Johanneum Lüneburg	Dr. Dörte Haftendorn Teacher at the Johanneum
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	Chronicles    Riemann's Youth	deutsche Version

I held this lecture on Riemann again on the 24.06.97 at the Mathematical Faculty of Jena University.

Bernhard Riemann

one of the most important mathematicians

Bernhard Riemann (1826 - 1866), who is being called a genius not only in mathematical literature, but also for example in the Brockhaus Encyclopedia and in the internet, passed his Abitur exam 150 years ago at the Johanneum.
In a lecture held on the 20.09.96 because of the Johanneum's 590th anniversary Dr. Dörte Haftendorn has tried to honour Riemann both as a person and a mathema tician. A summarised version of the lecture (Johanneum intern No. 11, Dec. 96, Red. Frau Dr. Krämer) is available on this page. It is planned to extend this page to a more detailed document on Riemann. A first step is done with Riemann's Youth.

1. Childhood in the Hannover Wendland
2. Pupil at the Johanneum in Lüneburg Detailed pages on Riemann's school days
3. University in Berlin and Göttingen with Gauß
4. Important works
   1. Dissertation
   2. Habilitation
   3. Occupations as a Professor
   4. Further merits
5. Privat life
6. End of his life

Bernhard Riemann was born on the 17th September 1826 in Breselenz/Dannenberg where his father was a vicar. A photo was taken of his parents' house before it was broken down. Bernhard grew up with a brother and four sisters. His childhood can generally be called a happy one, they were but suffering from the family's poverty. Some of Riemann's biographers do see malnutrition during the childhood as the reason for his, his parents, and some of his siblings early death.
In 1833 they moved to a vicarage in Quickborn, a village close to Dannenberg in the Elbe lowlands. Until he was thirteen, Bernhard was taught at home by his father and a teacher called Schulz. In mathematics he did soon prove to surpass his teacher.
After his confirmation Easter 1840 he moved in with his grandmother in Hannover in order to visit a grammar school there. While he was troubled with great shyness at first, he made good progress very quickly.

After his grandmother had died in 1842, he went to Lüneburg and entered the Johanneum's Lower Secunda (Year 10). It is known that he used to live with one of the Johanneum's teachers, Dr. Seffer as a "pensionar for reduced food cost". To keep in touch with his family, he did occasionally walk 50 km to Quickborn.
The Johanneum's headmaster Dr. Karl Haage was an authorative educationalist, who managed to improve the quality of education immensely. A school inscpector from Hannover declared in 1829 that the Johanneum was not only the best school around Hannover, but also the best amongst all thirty schools he had visited as a Prussian school inspector. Bernhard Riemann did not only live at Dr. Seffer's house, but was also supported by him in his school work: He who would prove to be a brilliant thinker could hardly manage to hand in his essays in time: He "was always behind, [...] the teachers' conference was despaired because of the school rules."
After Haages sudden death in 1843, it was for the first and only time that with Friedrich Constantin Schmalfuß a mathematician became the Johanneum's headmaster. He did quickly manage to prove wrong all those doubting whether a mathematician would be suitable for this job. Which was good luck as well for mathematics as for Bernhard Riemann, for Schmalfuß estimated his talent correctly, and made books by contemporary mathematicians available to him. In a letter he wrote about his famous pupil Riemann later: "His grasp for mathematical issues was immediately clear to me, and only a hint of a mathematical law would be enough for Riemann to see it realised with all its consequences in its simplest form." Schmalfuß let Riemann participate in the normal maths lessons, but he "wanted to offer him something in every lesson, which was adequate to his abilities, and he has always surpassed that boundary that I saw as his but probably also as mine...".
The Abitur examination did almost extend the teacher's abilities: He examined Riemann in Legendre's number theory, and it turned out that: "everything which took me some effort to prepare for as an examiner, [...] was familiar to him." Bernhard Riemanns Maturitäts-Zeugniß erster Klasse ("Maturity Report First Class") does mainly list good grades - while yet again his slow (since he was always working too thouroughly) working style on essays was criticized. In both mathematics and physics he received the predicate excellent although "his time at school was interrupted several times by illnesses."

The teachers' recommendation that Riemann was "because of his abilities definitely suitable for the study of mathematical sciences" was not appreciated by his father. Bernhard had to start reading theology in Göttingen. He did also hear some mathematical lectures, and did finally manage to change his father's opinion.

In Göttingen Riemann did, amongst others hear Carl Friedrich Gauß's lecture on the method of the smallest squares. Since those few lectures that Gauß was reading at that time did not satisfy him, he moved to Berlin to hear, amongst others, Dirichlet.
Hardly anything is known from his personal life in Berlin. The 1848 Revolution is only mentioned in his letters as a fact. He did return to Göttingen in spring 1849 to hear the experimental physicist W. Weber . As a member of the educational institute, Riemann was occupied with nature philosophical questions. In November 1850 he stated his thoughts about a standardized mathematical-physical view on nature in an essay in which he demanded a "completely self-contained mathematical theory [...], which was leading from the elementary laws up to the actions in an actually given filled space, without making a difference between gravity, electricity, magnetism or the equilibrium of temperature". These thoughts are to be seen in a general mathematical-physical approach, which has, in the 19th century through J.Cl. Maxwell, H. v. Helmholtz and finally through H. Hertz in the 20th century lead to the attempt of a general field theory by Albert Einstein.

After years of thourough preparation Riemann was able to finish and publicly defend his dissertation "Foundation of a general function theory of one variable complex number" in December 1851. In this dissertation he introduces important notions such as the Riemann Area and the number sphere. The most important result of his thesis, which was also highly commended by Gauß, was the famous Riemann Projection Theorem. In 1853 Riemann became the assistent of W. Weber at the mathematical-physical institute.

