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The famed Wallace–Bolyai–Gerwien theorem has got its name from three mathematicians who proved it independently. More precisely speaking

Farkas Bolyai first formulated the question. Gerwien proved the theorem in 1833, but in fact Wallace had proven the same result already in 1807. According to other sources, Bolyai and Gerwien had independently proved the theorem in 1833 and 1835, respectively.

The odd thing that came to my attention was, there is no trace of a mathematician named Paul Gerwien anywhere on the web or history books as far as I know. This sounds strange since Gerwien has proved the theorem much later than Wallace, and I think that in order to get one's name labeled on an already proved theorem, one must be a famous and established mathematician.

Out of curiosity, I have searched quite thoroughly and yet, found no biography of a 19th century Paul Gerwien. There are no other contributions from this mysterious mathematician other than WBG theorem. So my question is

Who was Paul Gerwien and does he have any other contributions in mathematics?

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  • $\begingroup$ The German wikipedia article gives a few details: he has been a lieutenant in a Prussian infantry regiment; also, teacher in the Royal Prussian Cadet Corps. He published another article in Crelles Journal. This is given as note which google translates. $\endgroup$ – sand1 Feb 28 at 9:52
  • $\begingroup$ A 19th century google-books search for "P. Gerwien" brings up a few things (right-click, select "Translate to English" if you can't read German in the snippet excerpts). Also try "Gerwien, P" and Gerwien + Geometrie. However, I don't get much for the phrases "Paul Gerwien" and "Gerwien, Paul". $\endgroup$ – Dave L Renfro Feb 28 at 18:44
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    $\begingroup$ According to the article published in Crelle's Journal, Gerwien was a lieutenant in the 22nd Prussian infantry regiment at the time of publication in 1833. This regiment appears to have been stationed in Silesia (Breslau?). He appears to be identical with a Gerwien born around 1800 in East Prussia who entered the regiment around 1822 as a 2nd lieutenant and left it in 1845 as a major to serve in the General Staff in Berlin. Worked as a teacher for the cadet corps. He died in Berlin, having achieved the rank of general. $\endgroup$ – njuffa Mar 1 at 0:08
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    $\begingroup$ Co-author: H. v. Holleben and P. Gerwien, "Geometrische Analysis", published in two volumes in Berlin, 1831-1832. $\endgroup$ – njuffa Mar 1 at 0:25
  • $\begingroup$ @njuffa I think your comments satisfy the requirements of an answer. $\endgroup$ – polfosol ఠ_ఠ Mar 1 at 2:31
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I have not been able to find any primary sources that confirm that Gerwien's first name was Paul. Gerwien published two papers in Crelle's "Journal für die reine und angewandte Mathematik", where he is listed in the table of contents as P. Gerwien. High-quality scans of both these publications are available from the Göttingen Digitization Center.

P. Gerwien, "Zerschneidung jeder beliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke." Journal für die reine und angewandte Mathematik, 1833 (10), pp. 228-234. (online)

P. Gerwien, "Beweise einiger auf der Kugel Statt findenen Sätze", Journal für die reine und angewandte Mathematik, 1834 (11), pp. 130-135 (online)

Both articles identify the author as:

Gerwien, Pr. Lieuten. im Königlich. Preußs. 22sten Inf. Reg.

This tells us that Gerwien was a 1st lieutenant in the Royal Prussian 22nd Infantry Regiment at the time of publication. In 1831-1832 he also published, as co-author with a fellow officer, a textbook on geometry in two volumes:

H. v. Holleben and P. Gerwien, "Aufgaben-Systeme und Sammlungen aus der ebenen Geometrie, zu einem selbstständigen Unterricht in der Analysis geordnet und durch Gesetze vorbereitet", Berlin: Reimer 1831 & 1832

The announcement for this work in Crelle's journal identifies H. v. Holleben as a lieutenant in the 21st Infantry Regiment, P. Gerwien as a lieutenant in the 22nd Infantry Regiment, and both as teachers at the Royal Prussian Cadet Corps. There is a published history of the 22nd Infantry Regiment that lists an officer by the name of Gerwien who is very likely identical with the author of the above publications:

"Geschichte des 1. Oberschlesischen Infanterie-Regiments Nr. 22". Berlin: Ernst Siegfried Mittler und Sohn 1884 (Google scan)

Gerwien, geb. in Ostpreußen. Früher: im Garde-Ulan. Regt. Eintritt: vor 1822 als Sek. Lt. Austritt: 1845 als Maj. in den Gen. St. versetzt. 1830 Lebensalter 30 J. Dienstzeit 15. J. 2. Sek. Lt. und komm. als Lehrer beim Kad. Korps Berlin. 1840 4. Kapt. Starb als General beim Gr. Gen. St. in Berlin

This tells us that Gerwien was born in East Prussia around 1800, entered military service around 1815, started service with the 22nd Infantry Regiment prior to 1822 as 2nd lieutenant, and was posted as a teacher to the Cadet Corps in Berlin. He left the unit in 1845 as a major, transferring to the General Staff. He died as a general while working in the Great General Staff in Berlin.

