Michael:

A while ago, as you may remember, I blogged about Carl B. Boyer’s and Uta C. Merzbach’s “A History of Mathematics.” Well, having plowed through several hundred more pages of it, I must say that a historical account such as this one certainly humanizes the study of math—which otherwise can seem (to intellectual lightweights like me) a forbidding exercise in abstract thought. In fact, what strikes me on going through the book is that mathematicians, far from being ethereal creatures living on air and focused solely on matters of pure intellect, have often been rather remarkably accomplished in other areas as well.

To start with, it turns out that some mathematicians, at least, are pretty good at earning money. I was intrigued to note that Thales of Miletus (c. 624-c. 548 B.C.)—according to tradition, the first person to offer a demonstration or ‘proof’ of a geometric theorem—not only wandered around doing mathematical things like measuring the height of the pyramids in Egypt by the lengths of their shadows, but was also shrewd enough to corner the supply of olive presses one year when a particularly massive olive crop made the need for such presses quite urgent. (That must have paid for a number of years of abstract speculation, huh?) And Hippias of Elis, a sophist of the latter fifth century B.C., who was responsible for introducing the first curve other than a circle into mathematics, considered his proudest accomplishment to be having earned more money as a teacher than all of his intellectual rivals in Athens combined. (He thereby, of course, earned the mortal enmity of Plato, who burlesqued him in a dialogue, but that’s another story.) More recently, Carl Friedrich Gauss (1777-1855), a strong candidate for the ‘most-accomplished-mathematician-of-all-time’ award, somehow found it possible, despite having to raise a large family on a fairly modest salary, to amass a fortune by what Boyer and Merzbach describe as “shrewd investments.”

Okay, if making money doesn’t seem remote enough from the beauties of pure mathematics, how about making war? Archytas of Tarentum (428-350 B.C.) not only wrote on the application of mathematics to music (he apparently originated the term ‘harmonic mean’), but he was also a never-defeated general. Archimedes of Syracuse (287-212 B.C.), the greatest mathematician of the ancient world, didn’t scruple to devise, in the words of Boyer and Merzbach:

…ingenious war machines to keep the enemy at bay—catapults to hurl stones; ropes, pulleys and hooks to raise and smash the Roman ships; devices to set fire to the ships [during the siege of Syracuse by the Romans in the 2nd Punic War.]

Archimedes was so successful at sowing death and destruction that it took the Romans two full years to take Syracuse. Even when confronted by an enraged Roman soldier brandishing a sword in his face (a young man who seemed to take personally the many Roman deaths caused by Archimedes’ fiendish machines) the ultra-macho 75-year-old mathematician coolly ordered the boy to step away from the geometric diagram he was drawing in the sand, a request that got him run through.

Okay, at least mathematicians are, um, hyper-intelligent geeks with no ability to feel or express the finer emotions, right? Sorry, but it’s not true of all of them. The geometer Eratosthenes (276-194 B.C.), in addition to coming up with a remarkably accurate estimate of the circumference of the Earth, had a significant reputation in the Classical world as both a poet and historian. Omar Khayyam (c. 1050-1123), whose reputation in Islamic cultural history is based on his significant contributions to algebra, is of course somewhat better known in the West as the author of “The Rubaiyat.” A little closer to our time, Blaise Pascal (1623-1662) who of course made great contributions to the mathematics of probability and other problems, also went on to write two books, the Lettres provincials and the Pensees which have enjoyed a certain lasting literary fame.

Moving from literature to the visual arts, I would note at least three individuals, famous in the fields of art and architecture, who also made notable mathematical contributions. The first is Piero Della Francesca (1410? – 1492), author of the treatises De prospective pingendi and De corporibus reglaribus in which he noted the “divine proportion” in which diagonals of a regular pentagon cut each other and where he found the volume common to two equal circular cylinders whose axes cut each at right angles, thus unknowingly re-creating one of Archimedes’ problems. The second is Albrecht Durer (1471-1528), author of an Investigation of the Measurement with Circles and Straight Lines of Plane and Solid Figures. Boyer and Merzbach describe this work as containing

…some striking novelties, of which the most important were his new curves.