His habilitation thesis from 1854 "About the description of a function by arbitrary functions" does not only contain the Fourier Series, without which elektronic music would be unthinkable, but also the Riemann Integral, without which no-one can pass their A-levels nowadays. Riemann's habilitation lecture in 1854 did contain some ideas, which should provide him a permanent place not only amongst mathematicians, but also amongst the leading advocates of a scientific world view. His research on the existence of reasons for the objective real measured proportions and his demand, to reorientate physical research into that direction, is being recognised as one of the most ingenious achievements of science of the 19th century. They did finally influence Albert Einstein's foundation of the General Theory of Relativity.
It seems understandable that, despite being well-prepared, Riemann did have some problems with holding lectures at first, after all he had no teaching experience whatsoever. For the first time he did now recieve an annual salary of 200 Taler. Meanwhile he was appreciated so widely, that he was admitted to the Göttingen Science Society as an assessor.

His life was hard: He had lost his mother at an early age. His father and one of his sisters died in 1855. His brother, living in Bremen as a post secretary, had to pay for the other three sisters since Riemann's salary as a private lecturer was not sufficient. His already poor health had suffered from the excessive mental effort, so that a longer holiday seemed inevitable. After he had returned, he did finally become a senior lecturer with an annual salary of 300 Taler. When his brother and another sister died in 1857, his two other sisters moved to Göttingen. An illness raging in his family was tuberculosis, which was what Riemann himself was to die of six years later.

After the death of Lejeune Dirichlets, Gauß' successor in Göttingen, Riemann did in 1859 recieve a call as a full professor on the chair that Gauß had occupied only four years ago. He was now rewarded with adequate recognition, and the Berlin Academy of Science voted for him as a corresponding member of the physical-mathematical class.
Sharing his thoughts with several famous mathematicians from Berlin resulted in his treatise "About the number of prime numbers smaller than a fixed value". His suspicions concerning the allocation of prime numbers have neither been proven nor disproven up to date. When the outstanding German mathematician David Hilbert was asked what he would enquire about first, should he be able to meet mathematicians 100 years after his death, he is supposed to have answered: "Whether the Riemann Hypothesis is proven." Riemann's works that were mentioned so far as well as other treatises did result in him being honoured be the Parisian Académie as well as the London Royal Society.

End of life

In 1862 Riemann appeared to be on the peak of his scientific career. In the same year he married Elise Koch, one of his sister's friends. But the happiness was not to last long: Riemann did suffer from pleurisy, which did not heal properly although he spent the winter in Messina with his wife. On their way back through Italy the couple visited the famous art treasures in Naples, Rome, Livorno, Florence, Bologna, and Milano. Riemann did also meet up with Italy's most famous scholars. He made friends with the mathematician E. Betti. While travelling over the Alps, he was yet again infected by a severe cold, which forced him to travel to Italy again in summer 1863. Italian friends of his arranged the offer for him to teach at Pisa University, but Riemann refused since he feared not to be able to hold lectures because of his illness. Although his state of health kept getting worse, he returned to Göttingen in autumn 1865. In winter he was able to work for a few hours every day. He finished his treatise on Theta Functions. Other studies could not be continued. Despite the war between Austria and Prussia, which made travelling difficult, Riemann went to Italy for the third time in June 1866. His state of health was declining rapidly, and just a few weeks after his arrival on the Lago Maggiore he died on the 20th of July 1866, being in full conciousness about his close death, and working on his mathematical problems until the last minute.

Final recognition of his merits

The number of works that have been published during Riemann's lifetime or after his death is relatively small. But they have in their reach and variety still supported modern mathematic's development in numerous ways. Mentioned here are just some headwords contained in the 1992 Brockhaus Encyclopedia: Riemannian Areas, Riemannian Number Sphere, Riemannian Mapping Theorem, Riemann Integral, Riemannian Zeta Function, Riemannian Hypothesis, Riemannian Geometry, Riemannian Space, Riemannian Curvature Tensor. Riemann's main characteristic being that he managed to work out an exact basis for many mathematical concepts which are still applicable today. In that he formed contemporary mathematic's and theoretical physic's style. In 1990 the Indian scientist Raghavan Narasimhan re-published Riemanns Collected Works in Chicago: This edition contains texts in German, Italian and Latin with English notes. The publishers are situated in Berlin, Heidelberg, New York, London, Paris und Tokyo. Mathematics is global!

I hope to have given you an idea of the person Bernhard Riemann, and to have imparted to you a presentiment of the depth of his mathematical thought, although his importance as a mathematician is mainly based upon abstract foundations, with no respect to intellegibility.

I do finally want his teachers to take the word. Dr. Seffer wrote in the last sentence of his letter: "I had and have always liked him." Headmaster Schmalfuß admits: "I have learnt more from him, than he from me." And in the end he writes: "and I am still thankful to him because of the various suggestions he has made, and for the pleasure I had in his marvelous talent and development, and will be for my whole lifetime."

Now, 150 years after Schmalfuß, you have met Bernhard Riemann, a truly outstanding pupil of the Johanneum and son of this city. What conclusion can we draw from that? As teachers, we can be conscious of the responsibility we have for young people, for them to develop their abilities and learn to handle their weaknesses. As persons, young and old, we can learn how necessary it can be, to wander off the track and to open new perspectives in a thoughtful and sound way.

Dörte Haftendorn
References to literature you will find in "Riemann's Youth"
More mathematics in depth should be available here soon.

Author:[Dr. Dörte Haftendorn]    date: December 96. uupdated 27. Juli 2003
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