him.

The picture heading this post, and the next eight pictures are of the Abbey of St. Germain de Pres; the original church at this site was conceived in 512 AD and completed and dedicated in 558 AD, making it the oldest church in Paris.  It's bell tower is one of the oldest in all of France.  Descartes' tomb is located in one of the side chapels near the altar; sadly, I could not view the actual tomb because significant construction is currently taking place at the eastern end of the church.

The following two pictures are of the University of Rene Descartes in Paris.

Henri Poincare

Henri Poincare (1854-1912) was the most prominent French mathematician of his time.  Along with David Hilbert (1862-1943) he was one of the two most prominent mathematicians in Europe of the time.  I was thankful that Montparnasse Cemetery in Paris included Henri Poincare on their map of celebrities buried here.  During my travels it was the case that finding the graves of mathematicians was rather a hit or miss proposition and quite the treasure hunt in most cases - sometimes successful, sometimes not.

W. W. Rouse Ball

Walter William Rouse Ball (1850-1925) entered Trinity College, Cambridge in 1874, earned the spot of Second Wrangler in the Tripos, became a fellow of Trinity in 1875 and remained one the rest of his life.  In 1927 he established chairs at both Cambridge and Oxford.  Among those who have held the Rouse Ball Professorship of Mathematics are J. E. Littlewood and Abram Besicovitch (both at Cambridge) and Sir Roger Penrose (at Oxford).  Plaques commemorating Rouse Ball, Littlewood and Besicovitch can be seen in the chapel of Trinity College Cambridge.  Penrose is currently Emeritus Rouse Ball Professor of Mathematics at Oxford, and his famous tiles can be seen outside Oxford's Mathematical Institute.

When I expressed surprise to the professor hosting me at Cambridge at finding the name of Besicovitch here (I knew he was from eastern Europe), he replied, "Oh, yes, Besi was here!"

Penrose Tiling outside Oxford's Institute of Mathematics

Sir Isaac Barrow

Sir Isaac Barrow (1630-1677) held the Lucasian Chair of Mathematics  just prior to Sir Isaac Newton (1642-1726).  This professorship was founded in 1663 by Henry Lucas and was recently held by famed physicist Stephen Hawking from 1979 to 2009.  

Isaac Barrow resigned the chair in 1669 and was appointed chaplain to King Charles II in 1670.  Three years later, Charles II appointed Barrow to the Mastership of Trinity College, Cambridge, stating that he was the best scholar in England.  He is buried in Westminster Abbey and memorialized with a statue in the chapel at Trinity College, Cambridge.  

I'd always heard that it was Barrow who came up with the Fundamental Theorem of Calculus (before Newton) and that he was Newton's teacher, but during my time in Cambridge I learned in no uncertain terms that this was not the case and that Barrow was nowhere near existing in the same intellectual universe as Newton.  I have that on good authority!  That said, he clearly made contributions and was recognized for those contributions by the king at the time and is worthy of remembrance - as we see in Trinity College and at Westminster Abbey.

Sir Isaac Barrow - Chapel of Trinity College, Cambridge

Westminster Abbey, London - burial place of Sir Isaac Barrow

Mathematical Shapes and Objects

As well as taking pictures of places and things related to specific mathematicians I always had my eyes open for mathematical objects wherever they might be.  The first two pictures are of a sculpture in the grounds of Holyrood Palace, Edinburgh, Scotland.  I think it's pretty cool that the monarch has an icosahedron in her garden.  The pictures following those are of labyrinths whose locations are given in the photo captions.

Location - London Tube Station

Location - Paris - on the bank of the Seine

Location - Paris - on the bank of the Siene

Seattle - near the Space Needle - taken at the JMM Conference before I left for the European part of my sabbatical

In London, after visiting the Royal Society I was walking back toward Westminster Pier along the east side of St. James's Park.  As I was looking across toward Buckingham Palace, a conversation caught my attention.  Someone in a group of people approached another group and asked, "What do you call a seven-sided shape?"  Discussion ensued regarding "heptagon" vs. "septagon."  It caught my attention because this is something I talk about in certain classes I teach, but I'd never heard such a conversation just out and about before.  I thought, "Why on earth are people who are just walking down the street conversing about names of polygons?"  

It struck me later in the day that this must have had to do with British currency, for which, though most coins are circular, two of them are seven-sided polygons.

Transitioning to "The Other Place"

I'm a "Bodleian Reader" :-)

I arrived in Oxford (or "The Other Place" as those in Cambridge call it - of course I'm finding out in Oxford that it is Cambridge that is referred to as "The Other Place").  The first thing I did was to head to the Bodleian to get my reader's card.  Though they had just closed moments before I arrived they graciously made an exception and went ahead and made my card for me.  Tomorrow (Friday), I'll be reading correspondence between mathematicians Mary Fairfax Somerville and Ada Byron Lovelace in the special collections of the Bodleian.

Actually, earlier in the day I'll be at the library of Queen's College, Oxford, in their special collections, consulting a first edition Whetstone of Witte (1557) by Robert Recorde - the book which contains the first recorded use of the equals sign and the first use in an English text of the plus and minus signs.

Anyone recognize this building?

So, as you can imagine, this is all super cool - especially having a card to the Bodleian (for which I had to take an oath, by the way, among other things!) -  but I'm having a really hard time appreciating it right now because I've been super sick for over a week now - but more on that later.

