Carl ludwig siegel biography channel

Carl Siegel's father worked for the publicize office. Siegel entered the University of Berlin market , in the midst of World War Crazed, and attended lectures by Frobenius and Planck. Siegel wrote [15]:-

By conducting [beginners' classes] personally goodness professors could see, after only a few lectures, which of the students were the more brilliant by the work they handed in, and excellence professors could direct their work accordingly. This was the way I myself first came into friend with my teachers Frobenius and Planck

First his intention had been to study astronomy, however Frobenius's influence took him towards number theory which would became the main research topic of climax career. In , however, he had to exact his studies when he was called for personnel service. Most certainly military life did not provide with Siegel and he was eventually discharged from nobleness army as one of their failures, for notwithstanding their best efforts they had failed to be born with him adapt to army life. One would fake to believe that Siegel would have classed that as a success rather than a failure.

After the war had ended, Siegel continued surmount studies at Göttingen, beginning in His doctoral allocution at Göttingen was supervised by Edmund Landau nearby Siegel then continued to study for his habilitation. His dissertation, written in , [1]:-

was a landmark in the history of Diophantine approximations.

It extended an idea first noted by Liouville, then pushed forward by Thue who proved think about it, given a rational number r and any e>0 there are only finitely many rational numbers qp​(in their lowest terms) such that

∣r−qp​∣ ≤ q2+1+e1​.

Siegel improved this by showing that there shape only finitely many rational numbers qp​ such turn this way if r is an algebraic number of status n

∣r−qp​∣≤qm1​, where m=2√n.

Schönflies had been appointed as fellow at the Johann-Wolfgang-Goethe-University of Frankfurt in , interpretation year in which the new university opened. Take action was aged 61 when he was appointed stand for when he retired in Siegel was appointed orangutan professor to succeed him at Frankfurt. Although Schönflies spent the six years of his retirement inconvenience Frankfurt, his days as an active mathematician were over by the time Siegel took up representation professorship. There were, however, several young mathematicians tenacity the staff at Frankfurt who would with Siegel create an excellent centre for mathematics.

Hellinger, love Schönflies, had been appointed as a professor shout approval the new university of Frankfurt when it unfasten in , and Szász had been appointed tempt a Privatdozent in the same year. Szász was promoted to professor in , Epstein was decreed in , and Dehn in It was clean strong and exciting department which Siegel joined note

There were a number of activities habitual which the four mathematicians Siegel, Hellinger, Epstein, stomach Dehn collaborated. One was the history of calculation seminar instigated by Dehn in Siegel wrote show [15]:-

As I look back now, those public hours in the seminar are some of birth happiest memories of my life. Even then Wild enjoyed the activity which brought us together range Thursday afternoon from four to six. And afterwards, when we had been scattered over the sphere, I learned through disillusioning experiences elsewhere what exceptional good fortune it is to have academic colleagues working unselfishly together without thought to personal enterprise, instead of just issuing directives from their towering positions.

The history of mathematics seminar was gain last for thirteen years. They made a mean that they would study all the mathematical activity in their original languages and although this summary the number of students who participated in character seminar, there was never less than six. They studied the works of mathematicians including Euclid, Physicist, Fibonacci, Cardan, Stevin, Viète, Kepler, Desargues, Descartes, Mathematician, Huygens, Barrow, and Gregory. The aim of primacy seminar was [5]:-

to increase the upheaval of the participating students for the results suave in lectures and to provide the teachers plus aesthetic satisfaction of examining the outstanding works lay into past times in close detail.

The history past its best mathematics seminar was not the only one which Siegel participated in at Frankfurt, for the professors organised also a proseminar and a seminar. Undergraduate numbers rapidly built up after Siegel was decreed. At first he taught only a few genre and [15]:-

I remember having only bend over in one of the advanced courses. One way in they were both late for class, having bent delayed at the university bursar. When they dismounted, they were shocked to find I had going on without them and had already filled a finalize section of the blackboard.

By Siegel was instruction students in the differential and integral calculus total, and had to put in many hours drain correcting students exercises. It was at this sicken that the student numbers reached a maximum, for that reason they began to drop again.

On 30 January Hitler came to power and on 7 April the Civil Service Law provided the register of removing Jewish teachers from the universities. That did not affect Siegel who was an Caucasian (to use the terminology of the time which Siegel hated) and, at this stage it frank not affect Epstein, Hellinger or Dehn who, notwithstanding Jewish, fell under a clause which exempted non-Aryans who had fought for Germany in World Clash I. Szász, however, was dismissed from his mail. Although Siegel was not affected by the Courteous Service Law, he hated the Nazi regime pivotal this was the beginning of a very injured time for him.

In Siegel spent put in order year at the Institute for Advanced Study main Princeton in the United States. He returned nurture Frankfurt to find that the problems of her highness Jewish colleagues had become much worse. After decisions at the Nuremberg party congress in the drop dead of , Epstein, Hellinger and Dehn were laboured from their posts. They remained in Frankfurt, no good to teach. In late Siegel accepted a office at Göttingen and he moved there in exactly At Göttingen he [15]:-

led a less retiring life.

Life in Göttingen was still stirred by the Nazi policies and mathematicians reacted slope different ways to the political pressures. For notes Hasse in Göttingen wanted to accept the habilitation thesis of his assistant, but Siegel and Herglotz felt that this was a political rather best mathematical decision by Hasse and stopped the habilitation being accepted.

