In PERSON STAUDT-Prize

The " superbrain" is not easy to find. He resides in a historical Don Zagier building in the middle of the pedestrian zone in downtown Bonn, Don Zagier the MAX PLANCK INSTITUTE OF . The building was formerly the main post office in Bonn, and imposing old he shelves in Don Zagier´s bright Roman ruins stand across from it. Despite the cold weather in the middle of April, a cafe around Toffice bend under the weight of books and manuscripts. The table the corner has already set up tables outside. But who is this "Bonn superbrain"? It’s actually the can hardly be recognised as such, PROF. DON ZAGIER, who, along with other luminaries like Gerd Faltings, Günter buried under mountains of paper, and even the chairs are covered with Harder and Yuri Manin, is one of four directors of the Institute in Bonn. The "superbrain" title manuscripts. In Zagier’s bookcase, there are works on "Elliptic Curves" was invented by the "Kölner Express" newspaper, which recently did a portrait of Don Zagier. and "Modular Functions," as well as binders labelled "Ramanujan Prob- lems." But with many of the books, it’s impossible to tell what they’re about: the spines feature Cyrillic and Japanese characters. A relatively pulls a small paperback from the bookcases. It *is* obvious, however, mechanics and conformal field slim book, one of the easiest to deci- pocket of his sports jacket: nothing from the countless notes crammed theory." Zagier talks fast when he pher, is entitled "De laatste Stelling but Japanese characters. "‘Wild with scribbles on his desk. "That’s is enthusiastic about a topic. van Fermat." Oh, that’s right, that Sheep Hunt’ by Haruki Murakami, how I work," says Zagier. "Many of Now then, one thing at a time. was also in the "Express" article: Za- very nice, practically a thriller, but my colleagues can set up large theo- Modular functions are mathematical gier speaks nine languages fluently with lots of social commentary. I can rems in their heads and think them objects which also played a crucial and can understand even more. He really recommend it," says Zagier. through. In contrast, I always have role in the long sought-after proof of finished high school at age 13, his Then he points to a number of hand- to calculate on paper. I spend entire Fermat’s Last Theorem. As a result, undergraduate education at 16, his written notes in the book: "Of afternoons filling reams of paper these functions are one of the few Ph.D. at 19 and his Habilitation, the course, I can’t yet read it fluently, I with calculations and thoughts. This achievements of truly “esoteric” German qualification to teach as a still have to look up lots of words." can easily mean 100 sheets of paper mathematics to gain a certain professor, at age 23. In other words, Where does this love of foreign in one afternoon. Only then can I see amount of public attention – not the he is a kind of Wunderkind whose languages come from? "Perhaps it’s if an idea was good or not.” least of which through Simon greatest passion is mathematics. because my parents and I moved Singh’s famous Fermat book, which GROUND-BREAKING WORK "The language thing is somewhat around so much," explains Zagier. was long on the non-fiction best- IN exaggerated," says Zagier. "Of course "My father held five citizenships seller lists. Zagier can also be con- I speak German and English, as well over the course of his life. As far as Good ideas: Zagier has already had sidered to move in the realm of Fer- as French and Dutch, because I’ve I know that’s a record." Zagier grins plenty of those. His field is number mat mathematics. And successfully: lived and worked in America, Hol- again. He himself was born in Hei- theory, his tools the clever handling in May of this year, he received the land and Switzerland. I can under- delberg and grew up in America. of elliptic and modular functions, es- 120,000-DM Karl Georg Christian stand Russian and Italian quite well. The fact that Don Zagier is a pecially Jacobi forms. These are in von Staudt Prize for his pioneering

That’s it really. But languages inter- LBUS mathematician is not necessarily ob- principal something between elliptic work in number theory – just one of est me. For instance, on my under- A vious from the large computer, a Sun and modular functions, "which also Don Zagier’s many awards. UTH

ground commute, I’m reading a : R workstation, sitting under his desk, play an important role in physics, for What exactly is his work about? HOTOS

