Hardy was bewitched by this image, was determined to become a Fellow of Trinity, and decided that mathematics was his ticket to it.
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| Interior of Trinity Great Hall, Cambridge* |
Before moving on with information about Hardy, I need to add that my hosts at Cambridge took me utterly by surprise by treating me to lunch IN the Great Hall! After I expressed my thanks the first time, the response was, "I thought you would like that." After I expressed my thanks a second time, the response was along the lines that it wasn't really such a big deal, " . . . after all, Hardy ate there every day."
YES! EXACTLY!!
HARDY ate there every day!
OK, calming down now - and getting back to Hardy.
It's not surprising that Hardy saw mathematics as his ticket to Cambridge; he always did have an affinity for numbers. As a child, when his mother took him to church, he would spend his time factoring the numbers on the hymn board.
Both of Hardy's parents were devout Christians, but both Hardy and his only sibling, a younger sister Gertrude, grew up to be staunch atheists. He and his sister were very close and remained so throughout their lives. Hardy's atheism didn't end with disbelief but with active dislike to the point where he made God very real in his life by considering God to be his enemy. Though he didn't believe in God he somehow believed that God was out to get him, which led to some interesting tactics on Hardy's part.
If there is anything that rivaled mathematics for Hardy's affection it was the game of cricket; therefore he feared when he was headed to a game that God would make it rain and spoil his joy. Because of this Hardy would take papers to grade, extra sweaters and an umbrella so that God would think he was hoping for rain so that he could do his work and would thus provide sunshine instead in order to thwart Hardy's supposed wishes.
Another such story has to do with a crossing of rough seas after having spent time in Denmark with another mathematician. Before boarding the ship Hardy sent a postcard to the other mathematician stating, "I've solved Riemann." The Riemann Hypotheses remains today the most famous unproven hypothesis in mathematics. Hardy felt that God would not let him die leaving the world thinking he had proven Riemann.
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| Plaque for Hardy in Trinity College Chapel, Cambridge |
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| Trinity College Chapel, Cambridge |
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| Ceiling of Trinity College Chapel, Cambridge |
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| Trinity College Chapel, Cambridge |
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| Trinity College Chapel, Cambridge |
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| Facing west, Trinity College Chapel, Cambridge |
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| Statue of Newton in Trinity College Chapel, Cambridge |
Hardy may have played tricks on God in order to ensure that things went his way, but it is no trick to say he was the greatest British mathematician of his time. England had been a mathematical backwater since the time of
Newton (1643-1727) and
Leibniz (1646-1716) and the fight over who invented the calculus, after which England turned its back on the mathematics being done on the continent and focused on applied mathematics to the near exclusion of pure mathematics. The work done in applied mathematics (mathematical physics) was amazing and included such names as Kelvin, Maxwell, and Thomson, but as far as pure mathematics, England was an utter backwater. Hardy led the way in changing that.
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| Senate House, Cambridge University (King's College Chapel on left) |
Though Trinity was the center of mathematical work in England it had really become ossified by the Tripos (pronounced "try-poss") system, a test to rank mathematics students that had its beginnings in the 1700s and which had become more and more "important" over the years, harder and harder over the years, and less and less connected with ability to do real math. In other words, it had become Tradition. If you did well on the Tripos you could basically write your ticket to any university mathematics position you wished.
Talk about high stakes testing!!
It got to the point where going to lectures became a luxury and students instead focused on hiring coaches specifically to help them be successful at this one test. It was a big deal to be "First Wrangler" (top scoring student) on the Tripos - kind of like being a rock star, an All-American athlete and a Rhodes Scholar but bigger than those three combined! Even if you were among the top ten scorers, that fact would be noted in your obituary no matter how many years later. After scoring had taken place, the rankings would be read out at the Senate House, and a large crowd - including women! - would show up to hear the rankings.
The test became an end in itself. Instead of learning deep mathematics or new ideas, students would be trained to look for tricks. Doing well on the Tripos became more like doing a crossword puzzle than like doing mathematics. Students were learning to jump through hoops rather than to do real mathematics. It has been called "impossibly arduous" and "the most difficult mathematics test in the world." No other institution had anything remotely like it. Students would memorize Sir Isaac Newton's
Principia Mathematica as if it were scripture: chapter and verse.
