Thursday, May 19, 2016

James Clerk Maxwell

James Clerk Maxwell (1831-1879) is comparable to Isaac Newton and Albert Einstein in terms of the importance of his work, but he is not as well known.  As well as being a mathematician and mathematical physicist he was a published poet, and his Christian faith was central to his life.  
It was in 1861 that he unified electricity, magnetism and light with his equations, so the 150th anniversary of this discovery was recently celebrated.  The year 2011 was quite a year of anniversaries in physics, from Boyle's publication of "Sceptical Chymist" to the discovery of superconductors to Rutherford's model of the atom and more!

I said earlier that Maxwell is comparable to Einstein and Newton.  I think this quote from a 2011 article in The Economist puts it well:

"Worthy intellectual accomplishments, all.  Yet they pale in comparison with Maxwell's.  This is not just because, unlike a lot of subsequent theoretical advances, his insight has already yielded a century's worth of tangible results, from radio to mobile phones.  (Only a century because it took scientists several decades before they had grasped the theory's full significance and put it into practice.) . . . . He showed that nature ought not to be taken at face value, and that she can be cajoled into revealing her hidden charms so long as the entreaties are whispered in mathematical verse.  In doing so he paved the way for the pursuit of physicists' holy grail: the grand unified theory, a set of equations which would explain all there is to know about physical reality. . . . Maxwell remains the great unsung hero of human progress . . . . His life's work, which also includes remarkable contributions to thermodynamics (not to mention taking the world's first colour photograph, also 150 years ago) is among the most enduring scientific legacies of all time, on a par with his more widely acclaimed peers, Isaac Newton and Albert Einstein.  It deserves to be trumpeted."

Maxwell was born at the house pictured above, at 14 India Street, Edinburgh, though not long after his birth his family moved to their home in Glenlair in the countryside of Scotland where his natural curiosity was soon apparent, and he always wanted to know how everything worked.  The family planned his education to be carried out by his mother until it was time for him to attend Edinburgh University.  Sadly, his mother died when he was 8 years old, and, after an unsuccessful attempt at having a tutor work with him at home, he was sent to the Edinburgh Academy.
Maxwell was 14 years old when he wrote his first mathematical paper, an exploration of the ellipse and of curves with more than two foci.  This work was read to the Royal Society of Edinburgh, though not by Maxwell, as he was considered too young to present his work. 

At age 18, while attending the University of Edinburgh, he wrote two further papers for the Transactions of Edinburgh's Royal Society, but he was still considered too young to read them, so they were read to the society by his tutor instead.
Main Campus, Edinburgh University

Though Maxwell had chosen to do his undergraduate work at Edinburgh University he did head to Cambridge for his graduate work and earned his degree in mathematics there.  In the famous tripos testing he earned the position of "second wrangler."  He is better known as a physicist or a mathematical physicist but his degree was in mathematics.
Looking down on Trinity from Great St. Mary's - Clock Tower, Chapel, Great Gate

While a student at Trinity he decided to examine his faith deeply.  He wrote:

"Now my great plan, which was conceived of old, . . . is to let nothing be wilfully left unexamined. Nothing is to be holy ground consecrated to Stationary Faith, whether positive or negative. All fallow land is to be ploughed up and a regular system of rotation followed. . . . Never hide anything, be it weed or no, nor seem to wish it hidden. . . . Again I assert the Right of Trespass on any plot of Holy Ground which any man has set apart. . . . Christianity — that is, the religion of the Bible — is the only scheme or form of belief which disavows any possessions on such a tenure. Here alone all is free. You may fly to the ends of the world and find no God but the Author of Salvation. You may search the Scriptures and not find a text to stop you in your explorations . . ."
Trinity Great Court
He was elected a fellow of Trinity - eventually also accepted a professorship in Marischal College in Aberdeen, Scotland - and later moved to London and became professor at King's College there.  His time in London was a very productive period of his life - perhaps the most productive.  
King's College London
He resigned his chair there in 1865 and returned to his Scottish family home with his wife, but in 1871 he accepted, somewhat reluctantly, an offer from Cambridge to be the first Cavendish Professor of Physics.  He was there in charge of developing the Cavendish Laboratory, overseeing every element of its construction and design.

The photographs below are of the "Maxwell Lecture Theatre" in the Old Cavendish (which currently belongs to the Sociology Department, and for a time until quite recently had been being used for storage; the fate of this historic hall is uncertain at this point.)

Maxwell died of cancer at the age of 48 in Cambridge.  He remained calm and firm in his faith through to the end.


Edinburgh University has expanded over time, and in 1919 an area to the south of the town of Edinburgh was purchased for the relocation and expansion of its science departments.  One of the buildings here is named for Maxwell.  (You can see more about Edinburgh's Universities at this link.)