Finally, there was the architect Christopher Wren (1632-1723) who held the Savilian professorship of astronomy at Oxford and corresponded with Pascal over the rectification of the cycloid (whatever the heck that is—oh, wait, it’s got something to do with conic sections). As Boyer and Merzbach remark:

…[H]ad not the great fire of 1666 destroyed much of London, Wren might now be known as a mathematician rather than as architect of St. Paul’s Cathedral and some fifty other churches.

Well, at the very least we can dismiss mathematicians as a bunch of brainy recluses, uninvolved in wider society and never dirtying their hands with political or administrative affairs, right? Umm, that one fails big-time. For example, an early pillar of British mathematics, Thomas Bradwardine (1290?-1349), ultimately rose to the position of the Archbishop of Canterbury. Boyer and Merzbach note that after a youth spent as a perpetual college student, the famous Nicholas Copernicus (1473-1543) spent his mature years as Canon of Frauenburg in his native Poland, where his celebrated work on heliocentric astronomy (which included significant advances in trigonometry) was completed despite

…multitudinous administrative obligations, including currency reform and the curbing of the Tuetonic Order.

Two great early modern French mathematicians, Francois Viete (1540-1603) and Pierre de Fermat (1601-1665), were both lawyers and politicians—one has to wonder where they found the time to dabble in arcana like analytic geometry. Gottfried Wilhem Leibniz (1646-1716), the co-inventor of calculus with Newton, was not only a lawyer but also a big-shot international diplomat, representing, among other clients, the Hanoverians (including the future George I of England.)

Well, at the very least, mathematicians must all lead fairly boring, stuck-inside-their-own-head sorts of lives, no? Regrettably, I must also shoot that one down. A prime counter-example is that of Geronimo Cardano (1501-1576) whose publication of 1545, Ars magna, made such huge strides in algebra that many historians use that year to mark the beginning of the modern era of mathematics. But that’s only one of the ‘dramatic’ (melodramatic?) elements in Cardano’s life:

Cardano…had achieved worldly success as a physician. So great was his fame that he was once called to Scotland to diagnose an ailment of the Archbishop of St. Andrews (evidently a case of asthma.) By birth illegitimate, and by habit an astrologer, gambler and heretic, Cardano nevertheless was professor at Bologna and Milan, and ultimately he was granted a pension by the pope. One of his sons poisoned his own wife, the other son was a scoundrel, and Cardano’s secretary Ferrari probably died of poison at the hands of his own sister. Despite such distractions, Cardano was a prolific writer on topics ranging from his own life and praise of gout to science and mathematics.

Well, okay, I have to admit some feelings of inadequacy here; not only do I struggle intellectually to keep up with the discussions of the math in this book, but I have to recognize that even outside math proper a lot of mathematicians have accomplished far more than I am ever likely to (or, at the very least, led such wild and crazy lives that my experiences look pretty tame in comparison.)

Okay, you math guys, like, cool it! You’re showing the rest of us up! And not just in math! Don’t make me bring up the cautionary tale of analytical geometer (and ‘typical’ over-achiever) Jan De Witt (1629-1672) who held public office as the ‘Grand Pensionary’ of Holland:

He led a hectic life while directing the affairs of the United Provinces through periods of war in which he opposed the designs of Louis XIV. When in 1672 the French invaded the Netherlands, De Witt was dismissed from office by the Orange party and was seized by an infuriated mob that tore him to pieces.

Let that be a lesson to the excessively ambitious segment of the mathematically inclined.

Cheers,

Friedrich

P.S. Did anybody else notice how long lived these guys seemed to be? I just did the math on the dates listed in this post, and the average life-span was 68.5 years. This must have been close to twice the normal life span during this period. Does mathematics innoculate against aging, too? Or does resistance to disease correlate in some way with high intelligence or mathematic ability?

Cardano wrote one of the first autobiographies, that is remarkable in the sense that he sometimes writes almost modern sentences. When he counts his blessings. [Like the number of teeth he still has].

But on the other hand, it is a bit difficult to make out how much of a genius he really was. I mean, he wrote the first treatise about game theory that preludes much that Pascal did with statistics.

But Cardano had to. He was so hooked to gambling, he already had pawned his wife's jewelry to pay for his debts. So circumstances forced him to look into the logics behind throwing dice.

