Wednesday, May 02, 2012

Top Six Mathematicians of All Time

(Note: April 29--I have been on vacation for a week, I was unable to get anything done for two weeks before that, and now the Blogspot site is all changed and I am having difficulty even in moving my cursor up and down the edit page with any of the speed to which we have become accustomed. I was also planning to reinvent myself during the hiatus but I have had to shelve that plan, for the moment anyway).

I was looking for a questionnaire, 'meme' or top whatever list to plug in here, not having done one for a while, when I came across someone's list of the 100 greatest mathematicians. I realized that I could not, without some struggle, name a personal top 10. It's pretty disgraceful, at least for a 42-year old man who is supposed to be interested in the life of the mind. I had meant of course to re-engage with both the history of math and some advanced mathematical studies at some point--once I had become established in my main career, I think--well, we all know how that goes. (Note: I was back at my alma mater last weekend. These visits always produce an odd muddle of sensations, most of which I will not get into here, but the book store there remains highly satisfying, the more so as places anything like it grow increasingly rare. Even the bookstores at colleges like Harvard and Dartmouth are Barnes and Noble-like, and while not bad, contain a lot of topical or practical-oriented material, as well as some total fluff. St John's is still having very little of that even in the general non-fiction categories, and the outsized portion of space given over to books of pure mathematics, Greek literature, musical scores, and philosophy make it quite unlike any other place in the world and maintain a tone of seriousness despite the increasing, though still modest, quotient of T-shirts and other souvenirs, which were almost non-existent in my time. At the same time all of this, as well as the displays of the college's collection of antique scientific instruments the purposes of which I for the most part cannot identify, serve as a sad reminder of all the learning I not only failed to retain, but failed to acquire in the first place. And the stuff they teach in liberal arts schools is supposedly child's play that the typical engineering graduate picks up in his free time over the internet.) (Another note: I am so desperate to finish this post that I am trying to distract my 3-year old with television and junk food. Unfortunately even that is not working). Since I cannot make up my own list, I am going to see what I know about the top 6 on that referred to above before looking up what they actually did (I am doing the top 6 instead of the top 5 because Euclid was ranked #6, and I have actually heard of him).

6. Euclid

Scene from the "School of Athens", of course, one of the central paintings of the western world, and, as I believe I had written elsewhere here, one of the more thrilling moments in tourism to see in person, not least perhaps because what is technically the 'main attraction'--that being the Sistine Chapel, which is however much more difficult to see and concentrate on in real time--still awaits.

We read the Elements, or much of it--all of the first 3 books, the 5th (? the one on proportions), the 10th--in the first year at the old school, and while it was always hinted that everything in its pages was subject to disputation, naturally it was hardly obvious to me where the vulnerability lay, and as such seemed perfectly reasonable and representative of some kind of truth, probably something along the lines of, there is an order to be found in existence that is independent of death and ugliness and stupidity, and the best part of our minds is that which enables us to make out what that is. The greater genius of moving/seeing beyond it, or even imagining that one must desire to do so, I was not to have a portion of, however. I was deeply impressed by the actual squares drawn onto the lines for the proof of the Pythagorean Theorem, as were most of the mathematical naifs. That conception had simply never been hinted at anywhere in my previous life.

5. Bernhard Riemann

I don't know anything at all about this guy. I have never even heard of him

3. Carl Gauss

My pictures got out of order, so number 3 comes before number 4.

I have heard of Gauss, though I have very little idea of what he did. The picture of the bell curve on the 10-Deutschmark bill reminds me that his name is associated with that device, but I am assuming that if he is the 3rd greatest mathematician of all time this was not his signature accomplishment, or that there is much more profound import in it than is generally known.