In his youth, while at the Edinburgh Academy, Maxwell had a bit of a rough start socially.  He was looked upon by some of the other students as a bit of a "country bumpkin" and because of that had the nickname "Dafty," which didn't seem to bother him.  Eventually he met two other boys who were close in age and intellect to him who remained lifelong friends.  One of these was the future mathematician Peter Guthrie Tait (1831-1901), who, along with Maxwell and Thompson (aka Lord Kelvin) pursued topology and knot theory for a time.  When I read the following poem I see a confluence of Maxwell's faith and his work - knots, divine intellect, higher dimensions and the soul.

My soul is an entangled knot,
Upon a liquid vortex wrought
By Intellect, in the Unseen residing,
And thine cloth like a convict sit,
With marlinspike untwisting it,
Only to find its knottiness abiding;
Since all the tools for its untying
In four-dimensional space are lying

Full poem can be found at this link.

Monday, May 16, 2016

Stadtgottesacker, Halle

On my first full day in Halle, prior to visiting the market place ("maktplatz") and church ("kirche"), my wonderful host, Dr. Manfred Stern, took me to see graves of mathematicians in the Stadtgottesacker.  It you take apart that word you see "stadt" for city, "gottes" for God's and "acker" for "acre."  So it is "God's acre of the town;" I think that's a great name for a cemetery!

I believe this is the only Renaissance-style cemetery in Europe north of the alps.  It was designed in the same fashion as the Campo Santo in Pisa, Italy and has been here since 1557.

 The tombstone below, which is also visible in the center of the photograph above, is that of little-known mathematician Friedrich Meyer.  He was not a university professor but rather a teacher at the Stadtgymnasium.  However, he was on close terms with Halle University and professors Eduard Heine and Georg Cantor there.  He was awarded an honorary doctorate from Halle University in 1894.
 Manfred, who had discovered this tombstone years ago while looking for the tombstone of famed mathematician Eduard Heine, showed me this particularly stone because this mathematician and I share a surname and because the tombstone is mathematically interesting - inscribed with mathematical objects somewhat reminiscent of what was said to be on the tombstone of Archimedes.
We also looked for Heine's grave, which Manfred had taken a picture of in about 1980.  It was in good shape then, but it looks like in the past 36 years it has either deteriorated or been removed.  It should be in the area of what is shown in the photograph below.  If there's one thing I've learned on these travels it is that our memorials are not permanent!
We did see the tomb of mathematician Johann Andreas Segner (1704-1777).  From 1735-1755 he taught physics, mathematics and chemistry at the University of Gottingen. He also founded the observatory there.  Then from 1755 until his death he taught physics, mathematics and astronomy at the University of Halle.  He invented a precursor of the turbine, which was known as the Segner wheel, and he was visited in Halle by Leonhard Euler (1707-1783), who used Segner's results in his own mechanical investigations.*

*Information on Segner taken from the Mathematical Intelligencer (vol. 15, no. 2, 1993) article The Stadtgottesacker in Halle by Dr. Manfred Stern.

Thursday, May 12, 2016

Actually, Yes I Did!

This is ME writing some results and a hypothesis of Georg Cantor's
 IN  .  .  .  HIS  .  .  .  FORMER  .  .  .  CLASSROOM!!!

<pausing here for effect>

My department, my dean, and the sabbatical committee have been absolutely supportive of my explorations this semester.  As I reflect on my experiences today, however, I remember one comment the chair of the sabbatical committee made to me before my trip.  It wasn't negative; I think he was just trying to let me down easy.  I had put together a very ambitious proposal in which I stated that, among other things, I was going to truly walk where the mathematicians walked - that at Cambridge I was going to find the rooms that Hardy lived in - that near Lincoln I was going to see the apple tree that inspired Newton - that I was going to enter the actual classrooms where the great mathematicians taught -

The comment was gently made to me that I probably wouldn't be able to quite accompish the things I had proposed.  The committee approved my proposal (obviously), but evidently there was a sense, at least on the part of the chairman, that though I would certainly do much of what I'd proposed and that it would be valuable to our college community, that I couldn't actually do ALL of it.

Well, guess what?

These things that were seen to be (perhaps) impossible - I've done them!
Here I am at the front of the classroom where the phenomenal mathematician Georg Cantor (1845-1918) taught.  Yes, it's been refurbished, but he taught in THIS room, that exists inside THIS classroom building -
 - just up THESE stairs, through the next doorway, first door on your left.
Here's the teacher's-eye view of the classroom, and that's my contact here (and now my friend) Dr. Manfred Stern standing on the left.  He is very knowledgeable about Cantor and has just rolled out the red carpet for me and has helped me to access all things Cantor-related.
This classroom is in Martin Luther University Halle-Wittenberg (which I had always just known as Halle University).  Here is the quad of the university main campus with the classroom building on the left and the main hall or "aula" of the university on the right up the stairs.
Central area of the aula
Lion in front of the aula
After my little bit of board work he stepped up to the board, and we had a discussion about mathematical notation in the U.S. and Germany - similarities and differences -

Dr. Stern, by the way, regularly taught in this classroom!