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Saturday, October 8, 2011
Math: Can't Live Without It
Mathematics is all around us and a part of our everyday lives. Imagine living without numbers, shapes and measurement...impossible! Technology is a world full of numbers and their relationship to one another. It's not surprising then to find so many wonderful web-sites that engage us in learning more about math. We hope you enjoy the web-sites recommended by our Quindaro Staff in the Math Resources Folder.
THE IMPORTANCE OF MATHEMATICS
It is with some disbelief that I stand here and prepare to address this gathering on the
subject of the importance of mathematics. For a start, it is an extraordinary honour to
be invited to give the keynote address at a millennium meeting in Paris. Secondly, giving
a lecture on the significance of mathematics demands wisdom, judgment and maturity,
and there are many mathematicians far better endowed than I am with these qualities,
including several in this audience. I hope therefore that you will understand that my
thoughts are not fully formed: if I had been asked to speak on this subject five years ago,
I would have given a completely different lecture, and I am con dent that in ve years'
time it would again have changed.
My title (which I did not actually choose myself, though I willingly agreed to it) also
places on me a great burden of responsibility. After all, I am speaking to an audience which
contains not just mathematicians but journalists and other inertial non-mathematicians.
If I fail to convince you that mathematics is important and worthwhile, I will be letting
down the mathematical community, and also letting down Mr Clay, whose generosity has
made this event possible and is benefiting mathematics in many other ways as well.
Unfortunately, if one surveys in a superficial way the vast activity of mathematicians
around the world, it is easy to come away with the impression that mathematics is
not
actually all that important. The percentage of the world's population, or even of the
world's university-educated population, who could accurately state a single mathematical
theorem proved in the last fifty years, is small, and smaller still if Fermat's last theorem is
excluded. If you ask a mathematician to explain what he or she works on, you will usually
be met with a sheepish grin and told that it is not possible to do so in a short time. If
you ask whether this mysteriously complicated work has practical applications (and we all
get asked this from time to time), then there are various typical responses, none of them
immediately impressive.
Games Mathematicians Play
The word "game" appears to be very ancient. It is a descendent of the Old High Gothic word "gomen", which means fellowship, and is thus related to gamble, gambol, and hence to gambit. It looks sort of like the Greek word "agon" (the ancestor of "agony": the Greeks took competition VERY seriously), and rather like the Sanskrit word "gam", which seems to refer more to large assemblies of people, animals, gods, etc., and hence to ... counting. My guess is that "game" is an Indo-European word. This raises the question of where the Arabic word "layba" came from: perhaps it is African (the Ethiopians, i.e., the Abyssinians, were in invasion mode way back when).
Language can tell us something about how people look at notions. The Romans were more decadent than the Greeks, and the Latin word "ludus" is more fun-oriented than "agon" (and more decadence-oriented than "gomen"). I have no idea where the Romans got "ludus", but it does live on, e.g., on the `play on words', i.e., "joke". Speaking of "play", the Greeks did not think much of it (from "paidos", or child, we get "paizo", or play, apparently not anything so serious as games). The Romans used the word "ludere"??, and the Arabs "yalayb": perhaps they knew something we don't.
It is not clear when mathematicians got interested in games. They probably always were, but there was a problem. Mathematics is serious and it is improper to approach such matters with an inappropriate levity. Fortunately, greed will find a way.
The classical tale of the origin of probability is that the Chevalier de Mere, a jaded roue, wanted to know how to adjucate a game. He went to M. Mersenne, who maintained a sort of pre-electronic newsgroup, and he passed the problem on to two amateurs, a customs official (Fermat) and a theologian (Pascal). For a no doubt accurate account of this tale, click here. Anyway, since then, dice, cards, and other such devices have found their way into studying a subject whose real objects of study were physics and finance.
(Here is an unpleasant truth behind this tale of innocent sin. During the High Middle Ages, when Europeans started getting filthy rich again, they discovered The Love of Money (see I Timothy 6:10). During the Renaissance --- the Late High Middle Ages --- Europeans went out on sea voyages to trade in nutmeg, gold, pepper, porcelain, sugar, human flesh, and so on. The profit margins were up to 1000 %, but the there were risks, like storms and pirates.
(This led to two inventions. One was insurance, which is an obvious application of probability. The other was an updated version of International Law, that said that when a privateer from one country pirated the cargo of a ship of another country, the lawyers should battle the matter out in a neutral prize court. Those cynical lawyers were soon interested in things like the odds of winning. The connection between probability and law still stands: S. D. Poisson wrote a book on the probabilities of correct decisions in criminal cases: it is a commentary on our state of denial that after two centuries, this book by a major mathematician has yet to be translated into English.
Language can tell us something about how people look at notions. The Romans were more decadent than the Greeks, and the Latin word "ludus" is more fun-oriented than "agon" (and more decadence-oriented than "gomen"). I have no idea where the Romans got "ludus", but it does live on, e.g., on the `play on words', i.e., "joke". Speaking of "play", the Greeks did not think much of it (from "paidos", or child, we get "paizo", or play, apparently not anything so serious as games). The Romans used the word "ludere"??, and the Arabs "yalayb": perhaps they knew something we don't.
It is not clear when mathematicians got interested in games. They probably always were, but there was a problem. Mathematics is serious and it is improper to approach such matters with an inappropriate levity. Fortunately, greed will find a way.
The classical tale of the origin of probability is that the Chevalier de Mere, a jaded roue, wanted to know how to adjucate a game. He went to M. Mersenne, who maintained a sort of pre-electronic newsgroup, and he passed the problem on to two amateurs, a customs official (Fermat) and a theologian (Pascal). For a no doubt accurate account of this tale, click here. Anyway, since then, dice, cards, and other such devices have found their way into studying a subject whose real objects of study were physics and finance.
(Here is an unpleasant truth behind this tale of innocent sin. During the High Middle Ages, when Europeans started getting filthy rich again, they discovered The Love of Money (see I Timothy 6:10). During the Renaissance --- the Late High Middle Ages --- Europeans went out on sea voyages to trade in nutmeg, gold, pepper, porcelain, sugar, human flesh, and so on. The profit margins were up to 1000 %, but the there were risks, like storms and pirates.
(This led to two inventions. One was insurance, which is an obvious application of probability. The other was an updated version of International Law, that said that when a privateer from one country pirated the cargo of a ship of another country, the lawyers should battle the matter out in a neutral prize court. Those cynical lawyers were soon interested in things like the odds of winning. The connection between probability and law still stands: S. D. Poisson wrote a book on the probabilities of correct decisions in criminal cases: it is a commentary on our state of denial that after two centuries, this book by a major mathematician has yet to be translated into English.
What Do We Mean by Mathematical Proof?
What is a mathematical proof? This question, and variations on it, have been debated for some time, and many answers have been proposed. One variation of this question is the title of this article: \What do
we mean by mathematical proof?" Here we may stand for the international community of mathematicians, a classroom of students, the human race as a whole, or any number of other mathematical communities. When the question is phrased this way, it becomes clear that any answer to this question must, in one way or another, take into account the fact that mathematics and mathematical proof are endeavors undertaken by people, either individually or communally.
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