Ludwig August Seeber

Only little is known of Seeber's origin and education. In 1810, he studied astronomy at the University of Göttingen with Carl Friedrich Gauss, a companion of this time was Christian Ludwig Gerling.{{Cite journal | last = Reich | first = Karin | author-link = Karin Reich | title = Gauß' Schüler | journal = Mitteilungen der Gauß-Gesellschaft Göttingen | issue = 37 | pages = 33–62 | year = 2000 | language = de}} pp. 36–37, 43{{efn|Gauss and Gerling mentioned Seeber several times in their correspondence.{{Cite book| title = Briefwechsel zwischen Carl Friedrich Gauss und Christian Ludwig Gerling | editor = Clemens Schaefer |publisher = Otto Elsner | place = Berlin | year = 1927 | language=de | url=https://gdz.sub.uni-goettingen.de/id/PPN335994989?tify=%7B%22pages%22%3A%5B5%5D%2C%22view%22%3A%22info%22%7D}}}} From 1819 to 1822 he was teacher at the cadet school at Karlsruhe. He got his doctor degree in 1824 from the University of Freiburg,{{Cite book | author-last = Schneider | author-first = Daniel | year = 2006| title = Universitätsarchiv der Albert-Ludwig-Universität Freiburg i. Br.. Bestand B 0038. Philosophische Fakultät 1760–1935 | publisher = Universitätsarchiv | place = Freiburg | page = 58 | language = de | url = https://www.uniarchiv.uni-freiburg.de/bestaende/provenienzbestaende/fakultaeten/2-4-4-philosophische-fakultaet/b0038/findbuchb0038}} where he was professor ordinarius for physics until 1834 and three times Dean of the Philosophical Faculty in 1814, 1829, and 1834.{{Cite book | author-last = Schneider | author-first = Daniel | year = 2006| title = Universitätsarchiv der Albert-Ludwig-Universität Freiburg i. Br.. Bestand B 0038. Philosophische Fakultät 1760–1935 | publisher = Universitätsarchiv | place = Freiburg | page = 27 | language = de | url = https://www.uniarchiv.uni-freiburg.de/bestaende/provenienzbestaende/fakultaeten/2-4-4-philosophische-fakultaet/b0038/findbuchb0038}} From 1834 to 1840, he was professor of physics both at the Polytechnicum and the Lyceum in Karlsruhe.{{Cite book | editor = Friedrich von Weech | editor-link = Friedrich von Weech | author-last = Lüroth | author-first = J. | author-link = Jacob Lüroth | chapter = Ludwig August Seeber | year = 1875 | title = Badische Biographien | volume = 2 | page = 295 | language = de | chapter-url = https://books.google.com/books?id=V1NlAAAAcAAJ&pg=PA295}}{{Cite book|author=Moritz Cantor|chapter=Seeber, Ludwig August|year=1891|title=Allgemeine Deutsche Biographie|volume=33|pages=565–566|publisher=Duncker & Humblot |chapter-url=https://de.wikisource.org/w/index.php?title=ADB:Seeber,_Ludwig_August&oldid=2507268}} Seeber applied twice in 1830 and 1838 for a professorship in Göttingen, but without success. In 1840, he took early retirement.

Seeber is known for his mathematical studies with special regard to crystallography. He tried to find explanations for the changing properties of crystals, such as thermal expansion or elasticity, what was impossible with the current theory of the late 18th century created by René Just Haüy, that used a bricklike model of crystal structure.{{cite book | last = von Laue | first = Max | author-link = Max von Laue | editor-last1 = Henry | editor-first1 = N. F. M. | editor-last2 = Lonsdale | editor-first2 = K. | editor2-link = Kathleen Lonsdale | title = International Tables for X-Ray Crystallography. Vol. I Symmetry Groups | publisher = Kynoch Press | year = 1952 | pages = 1–5 | language = de | chapter = Historical Introduction}} Seeber modernized Haüy's concept with introducing the idea of spherical particles (atoms or molecules) as basic components of the crystals, holding together in an equilibrium of attractive and repulsive forces.{{cite book | last = Scholz | first = Erhard | author-link = Erhard Scholz | title =Symmetrie, Gruppe, Dualität : Zur Beziehung zwischen theoretischer Mathematik und Anwendungen in Kristallographie und Baustatik des 19. Jahrhunderts | publisher = Birkhäuser | place = Basel | year = 1989 | pages = 66–67 | isbn = 978-3-0348-9267-4 | language = de | url = https://www2.math.uni-wuppertal.de/~scholz/preprints/Scholz1989Symmetriekonzepte.pdf}}

Following Max von Laue, Seeber's "essentially modern" concept from 1824 "was the earliest application of the scientific atomic theory to a purely physical problem."