There was an article in the New York Times last week (now a month ago) about a college student who died of alcohol poisoning in a fraternity hazing ritual. There are usually a couple of these a year. The comments were predictably full of indignation and disgust at the continued tolerance of this juvenile, anti-intellectual, and prelapsarian culture at many of our finest universities (the particular incident referenced in the article happened at Cornell). I am no lover of the fraternity scene myself. As a teenager I was so terrified of their reputed social and sexual power at the schools where they predominated that, knowing I could never be one of them, I was very much determined to go somewhere that didn't have them, and I don't regret having avoided them in my day. Nonetheless, it seems hardly to be disputed that, among those not constituting the true academic elite of the nation, which at most colleges is 1 or 2% of the student body if they are lucky, 15-20% at the better ones, and I suppose a little more than that at a few places like Cal Tech, the supposedly widely reviled fraternity boys are about the greatest winners, and greatest men, in our whole society. Have you ever met a member of a winners' fraternity who was stuck in support staff making $40,000 a year, or, God forbid, working retail, 10 years after graduation? Neither have I. It scarcely requires an effort to find examples of frat parties even at highly exclusive schools where the crudest, and by the supposed standards of respectable contemporary society most blatantly offensive displays of racism and misogyny are openly advertised and recorded for all the world to see that are well attended by scores of thin, physically desirable and willing women while legions of men for whom the thought of inadvertently causing offense to a minority or feminist or homosexual is a source of constant mortification enjoy another night of pizza, soft drinks, and dungeons and dragons, followed by a restful sleep unburdened by female company. Yes, the hazing rites sound ridiculous, juvenile, and unnecessarily dangerous, and certainly on the surface would appear to be wisely avoided; however, they evidently serve some important purpose that is essential to male development, since most men who successfully pass through them seem to do quite well in their careers and the social world of adulthood. I don't really understand it, but I suspect it's about demonstrating that you are one of 'us' in whatever milieu you are talking about, that you can be trusted to maintain the culture of success and achievement that you are gaining admission to, that you are worthy. How having to eat grapes that have been jammed up the buttocks of your fellow pledges directly from that place of storage--to give an example related by one of my high school friends--demonstrates this peculiar value is still rather mysterious to me, though again in this intance the gentleman I reference went on to attend Yale Law School and currently works intimately with the highest officials and most powerful interests in his state on matters of substantial and decidedly adult import, so I would have to say that at some level his socialization served him well.    

4. Leonhard Euler.
A complete blank. Nothing at all.

2. Archimedes

When I was in Annapolis last weekend I saw an attractive girl with Archimedes's quotation (in English) about being able to move the earth if he could find a place to stand on displayed across her upper back, in what looked to be a temporary tattoo.

A patriotic Syracusan, the mathematician turns up frequently in the ancient histories. Catapults designed by him provided an effective defense of the city, or at least caused the enemy no little consternation in its assault, on several occasions. The illustration above commemorates his famous bathtub epiphany. What was it again? I don't remember. It was not the lever problem. Was it the formula for cubic measurement? This is atrocious. I don't remember. I do remember that he was killed because he was so immersed in a geometrical problem that he ignored, or did not register, the commands of the encroaching army (were they the Romans? I seem to remember this from Plutarch. Archimedes lived later than the time of the Pelopponesian War I believe), though the overheated meathead who personally slayed him quickly became infamous among his own leaders when the identity of the old man was discovered.

1. Isaac Newton

My store of top Isaac Newton thoughts/knowledge:

I have the impression that Isaac Newton was the child of farmers, and that his mother was wholly illiterate and ignorant about the wider world. One legend about his precocity goes that given the first proposition in Book I of Euclid--perhaps it was even the first definition--at around the age of ten, he deduced the entirety of the remaining 47 propositions of that Book without further reference to its pages and stated that the work was rather obvious. I have no idea if this story has any credibility. I read it in passing once. Somebody, I presume his teacher or local clergyman, coming to the realization that they had a legitimate genius in their midst, got him some proper schooling and to Cambridge, where he doubtless belonged more than anybody else in the kingdom (or the Protectorate--I can't remember his exact date of matriculation) at that time. Author of the Principia, which is a dark horse candidate for the greatest book of all time, and was considered by many scholars at St John's to be the most genuinely difficult volume on the program there-- perhaps legitimately smart and educated people can work up to reading Hegel and Kant and even Einstein with some degree of familiarity, but the singular mind of Newton cannot be prepared for or really taught. Also a perennial candidate for the Most Important Figure in the history of the world, with his only challengers in recent decades usually being the now rapidly fading Jesus Christ, and Muhammed. He was reportedly unable to have satisfying relationships of any kind, personal or professional, his intelligence being so far beyond that of actual individual people that it was impossible for him to find any common ground with anyone on which to form an ordinary human friendship. His books are addressed to the collective knowledge of entire schools of hundreds or even thousands of scholars whose combined brainpower can only in rare instances begin to comprehend their meaning. Alexander Pope had a terrific man-crush on him.

I did look up the claims to fame of the mathematicians I knew nothing about, however I think it would be ridiculous even to copy the record of their achievements without having studied them, for the terms (Differential Geometry, Real Analysis, etc) mean no more to me than the names. I did look up Archimedes's biography, and he did live later than the Peloponesian War period (287-212 B.C.), and did die at the hands of the Romans. The discovery he came upon in the bathtub was of course that of the water being displaced by a mass inserted into it and that this principle could be applied to calculating volume. I definitely knew that, or at least I was familiar with the general parts of the story, at one long lost time.

Hopefully on to further (and better) posts after this dead period...I should do a link at least to the list I am taking these rankings from, but it will take too much time now at 10:52 in the evening. If lots of people complain about it I'll go back and put it in later...

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