Johannes Frischauf (17 September 1837 in

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

– 7 January 1924 in

Graz Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the popul ...

) was an Austrian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

, geodesist and alpinist.

Life and work

Frischauf passed the matura at the Academic Gymnasium in Vienna and in 1857 studied

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

at the

University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histor ...

, as well as geodesy,

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...

at the Technischen Hochschule Vienna. He obtained the

doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''l ...

in 1864, and became

Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...

for mathematics at the University of Vienna and assistant at the observatory of the university. In 1863 he was

habilitated Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

in mathematics. Starting in 1863, he was professor at the University of Graz for pure and applied mathematics. He worked together with Ludwig Boltzmann. Frischauf developed a new method of

map design Cartographic design or map design is the process of crafting the appearance of a map, applying the principles of design and knowledge of how maps are used to create a map that has both Applied aesthetics, aesthetic appeal and practical function. ...

and wrote textbooks on arithmetics and

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

– for instance in 1872 and 1876 he wrote summaries of the then current knowledge about non-Euclidean geometry (which he called "absolute geometry"). In 1885 he was elected as a member of the

Leopoldina Leopoldina may refer to: * Colônia Leopoldina, a Brazilian municipality in the state of Alagoa * Leopoldina, Minas Gerais, a Brazilian municipality in the state of Minas Gerais * Maria Leopoldina of Austria (1797-1826), consort of emperor Pedro I ...

.Berthold Sutter: ''Die Badenischen Sprachenverordnungen von 1897. Ihre Genesis und ihre Auswirkungen vornehmlich auf die innerösterreichischen Alpenländer''. Band 2. Böhlau, Graz 1965, p. 176f, 249 Starting with 1868, Frischauf pioneered the touristic development of the Sannthaler and Steiner Alps by opening ways and huts. The streets over the Paulitschsattel and the connection Sulzbach- Leutsch were built because of his initiatives. Together with Franz von Juraschek and Mathias Spreiz he was the first to climb the

Admonter Reichenstein The Admonter Reichenstein is a mountain in the Ennstal Alps and the highest and easternmost peak in the Reichenstein Group. An ascent of the mountain requires climbing ability sufficient to handle UIAA grade II climbs. Topography The Admonte ...

. Frischauf defended the view at a time of violent national conflicts, that alpinism should not be subordinated under nationalism or religion or political views. He participated in the foundation of the

Croatian Mountaineering Association The Croatian Mountaineering Association ( hr, Hrvatski planinarski savez) covers both mountaineering and a broad range of related activities. Unlike the majority of the international mountaineering associations, the Association's remit extends to s ...

. Frischauf's

Funerary urn An urn is a vase, often with a cover, with a typically narrowed neck above a rounded body and a footed pedestal. Describing a vessel as an "urn", as opposed to a vase or other terms, generally reflects its use rather than any particular shape or ...

was placed on the Scheichenspitze in the Dachstein Mountains. His estate is located at the University of Graz.

Works (selection)

* ''Über die Bahn der Asia.'' In: ''Sitz. Berichte Kais. Akad. Wiss. Wien, Mat.-nat. Cl.'' Band 45, 1862, pp. 435–442. * ''Bahnbestimmung des Planeten 67 Asia.'' In: ''Sitz. Berichte Kais. Akad. Wiss. Wien, Mat.-nat. Cl.'' Band 53, 1866, pp. 96–141. * ''Einleitung in die analytische Geometrie.'' Leuschner & Lubensky, Graz 1871. * ''Zum Rechnen mit unvollständigen Zahlen.'' In: ''Zeitschrift math. naturw. Unterr.'' Band 26, 1895, pp. 161–172. * ''Beiträge zur Landesaufnahme und Kartographie des Erdsphäroids.'' B. G. Teubner, Leipzig 1919. * ''Hochthor bei Johnsbach.'' In: ''Jahrbuch Steir. Gebirgsverein.'' 1873, p. 41. * ''Reichenstein bei Admont.'' In: ''Jahrbuch Steir. Gebirgsverein.'' 1873, p. 54. * * ''Die Sannthaler Alpen.'' Brockhausen und Bräuser, Wien 1877. * ''Ein Ausflug auf den Monte Baldo.''Wien 1883, Wiener Touristen-Führer.11. * ''Das Uskoken-Gebirge''. In: Zeitschrift DÖAV (1890), pp. 474–484

* ''Krakau bei Murau.'' Steirische Sommerfrischen, Band 1, Leuschner & Lubensky, Graz 1896, Hrg. vom Steirischen Gebirgsvereine.

References

External links

* * Martin Fürnkranz
''Bibliographie''

Publications of J. Frischauf
in Astrophysics Data System {{DEFAULTSORT:Frischauf, Johannes 1837 births 1924 deaths Austrian mathematicians