The Nazi regime had expressionless Germany to war in and Siegel felt deviate he could no longer remain in his picking land. In early he left Germany, lecturing chief in Denmark and then in Norway. In Stride he met up with Dehn in Norway. Dehn had fled from Germany in fear of top life and was teaching in Trondheim when Siegel visited him. Siegel saw German merchant ships boast the harbour and only later, having left Norge for the United States, did he discover turn this way the ships he had seen were the highest party of the German invasion force.

Siegel described his time in the United States primate [15]:-

self imposed exile in America.

Smartness worked at the Institute for Advanced Study irate Princeton from until , being appointed to put in order permanent professorship there in However, in he joint to Germany and again worked at Göttingen select the rest of his career.

The arrangement [8] lists Siegel's impressive contributions to mathematics answerable to seven headings. These are:

1. Approximation of algebraical numbers by rationals and applications thereof to Diophantine equations.
2. Transcendence questions, in particular values adherent certain functions at algebraic points.
3. Zeta functions counting applications to class numbers.
4. Geometry of book and its applications to algebraic number theory.
5. Hardy-Littlewood method, including Waring-type problems for algebraic numbers.
6. Quadratic forms: analytic theory and modular forms.
7. Paradisaic mechanics.

Siegel is especially famed for top work on the theory of numbers where misstep held an eminent role. Schneider, who was clean up student of Siegel's, gave three lectures on Siegel's contributions to number theory to the German Precise Union in These are reproduced in [13] suffer describe Siegel's most important results in number knowledge. These include his improvement of Thue's theorem, stated doubtful above, given in his dissertation, and its request to certain polynomial Diophantine equations in two unknowns, proving an affine curve of genus at nadir 1 over a number field has only trim finite number of integral points in Perhaps ruler two part paper which appeared in is [1]:-

.. his deepest and most original.

In rank paper Siegel made a substantial contribution to accomplishment theory, especially a new method for the algebraical independence of values of certain E-functions. He firm that if J0 is the Bessel function have index 0, then for any non-zero algebraic figure r he showed that J0(r) is transcendental.

He had earlier than this in , unavoidable papers on the functional equation of Dedekind's zeta functions of algebraic number fields and in /23 made contributions to additive questions such as Waring type problems for algebraic number fields. He forced further contributions to this latter topic in Siegel's research on the analytic theory of quadratic forms in /37 was of fundamental importance and type broke new ground in considering quadratic forms affluent which the coefficients were from an algebraic count field.

Klingen, in [9], discusses Siegel's assistance to complex analysis. In particular he studied automorphic functions in several complex variables, Siegel's modular functions, which have led to a much deeper pardon. In this general area Siegel considered the timidly of discontinuous groups and their fundamental domains, algebraical relations between modular functions and between modular forms, and Fourier series of modular forms.

Siegel's work in celestial mechanics, which came next acquaintance number theory in his list of favourite topics, is discussed by Rüssmann in [12]. The bradawl lists eight major contributions which Siegel made sure of yourself the subject. He studied:

1. the n-body interrupt and the theorem of Bruns on algebraic integrals.
2. the restricted problem of three bodies forward their integrals, which used the results Siegel difficult proved in (i).
3. the orbit of honesty moon, again essentially a three-body problem. Siegel gave a much improved version of lunar theory chimpanzee developed by Hill.
4. the Lagrangian solutions hunger for the three-body problem. Siegel developed general methods be familiar with determine periodic orbits near the equilibrium points.
5. the problem of small divisors, where Siegel chief obtained convergence results.
6. Birkhoff normal forms. He examined Birkhoff's work on perturbation theory solutions for probing Hamiltonian differential equations near an equilibrium point motivating formal power series. Siegel gave examples of systems which did not possess convergent transformations into straight normal form.
7. contributions to stability theory.

An interesting episode, which tells us a outline about Siegel's approach to mathematics, occurred in high-mindedness s. Serge Lang published Diophantine geometry in prep added to Mordell wrote a critical review of it pair years later. Siegel then wrote to Mordell[11]:-

When I first saw [Lang's Diophantine geometry], about tidy year ago, I was disgusted with the clear up in which my own contributions to the thesis had been disfigured and made unintelligible. My labour is very well expressed when you mention Hold on van Winkle!

The whole style of honourableness author contradicts the sense for simplicity and artlessness which we admire in the works of representation masters in number theory - Lagrange, Gauss, knock back on a smaller scale, Hardy, Landau. Just having an important effect Lang has published another book on algebraic statistics which, in my opinion, is still worse escape the former one. I see a pig in poor health into a beautiful garden and rooting up able flowers and trees.

Unfortunately there are indefinite "fellow-travellers" who have already disgraced a large finish off of algebra and function theory; however, until say to, number theory had not been touched. These persons remind me of the impudent behaviour of dignity national socialists who sang: "Wir werden weiter marschieren, bis alles in Scherben zerfällt!'' Ⓣ

I solidify afraid that mathematics will perish before the keep happy of this century if the present trend care for senseless abstraction - as I call it: intention of the empty set - cannot be obstructed up.

Dieudonné, writes in [1]:-

Siegel, who not ever married, devoted his life to research.

But Dieudonné explains why he believes that Siegel had doctoral students:-

the perfection and thoroughness have possession of his papers did not leave much room resolution improvement with the same technique, [and this] deterred many research students because to do better get away from he required new methods. Siegel enjoyed teaching, dispel, even elementary courses, and he published textbooks reversion the theory of numbers, celestial mechanics, and leadership theory of functions of several complex variables.

Operate was awarded many honours, perhaps the most prominent of which was the Wolf Prize in