The Mathematics Genealogy Project

Mathematician John Allen Paulos writes abcNEWS-columns that discuss the use of mathematics in current events and everyday life.
Theme of this week: Calculating Doom.

QUAT - ein Programm zur Berechnung quaternionischer Fraktale
(Homepage von Dirk Meyer)

Das Clay Mathematics Institute (CMI) hat im Jahr 2000 sieben mathematische Probleme benannt. Löst man nur eine dieser Aufgaben, wird man von der Stiftung des amerikanischen Multimillionärs Landon T. Clay mit einer Million Dollar belohnt.
Bevor man anfängt nachzudenken, sollte man sich den Artikel Mathematics With a Moral zu Gemüte führen.
Robert Osserman hat sich angeschaut, wie das mit der Problemlösung zum Großen Fermatschen Satz war (Andrew Wiles) und wie der gegenwärtige Stand zum Beweis der Poincareschen Vermutung ist (Grigori Perelman).
Nicht ganz überraschend kommt dabei heraus: Bei der Lösung solcher Probleme muss man sich auf schwierige Umwege einstellen und die Million Dollar wird man schließlich teilen müssen.

The moral of the story? There are at least two. First, a curious fact of mathematical life: When faced with a problem that seems intractable, the best strategy is sometimes to formulate what appears to be an even harder problem. By expanding one's horizons, one may find an unanticipated route that leads to the goal.

Second, mathematicians are often thought of as working in isolation, and that is occasionally the case, as with Andrew Wiles and his solitary struggle to prove Fermat's Last Theorem. But usually mathematics is a highly social activity, with collaboration between two or more individuals the rule rather than the exception.

Passend zum letzten Eintrag:
Debunked! ESP, Telekinesis, Other Pseudoscience tells good stories about human foolishness masquerading as science.
(gesehen bei Ch. Köllerer)

The book ... has a good chapter on "Amazing Coincidences." These are strange events which appear to give evidence of supernatural influences operating in everyday life. They are not the result of deliberate fraud or trickery, but only of the laws of probability. The paradoxical feature of the laws of probability is that they make unlikely events happen unexpectedly often. A simple way to state the paradox is Littlewood's Law of Miracles. Littlewood was a famous mathematician who was teaching at Cambridge University when I was a student. Being a professional mathematician, he defined miracles precisely before stat-ing his law about them. He defined a miracle as an event that has special significance when it occurs, but oc-curs with a probability of one in a million. This definition agrees with our common-sense understanding of the word "miracle."
Littlewood's Law of Miracles states that in the course of any normal person's life, miracles happen at a rate of roughly one per month. The proof of the law is simple. During the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of about one per second. So the total number of events that happen to us is about thirty thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month. Broch tells stories of some amazing coincidences that happened to him and his friends, all of them easily explained as consequences of Littlewood's Law.