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Bernhard Riemann's school days at the Johanneum in Lüneburg

These pages are a sketch for a publication at the Mathematical Society in Göttingen
It will not be necessary to mention the overwhelming importance of the mathematician Bernhard Riemann in this article. Besides his mathematical works, the complete edition of his works which was published by Narasimhan [GA Nar] in 1990 does also contain many sources from his private life. I am partly going to relate to these in this article. My aim is mainly to include hardly accessible information from the Johanneum's school history in his biography. From these it can be concluded, that the situation at his school was an extraordinary advantage for Riemann in many ways. This picture does portray him approx. as a school leaver. [GA]

The Hannovers Wendland is still a narrowly populated area in which the wendic form of settlement as "Rundlinge" (round villages) has been predominant for a long time. In one of these small villages, Breselenz on the edge of the range of hills Drawehn, Bernhard Riemann was born on the 17th of September 1826 as the second of the vicar's six children. In early childhood, his mathematical abilities exceeded both his father's, who had been teaching the children, as well as another teacher's who had been employed for teaching mathematics. [GA Ded]. Although his father changed to a vicarage in Quickborn close to the small town Dannenberg, higher education was still not available for Bernhard. A grammar school in Dannenberg has only opened in the 1970s. A. and D. Laugwitz [Lau] have published a pictured article in English on Riemann's youth in the Elbmarsch and in Lüneburg.
Several maps

After his confirmation at Easter 1840, the gifted boy was sent to Hannover to stay with his grandmother, a counsellor's widow, in order for him to visit the Tertia of the Lyceum. Dedekind [GA Ded], who has evaluated the family's private correspondance, is mentioning extraordinarily close family bonds. Contacting strangers is a hard task for Riemann in his youth as well as in his adulthood.

It may be of some interest in our context that his maths teacher was at first annoyed to be corrected by his pupils, but did then learn to accept Riemann's abilities and became "a special friend" to him, as Schering mentioned in his commemorative address. [GA Scher]. It seemed as a fortunate incident to Schering that Riemann changed schools to the Johanneum in Lüneburg after his grandmother's death.

Lüneburg's history is charaterized by the wealth which the town acquired during the Middle Ages and the Renaissance by producing and selling salt. The citizens were hence able to become independent of the predomination of clergy, cloister and the duke in 1406 and founded an own school, the Johanneum under the auspices of the town church St. Johannis. Thanks to the commemorative publication because of the Johanneum's 500th anniversary our knowledge of the school history is quite thourough. The 19th century is portrayed by director Dr. Nebe [FS Neb]. He does vividly describe the town's and the school counsil's effort in not only juvenating the staff, but also in trying to add some well-trained teachers to the staff. So far, an actual teaching profession did not exist. All subjects were taught by theologists, who were mostly striving to take over a vicarage as soon as possible.

To eliminate this unfortunate situation, Dr. Karl Haage, a young and extraordinarily able teacher from Gotha, was asked to become the Johanneum's headmaster in 1823. Thanks to his committed effort the school flourished.

He did also initiate the Johanneum's move to a different building since the old one had become "too small and dull" and did not have enough space "for a natural and physical cabinet, as it cannot be dispensable in long term." The re-organisation of Hannover's school administration took place during Haage's time at the Johanneum. It involved the introduction of an educational authority and maturity examinations. "To him (Haage) it was an 'extraordinary pleasure and satisfaction', that the Johanneum's leavers' exams were amongst the best in the first year of maturity exams, and that the school inspector Kohlrausch declared during his first visit to the school, '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'. Haage was being recognised so widely, that "he was appionted a honorary doctor by Georgia Augusta at her ceremony in Göttingen 1837".

Especially the lessons in mathematics were to suffer from the theologists' and philologists' predominance until Haage appointed as the first (and even the only one for a long time) mathematician Constantin Schmalfuß in 1829,"...who did, in an exceptional way, combine strict mathematical studies and strict thoughts with taste and esthetical education, and managed to assure his subject the deserved position in the Johanneum's curriculum as well as in the pupils' regard, an aspect which is not to be underestimated."

Schmalfuß did also come from Thüringen and had studied mathematics in Halle and Berlin. He was the deputy headmaster when Haage was still at the school, and took over the head's position after his sudden death in December 1842. "He was a great teacher and marvelous at administrative matters" and "has in his six years of occupation succeeded brilliantly in keeping the Johanneum's prestige high and to eliminate all doubts as to 'whether a mathematician would be suitable for this position'." In the whole kingdom of Hannover "this event had no match."

Looking at Riemann's biography, it seems quite remarkable that no mathematician or scientist has been headmaster of the Johanneum ever since. Apart from the school inspector's (who is mentioned above) son who had mathematics as his second subject, there had not been a mathematician as a teacher between 1849 and 1867.

Bernhard Riemann entered the Johanneum's Lower Secunda (year 10) at Easter 1842. 281 pupils attended the Johanneum at that time.