Japanese novel right now.” Zagier P nor from the many books in his instance in string theory, statistical Zagier picks up a pencil and ex-

THE STAUDT-PRIZE On May 11, 2001, in the atrium of establishment of a visiting professorship with a two-year rotation. distinguished himself with work in the field of applied mathematics. prizewinners up to now. Hans Grauert was honoured in 1991 for the Erlangen Castle, the mathematician and Director of the Max As chair of the mathematics department in Erlangen from 1921 to Through his calculations of orbits of planets and comets, for instance, his groundbreaking work in complex analysis. Stefan Hildebrandt Planck Institute of Mathematics in Bonn, Don Zagier, was awarded 1953, Otto Haupt was one of the successors to Christian von Staudt. he quickly earned the respect of his colleagues. Von Staudt’s main followed in 1994, for his overall scientific work in the calculus of the 120,000-DM von Staudt Prize. This renowned distinction for out- He died in 1988 at the age of 101, and left the Endowment a scientific work is Die Geometrie der Lage (The Geometry of Position), variations, the theory of non-linear partial differential equations and standing German who have distinguished themselves considerable fortune. which he published in 1847, twelve years after being named to the first the theory of minimal surfaces. In 1997, the Otto and Edith Haupt through pioneering work in the field of theoretical mathematics is Born the son of an aristocrat in Rothenburg ob der Tauber, von tenured professorship of the Mathematics Department in Erlangen. Endowment awarded the prize to Martin Kneser for his contributions named after Karl Georg Christian von Staudt, who chaired the math- Staudt gave important impetus to mathematics, especially geometry, This work heralded the real start of his academic career at the age of 37. to the theory of quadratic forms and the arithmetic of algebraic groups. ematics department at the University of Erlangen from 1835 until his that continues to have an effect today. He studied with the famous With The Geometry of Position, Christian von Staudt became one of the Don Zagier received the prize for his pioneering work in number theory, death in 1867. The prize is sponsored by the Otto and Edith Haupt mathematician Karl Friedrich Gauss in Göttingen and, after his PhD in pioneers in modern non-Euclidean geometry, the tool that Albert Ein- which solves old and new problems using methods from a variety of Endowment, which was founded in 1986 and also has as its goals the 1822 in Erlangen, initially worked as a secondary school teacher at stein later used in the creation of his theory of relativity. The von mathematical disciplines and which has significantly influenced the promotion of scientific work at the Mathematical Institute and the Gymnasien in Würzburg and Nürnberg. As Gauss’ student, he already Staudt Prize is awarded every three years. There have been only four development of number theory in the past years.

