Karl Friedrich Hauber

Karl Friedrich Hauber (born May 18, 1775 in Schorndorf ; † September 5, 1851 in Stuttgart ) was a German mathematician .

Life

Hauber attended the monastery schools in Blaubeuren and Bebenhausen and finally ended up in the theological monastery in Tübingen . There he obtained his master's degree in 1794 with a dissertation on Euclid's theory of proportions (V. Book of Elements ). He was then accepted into the local repetition college and in 1798 published a translation of Archimedes ' works on spheres and cylinders and circular measurements with annotations and additions . In the years 1798 and 1799 he traveled through Germany and stayed in Leipzig , Dresden , Berlin , Göttingen , Hamburg and Gotha . During this trip a geometric essay and two combinatorial-analytical treatises were written.

Back in Tübingen, Hauber added Simon L'Huilier's instructions for elementary algebra with a 16th and 17th chapter on continued fractions and their application. In 1802 Hauber became a professor in Denkendorf, later in Schönthal. Between 1820 and 1825 Hauber first published the annotated beginning of the first book by Euclid under the title “Chrestomathia geometrica”, then in 1824/25 in collaboration with Johann Wilhelm Camerer the six first books by Euclid in Greek with a Latin translation and detailed commentaries.

In Stuttgart in 1829 he published the work "Scholae logico-mathematicae", which contains, among other things, Hauber's theorem on the reversibility of conclusions in mathematics.

Hauber died as a prelate and retired Ephorus of the Maulbronn monastery .

Hauber's theorem

In Chapter VII of the "Scholae logico-mathematicae" the following sentence is proven:

If with and with and further applies and , then applies: and . ${\displaystyle A=b\cup c}$ ${\displaystyle b\cap c=0}$ ${\displaystyle A=\beta \cup \gamma }$ ${\displaystyle \beta \cap \gamma =0}$ ${\displaystyle b\subset \beta }$ ${\displaystyle c\subset \gamma }$ ${\displaystyle \beta \subset b}$ ${\displaystyle \gamma \subset c}$

Hauber's formulation of this sentence is:

Si genus aliquod dividatur in suas species duplici ratione, et singulis speciebus unius divisionis respondeant singulae species alterius ut attribute: vicissim etiam singulis speciebus alterius divisionis singulae species prioris ut attributa respondebunt. Ut si genus quoddam A dividatur primum in species b, c, ac deinde in species : ut Omne A sit aut b aut c, et rursus Omne A sit aut aut ; et praeterea, quae sint ex specie b, iis attribution ; quae ex specie c, iis ; his igitur positis, vicissim, quae sunt ex specie , iis attribuetur b; et quae ex specie , iis attribute c. ${\displaystyle \beta ,\gamma }$ ${\displaystyle \beta }$ ${\displaystyle \gamma }$ ${\displaystyle \beta }$ ${\displaystyle \gamma }$ ${\displaystyle \beta }$ ${\displaystyle \gamma }$

This sentence was first referred to in 1836 by MW Drobisch, E. Vilus and S. Busok in “New Representation of Logic” as “Hauber's theorem”.

In its propositional variant, the proposition gives a sufficient condition for the reversibility of a system of implications .

Individual evidence

1. ↑ Biographical information according to: Moritz Cantor , Julius Hartmann:  Hauber, Karl Friedrich . In: Allgemeine Deutsche Biographie (ADB). Volume 11, Duncker & Humblot, Leipzig 1880, p. 38 f.
2. ↑ Quoted from: Cyril FA Hoorman Jr .: "On Hauber's Statement of his theorem." In: Notre Dame Journal of Formal Logic, Vol. XII, Jan. 1971, pp. 86 ff.
3. ^ Voss, Leipzig 1836, p. 162
4. ↑ Schröter, Karl: "The benefit of mathematical logic for mathematics". In: Archive for Mathematical Logic, Vol. 1 No. 1, September 1950, Springer-Verlag Berlin / Heidelberg, p. 22 ff.