Posted by: ijsbrand on March 8, 2004 12:38 PM

That's uncanny- only recently I was reading the biography of Wren - by unrelated thread- and was astonished by his 'multitasking', too.
Unfortunately, nothing comes cheap, even to the geniuses.
Look at this passage;
... he married Faith Coghill, the daughter of Sir John Coghill of Bletchingham.... The marriage lasted for only six years for Faith died in September 1675 shortly after giving birth to their second child. Wren, left with two young children, soon married again, this time to Jane Fitzwilliam in 1677. Wren's second marriage was, sadly, shorter than his first since Jane died of tuberculosis in 1679. There were two children from this second marriage...
From a different source, another interesting detail:
...It ought never to be forgotten, what our ingenious countryman Sir Christopher Wren proposed to the silk stocking weavers of London, viz a way to weave seven pair or nine pair of stockings at once (it must be an odd number). He demanded four hundred pounds for his invention; but the weavers refused it, because they were poor, and besides, they said it would spoil their trade; perhaps they did not consider the proverb that light gains, with quick returns, make heavy purses. Sir Christopher was so noble, seeing they would not adventure so much money, that he breaks the model of the engine all to pieces, before their faces.

From John Aubrey's Brief Lives. (Edited by R Barber, Boydell Press, 1982)

And yet another quote:
...Summerson (biographer) writes:

The diffusion of his abilities is amazing and frustrating to us as it very possibly was eventually to himself.

Posted by: Tatyana on March 8, 2004 2:45 PM

Yeah, agreed. Mathematicians, please stick to being uptight, socially inept eggheads.

Posted by: . on March 8, 2004 3:35 PM

Dear .

You wouldn't happen to be a mathematician, would you?

Posted by: Friedrich von Blowhard on March 8, 2004 3:49 PM

I'm going back to school this fall to take a mathematics degree. I'm also afraid that I'm one of those wilder ones who likes making money, and as yet has lacked the capital to game the market (a gambling streak in those inclined towards math is not an isolated event! At one point many years ago I had the odds of improving a hand in draw poker to whatever hand you thought you needed to win. Then you compare those odds to the ratio of money you've put into the pot. Of course you need your gut to tell you what hand you'll need to win, but then the math tells you if it's worth it. I bought much booze and smokes with winnings that summer :-)

Posted by: David Mercer on March 8, 2004 4:32 PM

David,
you reminded me of the 30+ guy I met on a jury duty, who's a mathematics teacher in high school and who took to regular gambling trips to Atlantic City as means of 1)improving his salary (invariably, he said), 2)bring variety into monotonous boredom and 3)'meet crazy chicks' [you guessed it].
Incidentally, he was the last one to compromize on a verdict - tried to introduce logical arguments to the emotional audience. I wonder, if there is connection here...

Posted by: Tatyana on March 8, 2004 4:44 PM

The longer average lifespans may be a result of these men all being higher in status than the average peasant. Higher status people presumably had better nutrition and better health care, and thus would be expected to live longer. A peasant who might have been a mathematical genius in better circumstances didn't have those circumstances, and so didn't leave a record of mathematical accomplishment.

Wait a minute... if half of all people died by age 5, that would bring down the average age by a large amount. Maybe almost everyone else lived into his/her 60s.

Raymund

Posted by: Raymund on March 8, 2004 5:49 PM

Raymund:

After I wrote my postscript the same thought occurred to me; to wit, that since individuals dying in childhood weren't able to establish reputations as great mathematicians, the proper comparison was with the life expectancy in those societies for those who managed to stay alive until 15 or 20. I don't know the 'life expectancy at 15 or 20' for the ancient world, but I still strongly suspect that the mathematicians were long-lived in comparison with that more elite group--albeit not so decisively.

Posted by: Friedrich von Blowhard on March 8, 2004 5:55 PM

Math? What's math?

I read somewhere that most of the big diff between average lifespan in the ancient world and ours is accounted for by infant and childhood deaths. That is, if you lived through childhood, you probably lived as long as we moderns tend to. I wonder if that's true. Does anyone know? I've got a brain cell or two hinting to me that what I'm recalling wasn't science but anti-modern propaganda of some sort.

Posted by: Michael Blowhard on March 8, 2004 7:42 PM

Michael, if that is true, I would bet that is only true of males. Women had childbirth and postpartum recovery to live thru and on a more regular basis than war or fighting. I've read articles that talk about the medical issues of ageing in women as a modern concept since up til about 100-150 years ago, science was unable to keep women from dying young during or after childbirth. Which of course, has nothing to do with thier mathematical abilities.