It nearly broke many men who eventually went on to become some of the most prominent mathematicians of the century - including Hardy and
Bertrand Russel, both of whom considered giving up mathematics when faced with this path. After Hardy became a Fellow of Trinity he became secretary of a panel that was assembled to reform the Tripos. Though Hardy went along with the reform idea, what he really wanted was to do away with it all together. Over time what resulted was reform, and the Tripos, in altered form, still exists today, as I saw while looking at the bulletin board of a common room in the Center for Mathematical Studies in Cambridge:
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| Bertrand Russell's plaque, Trinity College Chapel, Cambridge - along with Hardy not a fan of the Tripos system of their day |
As I mentioned, this experience was so oppressive, stifling, tedious, lengthy and pointless to Hardy that he nearly gave up on mathematics, but the experience also made him desperate for a breath of fresh air, which came in the form of a book by French mathematician Camille Jordan,
Cours d'analyse de l'Ecole Polytechnique. This book on rigorous analysis was life altering for Hardy, and, as a proponent of the "new" rigor, Hardy was in a position to have a school of followers that brought England up-to-date mathematically.
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| Clock Tower, Great Court, Trinity College, Cambridge |
Although Hardy was tremendously influential in the course of English mathematics in the twentieth century, I think that if I were to ask most people who have some knowledge of math history what they know Hardy for it wouldn't actually be for his own work but rather for his "discovery" of another mathematician, Srinivasa Ramanujan.
Hardy's and Ramanujan's lives are quite intertwined.
In fact, as I write this post I am relying heavily on Robert Kanigel's biography of Srinivasa Ramanujan in order to write about Hardy! If you have any interest in either of them or in the history of mathematics generally, I strongly recommend Kanigel's book
The Man Who Knew Infinity: A Life of the Genius Ramanujan.
There is also a 1987 documentary of Ramanujan's life that can be found at
this link. Additionally there is a recent Warner Brothers film, released on April 29, 2016 based on Ramanujan's life (
trailer here). Though I haven't seen the movie I was warned by those I met with at Cambridge not to expect much of it - at least not in terms of accuracy. For instance, in one scene Ramanujan is shown in Trinity College Chapel looking up at the statue of Newton; in the movie there are names engraved on the wall behind Newton, just as there are in my picture earlier in this post. There's just one problem - the names could not have been there during Ramanujan's time, and that should be obvious. He was there during the time of WWI, and these names were engraved
after the war in memoriam to those whose fought and died in that war. It seems sloppy on the part of the film-makers not to have simply used some digital magic to remove the names for the sake of accuracy in the movie, so I'm left wondering what else is inaccurate. There were other complaints about the movie that were shared with me, but I don't remember the specifics. I'd been really looking forward to this movie coming out, so I find all of this quite disappointing, though I will probably still watch it at some point.
But, I digress . . .
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| Littlewood's and Ramanujan's plaques in Trinity College Chapel, Cambridge |
Though Hardy is known to have said that he had no patience for his less able students, and though he did have a formidable exterior, he had a soft heart for the downtrodden. His grandparents on both sides were poor, and his parents were unable to afford university for themselves, but they had educated themselves and become teachers. There was strong emphasis on education and academics in his home, and that stayed with him, though his religious training did not. He did not grow up in a home that was wealthy monetarily, but it was wealthy in terms of a rich life of the mind. And though his family was not wealthy he saw that he was more privileged than many around him, and he saw learning and academics as a way to continue to enjoy privilege in his life. Thankfully for him he lived at a time when education was becoming available not only to the aristocracy or to the utterly impoverished, so he was able to pursue this path. I mention this because though pictures of him can make him look quite haughty, and though he could come off as forbidding, and though he reached the great heights of a Cambridge Fellowship, he always had a heart for the downtrodden, even if he wouldn't admit it.
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| Bust of Srinivasa Ramanujan in the Center for Mathematical Sciences, Cambridge |
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| My humble work in the Center for Mathematical Sciences, Cambridge, under the gaze of Ramanujan's bust |
It was Hardy, whose heart was open to the downtrodden who "discovered" Ramanujan - a man with natural mathematical brilliance but without formal training. Ramanujan had sent letters to other European mathematicians, but his letters were ignored by all of them except for Hardy who took the time to look at Ramanujan's work carefully. Recognizing his genius, Hardy made a way for Ramanujan to come to Cambridge - with consequences that were both amazing and tragic (see Kanigel's book!).
Up to and including Hardy's era, women were not allowed to attend lectures in the Cambridge colleges (with the exception of two schools that were for women only). There was such strong sentiment against women that in 1887 a proposal to allow them to earn degrees was soundly defeated, and when it came up again a decade later, sentiment was still so strongly against it that a woman was hanged in effigy outside Senate House. (Also, up until 1882, Fellow of Cambridge colleges were not allowed to marry). Famous female mathematician Mary Cartwright (1900-1998), pictured below, said of Hardy that she had his favor because as a woman mathematician she was of a "depressed class."