The curriculum describes the forms the pupils spend two years in with Roman figures, II is hence Lower and Upper Secunda. Parallel to the classical stream, the Secunda and Prima could also be spent in "Realklassen", with stronger emphasis on mathematics and technical drawing, modern languages and "history of nature". According to his father's plans Riemann was to become a vicar, and was hence to follow the classical stream. Apart from that, a good knowledge of Latin was a necessity for any academic career. Since he had Schmalfuß as a maths teacher and was a lot quicker than the other pupils anyway, this was not going to be a disadvantage.

Curriculum 1842 (big, 14 K)

We know about Schmalfuß' relationship to Bernhard Riemann because of a letter Schering recieved from him before writing an obituary after Riemann's death in 1866 [GA /851ff]. He writes: "...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."

.... All I had about Euklidian things, with comments ...; and what I owned of the Archimedian literature, Apollonios and all that, he read all these books, and while reading they became his safe possession.

He was not less interested in Newton's Arithmetica Uiversalis and the Cartesius Geometria. ..."

Schmalfuß let him participate in the normal maths lessons, but "....wanted to offer him something which was adequate to his abilities in every lesson, and he has always surpassed that boundary that I saw as his but probably also as mine and did continue to offer me a variety of results I had never expected in such quantity"

Laugwitz [Lau] wrote that it should be considered that now, after the pupil had become famous, retrospective reports from his school days are possibly too positive. It does yet seem coherent with Constantin Schmalfuß' personality as described in depth by the classicist Nebe [FS Neb], that he empathized with Riemann's situation and personality and acted accordingly. Nebe is also mentioning "his fine and elegant, open and cheerful behaviour,...self-assured while having an ideal view on the teachers' profession,...a soft, extraordinarily melodious voice,....expertise and quick intelligence,..." It does hence seem fairly reliable, if Schmalfuß writes: "...I have learnt more from him, than he from me." "... I deeply regret that nothing is left to me from his prooves' and formula developments' cleverness and simplicity.

Even then he was a mathematician, besides whose talent teachers were bound to feel poor...."

At the end Schmalfuß writes:

"I have always seen it as great fortune to have taught a pupil like Riemann, and 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."



Another of Riemann's teachers was religion and Hebrew teacher Dr. Gustav Heinrich Seffer, who has mentioned Riemann to Schering in a letter dating from November 1866.[GA /849] He was only 25 years old when Riemann came to the Johanneum. He was good friends with Schmalfuß, who was ten years older. Both of them tried to solve the problem of a very gifted pupil together. Schmalfuß wrote about Riemann: "... just how hard it was for him to develop thoughts in a fluent speech. Added to that was the problem, that no expression seemed sufficient to him which did not cover everything, and him being very shy to accept any statements which were not ... perfectly precise. ...." Seffer says: ".... that he was always behind with his German and Latin essays,..., that the teachers' conference was despaired because of him." In today's vocabulary that would mean that Bernhard Riemann was not able to fulfil all compulsory requiremts. Since both of them did not want to watch Riemann's fail his Abitur because of "formal reasons", Seffer suggests a solution: "...I let him live in my house for reduced food cost and obliged to look after him, so that he would be able to hand his essays in on time. .... and on some evenings I have been sitting with him until deep in the night...."

Laugwitz says that seeing Seffer's house he would constantly have to think about Riemann's suffering, to see him as being imprisoned in body and soul...[Lau]. I have not found any evidence for this opinion. Quite contrary, Seffer does rather seem like a big brother, whose stubbornness and competence helped Riemann in finally learning how to bring a written work to its end.

At the same time Seffer was writing on a "Elementary book of the Hebrew language, which is now needed in German and Swiss grammar schools." The work was to contain matching texts for training for all chapters. To find those in the Bible, "was a difficult task, in which Riemann seemed vividly interested. ....so that my elementary book owns several of its exercises mostly to the great mathematician Riemann."

Riemann had visited Seffer again years later which seems to indicate a feeling of thankfulness rather than hate, and the teacher writes about it:

"he has later ... told me a lot about his philosophical work. .... While I had to admit that I was not able to follow him,...., but did have to admire his goals' greatness."

He finishes his letter " Riemann was quiet, modest and undemanding,..... namely shy with women....I had and have always liked him."

It could be foreseen - and did indeed happen -, that Riemann was not to be able to finish his final Abitur essay in the given time. Schmalfuß still wanted Riemann to achieve a "First class" report. It was clear to him as the only mathematician, that it was going to be hard to convince the classicists and theologists of Riemann's extraordinary mathematical abilities. He thought up the following perfectly legitimate plan: Bernhard had borrowed from him Legendre's number theory for one week over Whitsun. When he returned it after such a short time, the teacher suspected that it had been too difficult for him. Riemann denied that, he had found the book interesting and read it completely. Schmalfuß decided to examine him in that without a pre-announcement, for then even non-mathematicians would have to agree in the extraordinary achievement. He stated in the Abitur examination: "everything which took me some effort to prepare for as an examiner, ... was familiar to him".