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plains. “Let’s take this simple ques- using whole or fractional numbers is “Take the number 382. It looks Then has this seemingly simple tion: which numbers are sums of two actually one of the oldest problems completely harmless, but to express it task, which is even somewhat remi- cubes? For example, let’s consider mathematicians have studied and, at as the sum of two cubes, you need niscent of the Pythagorean Theorem, the number 35. the same time, still one of the most two fractions with a 52-digit denom- not yet been solved? “No,” replies modern ones. Already the Greeks inator, i.e. 8 122 054 393 485 793 Zagier. “And I don’t expect this Gor- 35 = 27 + 8 = 3×3×3 + 2×2×2 pondered over it, starting with Dio- 893 167 719 500 929 060 093 151 dian knot will be cut in my lifetime. = 33 + 23. phantus, who succeeded in formulat- 854 013 194 574. The numerators are But from the fact that I was able to ing algebraic equations using simple even larger. For this calculation, even present you with a solution for the That was easy. The number 7 is a systematic symbolism, about 1700 today’s fastest computers would re- number 382, you can see that we bit trickier: years ago. These are hard questions: quire orders of magnitude longer mathematicians have understood at Excursions into fascinating questions of “pure” mathematics: here computers fail. Diophantus’s work was lost for cen- than the lifetime of the universe. least something.” 7 = 8 + (-1) = 2×2×2 + (-1)×(-1)×(-1) turies, yet when it was rediscovered The key to the solution lies in a BAFFLING QUESTIONS = 23 + (-1)3. more than 1200 years after his completely different field of mathe- into cubes? Now things are getting conjectured for decades but was fi- THAT ARE A LOT OF FUN death, it was still far ahead of its matics, and Don Zagier is among more mathematical, but the connec- nally established only recently by As you can see, negative numbers time. Of course today we’ve pro- Gradually one begins to realise those who have helped to develop it tion is easily stated: Diophantine Andrew Wiles, the "conqueror" of are also allowed. But now consider gressed further, but the problems of why Zagier is fascinated by this recently. Here too lies the connection equations like x3 + y3 = 13 can be Fermat's Last Theorem – and exactly the number 13: Diophantine analysis are among the seemingly simple question. Why is it to Fermat’s famous problem, and it parametrised with elliptic functions. this proof was the key to his solution hardest and most fascinating ques- so easy for the number 7, and so is here that the elliptic, modular and Simply put, this means they can be of that millennium problem. This re- 13 = 351/27 = 343/27 + 8/27 tions of “pure” mathematics. hard for the number 382? And why Jacobi functions, with which Zagier “traced out” by such functions. The sult gave an important bridge be- = (7×7×7)/(3×3×3) + (2×2×2)/(3×3×3) Couldn’t the solution to Diophan- is there no solution at all for other is so familiar, come into play. following simple example will illus- tween two apparently distant fields = (7/3)3 + (2/3)3." tine equations like the one discussed numbers, like 5? Why do numbers What kind of exotic functions are trate this more clearly. The equation of mathematics. Now number theo- above be found by computer? “No,” behave like this? Zagier says, “The these? In essence, they are those fea- x2 + y2 = 1, as we know, describes a rists confronted with intractable Zagier briefly stops writing. “With says Zagier. “First of all, such a selection of the problems one deals turing not only a simple periodicity circle. But a point that moves Diophantine equations like Zagier's this example, you can see that we’ve ‘brute force’ approach would no with is an art. Just as musicians in one direction, like the functions through a co-ordinate system with can try to use modular functions to made the question a bit more inter- longer be true mathematics, because compose a melody from the in prin- sin(x) and cos(x), but are periodic in the co-ordinates x = sin(t) and y = get results about the puzzles facing esting for ourselves. We’re not limit- although we could perhaps find out ciple endless number of possible a variety of directions. While cos(t) also moves with increasing t them, and this often leads to success, ed to whole numbers; fractions of which numbers could be decom- melodies, we mathematicians also trigonometric functions like sine and along a “circular path” – identical to since a lot is known about modular whole numbers are also allowed in posed, we still wouldn’t know ac- choose, from the infinite number of cosine have a simple periodicity (e.g. that described by the circle equation. functions. the solution. But despite this conces- cording to what rule this occurred. open questions, those from which we sin (t+2π) = sin (t) for all t), elliptic This is in the same way that the su- SOLID BRIDGES sion, decomposing the number 13 is And in any case, computers would can learn something. It’s often not functions have a very simple kind of perimposing of two sine waves from FOR MATHEMATICIANS still not so simple. And some num- be completely overtaxed in such a until the second look that one realis- double periodicity: they fulfil the the x and y input terminals of an os- bers cannot be decomposed this way search.” es what’s really behind a certain equations f(x+A) = f(x) and f(x+B) = cilloscope results in circles and el- Can Don Zagier explain more ex- at all.” question, or how it can help us get f(x) for two independent numbers A lipses on the display. In other words, actly how one reaches the solution The question of how to find solu- further. Then it’s a lot of fun. This is and B. One can picture a chequer- the equation of a circle can be para- to the previously-described puzzle tions of an indeterminate equation such a problem.” board pattern as an especially simple metrised with trigonometric func- about numbers, using such modular elliptic function that assumes only tions. functions? “Unfortunately, you’d two values: black or white. Exactly the same thing happens have to study mathematics for five Finally, the modular functions also with the Diophantine equations we years beforehand,” replies the math- Fig. 1: Trigonometric functions have a “simple” periodicity – like the band below. In contrast, the tiled pattern of have a periodicity (or symmetry) in are considering and elliptic func- ematician, but you can see that he’d fishes and boats (left) is periodic in two directions, like two or more directions, but now tions. This was known already in the love to explain it anyway. Zagier re- an elliptic function. Finally, modular functions feature these different symmetries have a mid-19th century. Far newer and far turns to the pad of paper, draws a an even more complex symmetry – like the arrangement complicated interrelationship: they deeper is the realisation that these few curves, and says: “In the 1960´s, of angels and devils, for example (right). Despite their do not “commute,” as mathemati- same equations can also be para- the two English mathematicians complexity, a lot is known today about modular functions. And since the successful proof of Fermat’s famous Last cians say (Fig. 1). metrised by modular functions, with Birch and Swinnerton-Dyer pro- Theorem a few years ago, they may become the key to im- And what does this have to do their much more complex symme- posed a conjecture, now named after portant mathematical puzzles in the realm of number theory. with the problem of decomposition tries. That this is possible had been them, which in the meantime has be-