Some evidence for this biographical sketch is provided in the following four publications:

Militair-Wochenblatt, 18. Jahrgang 1833, No. 892 (Google scan)

  1. Juli 1833
    Gerwien, Pr. Lt., com. beim Cadett. Corps, tritt ins 22. Inf. Regt. zurück

This tells us that Gerwien, with the rank of 1st lieutenant, previously posted to the Cadet Corps, was assigned back to the 22nd Infantry Regiment on July 12, 1833.

Rang- und Quartierliste der Königlich-Preußsischen Armee für das Jahr 1847 (Google scan)

Gerwien, Gen.-Stab, Major 12. Juni 1843

This tells us that Gerwien was promoted to major on June 12, 1843 and that in 1847 he served in the General Staff.

Militair-Wochenblatt, 33. Jahrgang, 1849, No. 28 (Google scan)

  1. Juni 1849
    Gerwien, Major vom gr. Generalstabe, zum Abtheilungs-Vorsteher

This tells us that Gerwien, a major serving in the Great General Staff, was promoted to department head effective June 26, 1849.

Königlich Preußischer Staats-Anzeiger, 1856 (scan by Bavarian State Library)

Berlin, 4. Juli. Seine Majestät der König haben den nachbenannten Offizieren und Beamten die Erlaubnis zur Anlegung der von des Kaisers von Rußlands Majestät ihnen verliehenen Orden Allergnädigst zu ertheilen geruht. Es haben erhalten:
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der Oberst Gerwien im großen Generalstabe;
den St.-Wladimir-Orden vierter Klasse

On July 4, 1856, Gerwien, then colonel in the Great General Staff, received royal permission to wear a Russian order he had received, the Order of Saint Vladimir, 4th class.

In the Berlin address directory for 1855 we find colonel P. Gerwien, department head in the Great General Staff, residing in Berlin at Bernburger Straße 30 (this address in Google Maps today):

Gerwien, P., Oberst und Abtheilungs-Vorsteher im großen General-Stabe, Bernburgerstr. 30

I have not been able to find anything about a date of death. I have some tentative information that Gerwien may have had a daughter Clotilda born around 1831, and that he had already passed away when she married Peter Bayne on April 26, 1858.

A poorly cropped scan of the Militärzeitung from 1858 reports on the death of Gerwien, who was a major general and the commander of the 15th Infantry Brigade in Münster at that time. It should be noted that in the Prussian army of that time a Generalmajor (major general) was the lowest rank of general, with the modern equivalent being the Brigadegeneral (brigadier general). Using other news items for temporal context, his death seems to have occurred in late April of 1858:

Zu Münster verschied in der letzten Woche des v. Mts. nach längerem Leiden der k. preußische Generalmajor und Kommandant der 15. Infanteriebrigade Gerwien, ein hochverdienter Offizier, der sich nicht allein in der preußischen, sondern fast in jeder europäischen Armee sich eines höchst ehrenvollen Rufes erfreute.

Finally found a notice detailing the date of death:

Zeitschrift für Kunst, Wissenschaft und Geschichte des Kriege (1859) (Google scan)

Während des Jahres 1858 starben im Preußischen Staate folgende, noch im Dienste befindliche oder zur Disposition gestellte und verabschiedete Generale:
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Gerwien, General-Major und Kommandeur der 26sten Infanterie-Brigade, 59 Jahre alt, am 24sten April in Münster

Gerwien, major general and commander of the 26th Infantry Brigade died on April 24, 1858 in Münster at the age of 59. This suggests he was born in 1799.

In his autobiography "Ein Leben voller Abenteuer", in the chapter covering his life as a young cadet, Otto von Corvin (1812-1886) describes Gerwien as a young lieutenant with blonde curls. Corvin feared him as a strict math teacher, but also states that he was a well-meaning person who simply took his job very seriously.

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