In his second work from 1831, Seeber continued the research on positive ternary quadratic forms Gauss had begun thirty years ago in his Disquisitiones Arithmeticae. Seeber derived criteria for equivalence or non-equivalence of the reduced forms for the determinant of ternary forms.{{cite book | last = Gauss | first = Carl Friedrich | author-link = Carl Friedrich Gauss | editor = | title = Carl Friedrich Gauss Werke. Vol. II Höhere Arithmetik | trans-title = Collected Works. Vol II | publisher = | year = 1863 | pages = 188–196 | language = de | chapter = Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeber, Dr. der Philosophie, ordentl. Professor der Physik an der Universität in Freiburg | chapter-url = https://gdz.sub.uni-goettingen.de/id/PPN23599524X?tify=%7B%22pages%22%3A%5B192%5D%2C%22pan%22%3A%7B%22x%22%3A0.309%2C%22y%22%3A0.326%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.856%7D}}

He derived two lemmas for the relation of determinants with the coefficients of the reduced forms, but could only prove one of them, the second one remained as a conjecture. Gauss was able to prove this very shortly on three pages of his unusually detailed review of Seeber's work.

Gauss claimed Seeber's work for its exemplary thoroughness and protected it against the possible reproach of "repulsive long-windedness". The reduction of ternary forms was later simplified by Gauss's successor Peter Gustav Lejeune Dirichlet (1847).{{Cite book | author-last = Bachmann | author-first = Paul | author-link = Paul Bachmann | year = 1923 | title = Zahlentheorie, Vierter Teil: Die Arithmetik der quadratischen Formen | location = Leipzig | language = de | url = https://archive.org/details/arithdquadrachen02bachrich | pages = [https://archive.org/details/arithdquadrachen02bachrich/page/n220 191]–194}}

{{Cite journal | author-last = Dirichlet | author-first = G. Lejeune | title = Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen | journal = Journal für die reine und angewandte Mathematik | volume = 40 | pages = 209–227 | year = 1850 | language = de | url = https://www.digizeitschriften.de/id/243919689_0040%7Clog1?tify=%7B%22pages%22%3A%5B221%5D%2C%22view%22%3A%22info%22%7D&origin=%2Fsearch%3Ffilter%255BZeitschriften%255D%255B1%255D%3D243919689%257Clog1%26filter%255BObjekttyp%255D%255B1%255D%3Dvolume%26page%3D3}}

• {{Cite journal | title = Versuch einer Erklärung des inneren Baues der festen Körper | journal = Annalen der Physik und Physikalischen Chemie | volume = 16 | pages = 229–248, 349–371 | year = 1824 | language = de | url = https://babel.hathitrust.org/cgi/pt?id=uc1.b4433540&seq=247}}
• {{Cite book | year = 1831 | title = Untersuchungen über die Eigenschaften der positiven ternaeren quadratischen Formen | place = Mannheim | language = de | url = https://books.google.com/books?id=QKJGAAAAcAAJ | last1 = Seeber | first1 = Ludwig August }}
• {{Cite book | year = 1840 | title = Ergänzung des Euklidischen Systems der Geometrie, in Rücksicht seiner ungenügenden Beweise der die Parallellinien und ihre Eigenschaften betreffenden Lehrsätze | publisher = G. Braun'sche Hofbuchhandlung | place = Karlsruhe | language = de | url = https://books.google.com/books?id=j8lTAAAAcAAJ}}

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Category:1793 births

Category:1855 deaths

Category:19th-century German physicists

Category:19th-century German mathematicians

Category:University of Göttingen alumni

Category:Academic staff of the University of Freiburg

Category:Academic staff of the Karlsruhe Institute of Technology

Category:Scientists from Karlsruhe