That way he did manage to achieve a Maturity report "First Class", which is quoted in full lenths in the following paragraphs. [Abi]


Maturitäts-Zeugniß erster Klasse



Bernhard Georg Friedrich Riemann, born on the 17th of September 1826 in Breselenz, the Quickborn/Dannenberg's vicar Riemann's son, Lutheran of denomination, visited the Hannover Lyzeum for two years, since Easter 1842 the Gymnasium Johanneum, the first class since Easter 1844.

His moral behaviour in and out of school was very good. He visited school regularly, but interrupted several times by illnesses in the last year, he is paying attention sufficiently well, but not equally well in all subjects, his diligence was strained, but dependant upon his own favours and hence not always meeting the school's demands sufficiently, he did especially usually hand in his free essays too late. General predicate of diligence good.

Knowledge

1. Religion. He is generally familiar with the basic truths of the Christian doctrine of belief and ethics including the differences of the most important confessions with the major moments of church history and the contents of the Biblical books.

General predicate quite good.

2. German language. Grammar and style are well-known to him and he is renowned for having read a considerable number of classics. His essays had been worked on with great effort and strict slowness. His final assessed work remains unfinished. His essays are commended by their logical structure and connection of thoughts, by correct consequences drawn from the arguments and a coherent and simple, while mostly fluent and clever presentation, while they do occasionally lack the variety of content and lively effusion of phantasy. His oral expression is good.

General predicate good.

3. Latin language. When reading, he is generally able to understand, if slowly, meaning as well as context even of the most difficult sentences. His knowledge of grammar is good, from his stilistic work his logical understanding and usage of the Latin tongue can be deduced, while he does not seem to have a wide variety of sayings and phrases. His expression is commendable because of precision and correct grasp of order of precedence while lacking easiness of fluency. He is hardly used to speaking.

General predicate good.

4. Greek language. About his understanding of Greek literature the same as about the Latin tongue applies. His knowledge of grammar is good. General predicate good.

5. Hebrew language. He reads with sufficient fluency, does have a thourough knowledge of grammar and does translate easy parts of the Old Testament with skill.

General predicate Very good.

6. French language. He does translate even difficult modern writers with ease and writes with almost no grammatical mistakes.

General predicate good.

7. English language. He does still lack competence in both pronounciation and grammar, while he is quite skilled in understanding and translating writers.

General predicate good.

8. History and geography. His knowledge of all parts of history have gained him the predicate quite good , in geography good.

9. Mathematics. His knowledge is thourough and competent and does by far exceed broadth and depth of the curriculum that is taught at schools, in understanding mathematical teachings he is clever, quick and clear in his thoughts to an extraordinary extent. He is being supported by a reliable memory, a brilliant power of deduction, and an agile constructing phantasy. Because of his abilities he is generally most suited for continuing his mathematical studies.

General predicate excellent.

10. Physics. Equally as on his abilities in mathematics can be judged on his achievements in those parts of physics, to which a mathematical reasoning and handling applies.

After thourough examination and discussion this first class report has been decided on and executed

by the examination commission of the Gymnasium Johanneum

in Lüneburg the 10th of March 1846

Schmalfuß


Schmalfuß has not missed out on writing a clear remark in the report for mathematics for Riemann's father, who was still convinced that his son would have to become a vicar.


Bernhard Riemann did now go to Göttingen to read theoology for one semester, as his father wanted him to, but was then able to -probably by referring to the comment in his report- give his undivided attention to mathematics.

Both of his teacher did also leave the Johanneum, Seffer at the same time as Riemann, in order to become the Seminar's inspector in his hometown Alfeld. He did shortly afterwards become government and school inspector in Hannover.
In 1849 Schmalfuß was elected president of the general teachers' conference of the Kingdom Hannover. Because of his abilities and his persuading personality he did also become a school inspector in Hannover.
The Johanneum does still exist as a grammar school, which feels obliged to classical and modern languages, but also in a very special way to mathematical-scientific education.

Riemann's further development is not going to be discussed here. Since generally the thouroughness, terseneses and independence of his works is acknowledged, one can reasonably say that he has met an especially advantageous constellation at the Johanneum in Lüneburg. Sensitive and clever teachers challenged his mathematical abilities and helped him to overcome his weaknesses, so that his extraordinary strengths could fully develop.

Literature:


Author:
Dr. Dörte Haftendorn, dipl. math.
Barckhausenstr. 44
D-21335 Lüneburg
http://www.fh-lueneburg.de/u1/haftendo

Senior assistant master at the Johanneum, lecturer at Lüneburg University and University of Advanced Studies
Tranlated by Rosa Lou Freund, stud. math., Abi 97



topAuthor:[Dr. Dörte Haftendorn]   date: February 99. updated  28. Juli 2004
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