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L(s)

No zero:

No solution The mathematics behind this is For the number 6, on the other hand, higher-order zero, things are no s less abstract than one might think. A there is a zero at this position in the longer so certain. This means that it 1 small sheet of paper is enough to ex- table (6 = (17/21)3 + (37/21)3), and may be possible to decompose the plain what it’s about (Fig. 2). Assign- for the number 7 as well – and for number, but we don’t know whether ing one number to another can be the number 382, with its gigantic this has to be. L(s) achieved, for instance, with the help fractional cubic factors. This already However, “until now, we’ve always of functions, as we already learned brings the number theorists a long found solutions for numbers whose L Simple zero: in school. Zagier draws one of these way. And Zagier also has a partial functions indicate a possible solu- There is always on the blackboard in the lecture hall solution for the problem of actually tion,” says Zagier. Despite any aver- a solution at the Institute, a room which, many finding the complicated cubes into sion to “brute force computer mathe- “Mathematics is sometimes more of an art than a hard science.” decades ago, used to house 400 tele- which such numbers, once “exposed” matics,” this is a strong indication 1 s phone operators connecting callers. in this manner, can be decomposed. that the BSD Conjecture probably “Here is a function L(s). For every It involves so-called Heegner points holds. The mathematician from Bonn which hides yet another problem proached it, how I exactly wrote out Diophantine equation, such as the and formulas likewise over half a says, “It is actually an interesting which is fun to work on, because it the chain of proof step by step. equation x3 + y3 = 13 previously page long and relatively complex, irony of nature that numbers with feels as if it should have a solution Many of the steps I wouldn’t even discussed, such a function can be but it works. There are already a higher-order zeros in their L func- from which one can learn more mention today. Of course, my stu- Higher-order zero: L(s) constructed. If L(s) does not vanish handful of computer programs based tions can be decomposed especially about the crazy behaviour of num- dents sometimes suffer a little bit be- The existence of a at the point s = 1, then the corre- on these formulas that, within frac- easily. One example is the number bers and the astounding complexity cause of this,” says Zagier. solution is suspected, sponding equation has no solution, tions of a second, can calculate the 657. The L function corresponding to behind it. WHERE DO ALL THESE but not certain and the corresponding number can- cubic factors of such a number that this number has a second-order ze- With such demanding calculations GOOD IDEAS COME FROM? not be expressed as the sum of two has been identified as decomposable, ro.” Zagier starts a small program and arguments and such a complex s cube numbers.” This has already like the previously seen fraction with and types in the number 657. Within proof, how do you know you’re on So it’s really nothing but sweat 1 been proven by the Fermat pioneers the 52-digit denominator. a few fractions of a second, the the right path? How do you come up and tears? “Of course, one has flash- Fig. 2: The L function indicates whether or not the Coates, Wiles and Kolyvagin. Don monitor is filled with results, none of with good ideas? Or better: how do es of inspiration from time to time, “INTERESTING IRONY equation x3+y3 = n can be solved. Every n has its own Zagier and his American colleague which has 52 digits. Here are just good ideas find you? Do they pop but it actually works much different- OF NATURE” L function. If it has a simple zero at s=1, the corres- provided the coun- two of them: into your head in the shower? At ly,” says Zagier. “If I notice, for in- ponding Diophantine equation can be solved. The proof terpart, so to speak: the