Posted by: Deb on March 8, 2004 11:10 PM

Oh, true: childbirth used to knock of lots of women. I've visited cemetaries and been amazed by how many women in old days lived to be only 17 or 25 years old. I read somewhere that, because of this, many men wound up marrying three or five times ...

Posted by: Michael Blowhard on March 8, 2004 11:12 PM

Well, I notice you don't include any mathematicians in the last 100 years. I think you might find there were a few more "nerds" in that group. Reason why: the 20th century begins the Age of Specialization (also known as the Age of Wonkery). There are no Renaissance Men (or Women) in our age. In ages past it was still possible to have a cutting-edge knowledge of many fields. Thomas Jefferson's knowledge of philosophy, politics, and the sciences was specialized and also broad. But then again the understanding of these fields were not nearly so broad as they are now. A person in Jefferson's age could hope to wrestle with the biggest problems in physics, for example, and still make hay in politics. Today physicists are so specialized they hardly know what their colleagues are doing.

Posted by: delighted I'm sure on March 9, 2004 1:11 AM

One contemporary mathematician who is also an artist and, more controversially, a historian: Anatoly Fomenko.

Posted by: misteraitch on March 9, 2004 4:02 AM

Michael, you brought up the possibility that anti-modern propaganda is the source of the idea that the life-expectancy estimates of the pre-modern era are so low due to greater infant and mother mortality. I've long felt that it's pro-modern propaganda which touts those figures as a way of suggesting that this is the best of all times to be alive. My personal term for such writers is "technapologists".

Larry

Posted by: Larry Ayers on March 9, 2004 9:38 AM

A good book on the lives of various mathematicians that I read recently was "Men of Mathematics":

http://www.amazon.com/exec/obidos/tg/detail/-/0671628186/ref=sib_rdr_dp/102-9967808-5139367?%5Fencoding=UTF8&no=283155&me=ATVPDKIKX0DER&st=books

Yes, it only concentrates on men, but it's a good book. I particularly enjoyed the author's dry humor and erudition.

Posted by: mallarme on March 9, 2004 12:57 PM

That is, if you lived through childhood, you probably lived as long as we moderns tend to. I wonder if that's true.

In part. The other thing which tended to finish off our male ancestors was tooth decay, which in those halcyon days before hygiene tended to strike in the early 40s. If the boys were lucky enough to get their teeth knocked out before their mouths slowly rotted under half a dozen infections, they generally lived to a ripe old age, perhaps even outliving another wife or two.

Posted by: Tim Hulsey on March 9, 2004 3:30 PM

I've long felt that it's pro-modern propaganda which touts those figures as a way of suggesting that this is the best of all times to be alive.

Larry, are you suggesting it's not?

I don't think one must be a starry-eyed technophile to admit that indoor plumbing, running water and flush toilets are generally good things.

Posted by: Tim Hulsey on March 9, 2004 3:37 PM

Medicine didn't really exist until Pasteur: Vaccines, Antiseptics, Antibiotics – unless you consider blood-letting medicine (which was in practice in the USA up until the 20th Century). Consider the multitude of diseases without these modern advances (also consider modern pesticides as defenses against, historically, periodic plagues that were devastating – and nutritional deficiencies a consequence of pre-modern food supply deficiencies) ...

Isaac Newton ran the Mint. What a government employee! The technocrats! He doesn't strike me as a central-planner with hubris though.

Also, the thug who offed Archimedes, summarily got his head lopped off when it became clear what he did. small restitution ...

Posted by: reader on March 9, 2004 11:02 PM

Mathematician - I don't think so. I'm a computer guy, so I have experience with some sorts of higher math, and I get excited about theoretical aspects of math, but am not terribly great at it.

Posted by: . on March 10, 2004 1:07 AM

Hey, don't call the guy who wacked Archimedes a "thug." He was just doing his job: killing. Besides, Archimedes was so absorbed in sandbox games he didn't even notice his neighbors were having their heads lopped off. Now that's what I call cheek!