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| Photograph of mathematician Dame Mary Cartwright, which hangs in the Royal Society in London |
There is so much more I could say about Hardy - about how he remained youthful-looking and handsome (according to the fashion of his time) until late in life, yet how he hated his own image so much that he would cover mirrors with towels when he stayed in hotels because he couldn't stand to see his own reflection - about his collaboration with Littlewood and how it was said that in England at that time there were three great mathematicians: Hardy, Littlewood, and Hardy-Littlewood (and how at least one foreign mathematician traveled to England in order to verify Littlewood's existence because he thought Hardy had just made him up to pin mistakes on if there were any in his publications) - about his time in The Apostles (and connections to the Bloomsbury Group) - about his beloved book
A Mathematician's Apology - about his mathematical work - and on and on. Instead I will close with some pictures, and just a little bit of commentary, about where his rooms were on campus at Trinity - as a student and then as a Fellow. If you want to put them in context, there is a nice map at
this site.
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| Whewell's Court, Trinity College, Cambridge where Hardy had rooms as a student |
After becoming a fellow, Hardy had rooms in Great Court - pictured above - though I'm not sure exactly which rooms were his. At some point later, during the time he was interacting with Ramanujan, his rooms were in New Court. His rooms can be seen in the picture below; they were on the second floor above the gate - pictured more clearly in the second photograph down from here. If you scroll up to the very first picture in this post you can see his rooms from The Backs on the far right of the picture above the gate - what a view he had in that direction!
From Hardy's rooms in New Court it was a very short walk to his collaborator Littlewood's rooms in Nevile's Court - just through one of the arches that you can see on the right in the picture above. Kanigel states that this was 19 steps down Hardy's staircase, 40 paces through the arch, and then up the D staircase to Littlewood's rooms. (I can verify the proximity from having been there, though not up either staircase.) And yet, though they collaborated so frequently and lived so close, they almost never worked together face-to-face, but rather would send written notes back and forth via messenger!
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| Nevile's Court, Wren Library in center, Littlewood's rooms on left |
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| The D Staircase in Nevile's Court where Littlewood had rooms |
The next two pictures are views from the bottom of staircase D into Nevile's Court. Though Hardy moved around a bit during his career, Littlewood stayed in these rooms for 65 years, until his death in 1977. With views like this, who can blame him?!
As I close I confess again my indebtedness to Robert Kanigel's writing in the preparation of this post, and I again heartily recommend his biography of Ramanujan. I also cannot close without expressing profuse thanks to Cambridge professor Dr. Piers Bursill-Hall and his doctoral student Richard Chapling for the access they granted me to these places, the helpful conversations we had together,the information they provided me with (all errors in this post are, of course, my own), and their incredibly gracious hosting of me during my time in Cambridge.
I've mentioned in
another post that I'd been told (kindly and so as to let me down easily, I think) by the chair of the sabbatical committee that I probably wouldn't be able to do all I had proposed - was just too unlikely in some instances - and this was one of those instances. The pictures above testify to the fact that it is truly the case that you should "never say 'never'."
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* This photograph is the only one on my blog that I did not take myself. My host wasn't sure if pictures were allowed in Hall, so I, respectfully, didn't take one. This is one I found online, but I don't know who to credit. If you recognize it and know who took it, please let me know, and I will gladly give credit.
Both of Hardy's parents were devout Christians, but both Hardy and his only sibling, a younger sister Gertrude, grew up to be staunch atheists. He and his sister were very close and remained so throughout their lives. Hardy's atheism didn't end with disbelief but with active dislike to the point where he made God very real in his life by considering God to be his enemy. Though he didn't believe in God he somehow believed that God was out to get him, which led to some interesting tactics on Hardy's part.
After becoming a fellow, Hardy had rooms in Great Court - pictured above - though I'm not sure exactly which rooms were his. At some point later, during the time he was interacting with Ramanujan, his rooms were in New Court. His rooms can be seen in the picture below; they were on the second floor above the gate - pictured more clearly in the second photograph down from here. If you scroll up to the very first picture in this post you can see his rooms from The Backs on the far right of the picture above the gate - what a view he had in that direction!
As I close I confess again my indebtedness to Robert Kanigel's writing in the preparation of this post, and I again heartily recommend his biography of Ramanujan. I also cannot close without expressing profuse thanks to Cambridge professor Dr. Piers Bursill-Hall and his doctoral student Richard Chapling for the access they granted me to these places, the helpful conversations we had together,the information they provided me with (all errors in this post are, of course, my own), and their incredibly gracious hosting of me during my time in Cambridge. 
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