proof that Zero or non-zero: shouldn’t every- your desk? In the subway? Are they stance, that an idea is leading to- of this statement is 96 densely printed pages long 3 3 and uses modular functions. the number n corresponding to L(s) thing then be clear? No, not neces- 657 = (17/2) + (7/2) and just there in the morning? “No,” ward a dead end, I still continue with can be decomposed if the graph of sarily. The fact that the Birch-Swin- 657 = (163/19)3 + (56/19)3 replies Zagier, “they’re the result of it for a while. Later I can then recog- the function L crosses the s-axis, i.e. nerton-Dyer Conjecture has not yet hard work.” nise where the problem was, and come one of the most famous un- the L function has a finite slope at s been completely proven has to do “This means that in exactly those “I myself always need concrete work around it the next time. This is solved problems in mathematics. In = 1. The proof is 96 densely printed with the definition of “zero.” And cases that are difficult for us, it’s starting points for my work, often how I gradually work my way to- fact, it’s one of the seven mathemat- pages long; the central formula in the problem is so complex that it very easy for the computer. You see, problems other colleagues have wards the solution. And at some ical problems for whose solution the this proof, which also happens to be may prolong the race for the solu- we know that whenever there is one brought me, for instance. That’s why point in time, you notice that the American Landon Clay has offered the longest one, runs over half a tion to the cubic decomposition puz- possibility of decomposing the num- I have so many joint publications. In connections are becoming clearer, prizes of one million dollars each. page. zle for quite some time. The problem ber, there must automatically exist this way, I’ve gained a lot of experi- that you’re on the right path. And This conjecture implies that with the With the L function, number theo- is the following: “zero of the L func- an infinite number of additional so- ence over the course of my years as then suddenly, everything is just sit- help of modular function theory, to rists can now set up a table; every tion” can mean a simple intersection lutions. In other words, there are ei- a mathematician. When you work a ting right there in front of you. every natural number n one can, whole number n (in the case of the with the s-axis (finite slope) or a ther no solutions or an infinite num- lot, you also have a lot of successes Things become simple when you get with a simple calculation, assign an- equation x3 + y3 = n) is assigned its higher-order zero (tangent, saddle ber of them. But if the L function and insights that you can use in close to the solution. Of two poten- other number with the following function L(s), made possible by the point). “Up to now, we’ve only been vanishes multiply at its zero, e.g. at a solving new problems. And at some tial solutions, the simpler one is of- property: if this number is equal to bridge between modular function able to prove the Birch-Swinnerton- saddle point, then the BSD conjec- point you simply see things. For ex- ten the better one. It’s often an aes- 0, the number n can be decomposed theory and number theory. If the Dyer (BSD) Conjecture for the case of ture predicts an “even bigger” infini- ample, I recently ran across an old thetic question. In this sense, mathe- into two cube numbers. If it is not value of the function at s = 1 is not a simple intersection with the s-ax- ty of solutions, with plenty of small letter of mine in which I helped a matics is really more an art than a equal to 0, the number n cannot be zero, as happens, say, for n = 5, then is,” says Zagier. In other words, if the ones,” says Zagier. Not much conso- colleague with a proof. Today I’m hard science. But the search can last decomposed into cube numbers.” n cannot be decomposed into cubes. L function has a tangent point or lation, perhaps, but one behind surprised at how naively I ap- for years.” ❿