Posted by: The Mercenary on March 10, 2004 2:40 AM

Well, it's what I'd call geek :-)

I ought to know as I am one. You have no idea how many times in my life someone thought I was ignoring them when they repeatedly called my name, but I was way too absorbed in some thought process to notice!

Posted by: David Mercer on March 10, 2004 3:59 AM

Check that, should be: Edward Jenner.

Coincidentally, am currently reading Tobias Dantzig's: Mathematics in Retrospect, where, ahem, he's got quite a takedown chapter on pseudo-math's. Almost too thorough.

Posted by: reader on March 10, 2004 10:26 PM

If you're looking for unexpected adventure, romance, and calamity in the lives of mathematicians, your search should really start with Evariste Galois.

Posted by: Colby Cosh on March 11, 2004 2:04 AM

This has to do with life expectancy.

I did my dissertation in demography at a Lousy Ivy University (Penn), so maybe I can add some information.

Most of the leverage in changing overall average life expectancy comes from changes in mortality of the very young. This is (roughly) because the statistic has to do with total person-years lived by a population measured by deaths over a short time-span. It is part of a life table calculation--a hypothetical population displaying mortality behavior at the time the data were reported. For instance, unabridged US life tables are for 1979-1981, 1989-1991, etc. High mortality at early ages chops out a lot more person-years-lived than deaths to older people.

Populations with low life expectancies might have a quarter of their babies die during the first year following birth. Today, advanced nations experience less than one percent death rates during that interval.

However, high and low mortality populations generally show different mortality rates for all ages, though the differences are not as dramatic as for the "infant mortality" just described. Therefore, a 25-year-old male born the same year as Gauss would have a lower (remaining) life expectancy than that of a 25-year-old American male of today.

This can be confirmed by comparing age-sex specific death rates from 19th Century life tables for England-Wales (or elsewhere) with rates for the same groups in recent life tables for advanced nations.

Hope I didn't lay on the jargon too thick and that you understand my points even though I had to leave out some details.

Posted by: Don Pittenger on March 13, 2004 12:29 AM

i am an abstract mathematician. this talent has caused me loneliness,but has enhanced my ability to feel a certain high.i feel the latter when i am alone, and gazing at the universe. when i attempt to figure out a problem in a four dimensional space, i feel i am communicating with God. God is cognizant of me.pure mathematics(not the God-less economic theories, or draconian applied physics, which use mathematics) are the gates which open into the hallways of our Creator.

Posted by: orlando buch on March 24, 2004 9:07 PM

i am an abstract mathematician. this talent has caused me loneliness,but has enhanced my ability to feel a certain high.i feel the latter when i am alone, and gazing at the universe. when i attempt to figure out a problem in a four dimensional space, i feel i am communicating with God. God is cognizant of me.pure mathematics(not the God-less economic theories, or draconian applied physics, which use mathematics) are the gates which open into the hallways of our Creator.

Posted by: orlando buch on March 24, 2004 9:07 PM

i am an abstract mathematician. this talent has caused me loneliness,but has enhanced my ability to feel a certain high.i feel the latter when i am alone, and gazing at the universe. when i attempt to figure out a problem in a four dimensional space, i feel i am communicating with God. God is cognizant of me.pure mathematics(not the God-less economic theories, or draconian applied physics, which use mathematics) are the gates which open into the hallways of our Creator.

Posted by: orlando buch on March 24, 2004 9:07 PM

i am an abstract mathematician. this talent has caused me loneliness,but has enhanced my ability to feel a certain high.i feel the latter when i am alone, and gazing at the universe. when i attempt to figure out a problem in a four dimensional space, i feel i am communicating with God. God is cognizant of me.pure mathematics(not the God-less economic theories, or draconian applied physics, which use mathematics) are the gates which open into the hallways of our Creator.

Posted by: orlando buch on March 24, 2004 9:07 PM

Hmm, do you think so?

Posted by: t-shirts-man on April 6, 2004 5:14 AM

Sometimes I think Math is Poetry. If a Poem is an abstrac view of the world, a theorem is the same.

Posted by: Johann on May 20, 2004 7:48 PM

DEar Sir,

I would like to have some Documentary of Recent Mathematicians,about their lives and contributions. Can you please send me the requested information. I would be glad to hear a positive response. Shall eagerly wait for your early response.

Thanking you

Posted by: Gadazai on June 19, 2004 12:11 PM






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