I was pretty worn out upon arrival, which took five hours composed of bus, train, tube, train, bus - via London - but which I have come to find out could have been accomplished by one bus straight from city to city.  I missed the second train, didn't have time for lunch, etc.  So once I finished up at the Bodleian I asked if there was an Italian restaurant nearby.  I needed something hearty and tasty that would make me happy.  I never did find it, but after walking further than I should have needed to I looked up and saw this, which I immediately recognized - was planning to eat there at some point anyway, so that settled it.  (Anybody know why this is famous?)

They make a wonderful macaroni and cheese - and just as I skipped the whiskey in Scotland, I'm skipping the beer in England - sorry folks, I realize that to some of you this sounds like heresy, but it's lemonade for me!

This morning I went to the Mathematical Institute, Oxford and toured the Andrew Wiles Building with its Penrose Tiles out front.

The entry is paved with Penrose Tiles.  I was told by my guide that because those who lay tile are inclined to form patterns and because the point of Penrose tiles is to be unpatterned, that Sir Roger Penrose himself had to be out here guiding the process so that the tiles were laid in the properly unpatterned way!

Roger Penrose - he of the tiles - has an office here and remains active at age 84.  I imagine Andrew Wiles has an office in this building named for him, but I didn't think to ask.  I did, of course, have lunch in the Cafe Pi.

So there's definitely cool stuff going on here, but I have to say I miss Cambridge and my connections there.  Thanks to Dr. Piers Bursill-Hall - who went so far beyond merely answering a question for me - doors were open to me like crazy, and I was able to see so many colleges and their chapels - and to eat in Trinity Hall (thanks to Richard!) - as well as to work in the Centre for Mathematical Sciences - and eat there too!

Yes, I have two libraries open to me here in Oxford and got a half-hour tour of the Mathematical Institute this morning, but this place feels like a really closed book.  At least at Cambridge even if I'd had no connections and was a tourist I could have paid to get into a variety of colleges:

St. John's Cambridge - open to tourists for a fee

Another Cambridge College - open to tourists for a fee

 Here's an Oxford college.  Can you tell?  Can you tell which one it is?  Can you get in?  Do you see the bouncer, um, I mean "porter" standing guard in black and white in the entry?

Oh, wait, what's that tiny, little sign just inside the left of the arch?  Oh! This is Somerville College!  I'd hoped to visit it because of my interest in Mary Somerville.  Maybe I will just leave it at this for this one.  If I were feeling better I might try, but not so much right now.  It just feels very closed-off here compared to Cambridge.

Obviously I miss my contacts - had no idea in advance that they would take me on board as they did.  Here's one of our LATE dinners in "The Core" of the Centre for Mathematical Sciences.  Many stories were shared, many math puns were bantered about, and, though I can't speak for them, a good time was certainly had by me!  Brilliant company, absolutely brilliant!

I was not feeling well then either, but somehow it's easier to deal with illness when one is not entirely and utterly solo.  I'm just going to be brutally honest, as awesome as a sabbatical in Europe sounds, when one has had a fever for over a week, feels like they've got bronchitis, cannot stop coughing, has a touch of stomach flu and also other very uncomfortable physical stuff going on too - it ain't pretty - especially when living in a small, cheap hotel room with pharmacies a half hour walk away and restaurants a half hour walk away and when there's no one around to look out for you or bring you stuff when you feel miserable.  (Piers took good care of me in Cambridge - got me to a pharmacy for cough meds and paracetamol - connected me by phone with a nurse who told me this is viral so no antibiotics - fine, but I wish I could get over it!  And now I'm totally solo and still just as sick if not sicker.)

If I didn't feel so miserable this would be kind of funny: when I open my mouth to ask someone something I actually do not know if any sound is going to come out at all or not.

Part of this is probably my own fault.  Just because a schedule can be put together like a tidy jig-saw puzzle with no gaps doesn't necessarily mean that it should be, I suppose.  If the idea of driving in totally foreign territory with a reversed car in a country that drives on the opposite side of the road than one is used to sounds TERRIFYING - especially if one isn't even really comfortable driving in their home country where everything is familiar - then perhaps the added stress could weaken the immune system.  And, though this piece couldn't be helped, being served breakfast by someone at a B&B (10 days ago) who kept complaining about how she's been really sick and just can't get well probably didn't help the situation - just some thoughts.

Here's a snap of part of my schedule:

But right now it just kind of looks like this:

If any of you reading this are of a praying persuasion, I would sure appreciate prayers.  Thanks!

Belated Penrose Post

Well, I'm "cheating" a little bit on this one. Though the post says I put it up in March of 2016, I'm actually posting this on January 22, 2018. Two months ago, the opportunity came up to revisit the amazing city of Edinburgh.

Even though I was there "just for fun" this time, I couldn't help but look into some of the things related to math that I had missed initially.  One mathematician I'm quite interested in is Roger Penrose whose "impossible shapes" made it into the movie Inception.

Penrose's mathematical work takes inspiration from many places, including the world of art.  He collaborated with artist M. C. Escher, and he had an uncle who was an artist and a collector of surrealist art.  This uncle was Roland Penrose, and his collection is housed at "Modern Two" in Edinburgh.  The rest of this blog consists of photographs I took in the Roland Penrose Gallery of "Modern Two."  They may give a sense of one influence in the life of mathematician Roger Penrose.

Maternity by Miro

Never Again by Tanguy

Magritte

The Black Flag by Magritte

Untitled by Roland Penrose

The Joy of Living by Ernst

Hat in Hand, Hat on Head by Ernst

Roland Penrose