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spectacular than when reading it in well, so that I had to catch up a lot. the headlines. Don Zagier was in fact Later I changed Ph.D. advisors and INSTITUTES a bad student initially. As with many came to Bonn” – to Friedrich Hirze- gifted persons, he found no stimulus bruch, the brilliant mathematician in the schoolwork. One day, his and founding director of the Max OBITUARY Franz Emanuel Weinert teachers suggested he skip a grade – Planck Institute of Mathematics in at that time in America an absolute Bonn. Here he received his Habilita- Prof. Franz Emanuel Weinert, Emeritus The text of the eulogy by Hubert Markl, President of exception to the rule. Zagier says, tion at the age of 23, was named Scientific Member and former Director the Max Planck Society, is reproduced below in memory “My parents let me decide for my- professor at age 24 and, when his of the Max Planck Institute for Psy- of Franz Emanuel Weinert: chological Research in Munich, died self, and I said yes.” And it helped: mentor went into retirement, suc- At home in the world of numbers: Professor Don Zagier suddenly on 7 March at the age of 70. wish I hadn’t had to experience this; not as someone he began to enjoy classes again, and ceeded him as Executive Director of in front of the new Institute building in downtown Bonn. He was internationally recognised as a “Iwho enjoyed a warm, close relationship with Franz at some point in time, skipping the Max Planck Institute of Mathe- leading researcher in the fields of de- Emanuel Weinert for many years; not as President of the grades became a kind of sport for matics. velopmental psychology and the psy- Max Planck Society in which he was active for 20 years and And in these years, almost every- him. “I wanted to see how far I could An impressive career. And yet: it chology of learning. Weinert was also achieved so much. thing with Zagier revolves around go with it. But I they didn’t make it only takes one look in Zagier’s of- involved in scientific administration It seems only yesterday that, on 22 September 1998, on the mathematics. Night and day, it’s tru- easy; not only did I have to pass all fice, at the bookcases and the piles of and was a member of the Senate of the occasion of his retirement, we thanked him for all he had done and ly his vocation. In the evenings after the exams, but I also had to take all densely-lined pagespages of notes, Max Planck Society for 15 years. He also wished him a long and happy future alongside his dear wife, now that he work, for instance, he enjoys dis- the mandatory courses, even those to recognise that this brilliant cur- served as Vice President of the Max Planck was finally relieved of his many duties. Former President Horst cussing theorems like Euler’s famous from the years I skipped.” Did he riculum vitae is perhaps not really so Society between 1990 and 1999. Fuhrmann, the trusty leader of the Bavarian Academy of Sciences and formula have to miss out on something then? important. It’s true that Zagier also Weinert was appointed Scientific Member of Humanities, even warmly invited this member who had been so promi- the Max Planck Institute for Social Sciences nent in the Academy since 1984 but to continue to play an active role 1 + 1/4 + 1/9 + 1/16 + ... = π2/6 “No, I led a completely normal life,” lectured in Utrecht and Bonn from in 1980 and, from 1981, was founding direc- nunquam otiosus, that is to the best of his ability. Now, so soon after- with friends, the way other people replies Zagier. “I had a girlfriend, I 1990 to 2001, and starting in May tor of the Max Planck Institute for Psycho- wards, a cruel fate has called him to eternal rest. talk about new movies. Or an old went ice skating. OK, maybe I didn’t 2001 will work part-time as a profes- logical Research in Munich, which, with the Death, although the most natural event in the world – the inescapable theorem by Fermat, which predicts always get enough sleep. But I did sor at the renowned Collège de help of his colleagues and staff, he developed future for all living things – is also the most dreadful demand which life which prime numbers can be decom- have the support of my fellow stu- . He has been, and still is, on into an internationally respected research has in store for each of us; a severing of unimaginable finality, which posed into two square numbers. dents. That helped a lot.” the road a lot. But listening to Zagier establishment. He taught at the Universities tears apart all that was joined together for so long. It is the one certain- There are now enough proofs of this talk about his work and about the of (from 1981) and Munich (from ty in every life and yet a truth, which can be endured painfully but only UNIVERSITY DEGREE theorem to fill a whole book, but Za- “enjoyment that a new task has to 1983) as honorary professor. He was also Vice accepted through the irresistible force of fate. IN TWO YEARS – gier’s is the shortest so far. Zagier bring,” one realises that, after he and President of the Deutsche Forschungsgemein- So closely was he often linked with the factors which determined my life DUE TO HOMESICKNESS says as a mathematician, it’s impor- his family were on the move so of- schaft between 1980 and 1986 and President that, with the death of Franz Emanuel Weinert, I feel as if part of my tant not to pore exclusively over big And what about college studies – a ten, he has finally arrived. And per- of the German Psychological Society (1984- own life over the last few decades has passed away. Above all, however, 1986). Following the reunification of Ger- his death leaves me with the disturbing feeling of a great loss which I do theorems, but also to occupy oneself university degree by the age of 16? haps even that he has always been at many, in his capacity as Vice President of the not know how to reconcile. I had the privilege of working with him twice with smaller problems, so to speak as “I was in a hurry,” answers Zagier. home, regardless of where he was, Max Planck Presidential Commission on “Cen- over the course of many years: first, when we were joint Vice Presidents recreation. After all, even Mozart “My parents moved to Switzerland whether in America, Oxford, tres for the Humanities”, Weinert played an of the Deutsche Forschungsgemeinschaft and then as he stood by me, didn’t constantly write great music, just as I finished high school. So I Switzerland or Bonn – because his influential role in shaping and developing the once again as Vice President, offering practical and moral support in the but also toyed with little pieces – returned to MIT in Cambridge, Mass- heart belongs to mathematics. And humanities and social sciences in the new early years of my presidency of the Max Planck Society. Those who expe- and possibly gathered inspiration for achusetts, and rushed through – be- then one leaves Zagier’s office with federal states. rienced working with him could not fail to admire how this man com- his important works. cause I missed my family.” His Ph.D. the feeling that even should he not Weinert’s scientific work focussed on cogni- bined tireless hard work, scientific curiosity, an excellent way with words, So not an overachiever after all? studies at Oxford – at age 19, finally succeed in finding the final solution tive development, especially differences in clear-headed rationality, an unerring sense of quality, wise powers of Graduated from high school at age in Europe, finally near his parents for his cubical decompostion prob- individual intelligence, motivation and per- judgement, uncompromising honesty, modesty and unblemished up- 13, the youngest professor in Ger- again – lasted a relatively normal lem, he will surely have a lot of fun sonality occurring during the course of a per- rightness with a deep humanity, only given to those who know human son’s life. He also concerned himself with the nature and perhaps love their fellow man precisely because they have no many at age 24? Not a genius? “No, three years. Zagier explains, “In the trying. STEFAN ALBUS links between regular events in cognitive de- misconceptions on that score. definitely not.” Don Zagier grins first year, I got practically nothing velopment, mechanisms of learning and op- One may perhaps wish to regard these as the many qualities of the top again and doesn’t seem embarrassed done. I had carried out my university portunities for improving teaching. In 1998, specialist in scientific psychology and educational theory, the expert in at all. And when he tells his life sto- studies a little too quickly, and the the Arthur Burkhardt Foundation for the understanding his fellow man and in leadership. But anyone who has ry himself, it seems considerably less material hadn’t really sunk in so

ILSER Advancement of Science within the Donors’ met enough psychologists and educationalists knows that it was not just F Association for the Promoting of Sciences professionalism of the highest level which Franz Emanuel Weinert em-

OLFGANG and Humanities in awarded Weinert bodied, it was above all the man Weinert who combined supreme ability

: W the “Arthur Burkhardt Prize” in recognition in the area of his wide-ranging scientific interests with the outstanding HOTO

P of this work. gifts of an honourable character, such as is only found in a few people who set an example and, in so doing, are most able to help and enrich us all. ❿

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