J. Arthur Seebach Jr (May 17, 1938 – December 3, 1996) was an American

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, mathematical structure, structure, space, Mathematica ...

. Seebach studied

Greek language Greek ( el, label= Modern Greek, Ελληνικά, Elliniká, ; grc, Ἑλληνική, Hellēnikḗ) is an independent branch of the Indo-European family of languages, native to Greece, Cyprus, southern Italy (Calabria and Salento), southe ...

as an undergraduate, making it a second major with mathematics. Seebach studied with A. I. Weinzweig at

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Chart ...

. He earned a Ph.D. with the thesis ''Cones and Homotopy in Categories''. Seebach began to teach at Saint Olaf College in

Northfield, Minnesota Northfield is a city in Dakota and Rice counties in the State of Minnesota. It is mostly in Rice County, with a small portion in Dakota County. The population was 20,790 at the 2020 census. History Northfield was platted in 1856 by John W. ...

in 1965. He, his wife Linda A. Seebach, and

Lynn A. Steen Lynn Arthur Steen (January 1, 1941 – June 21, 2015) was an American mathematician who was a Professor of Mathematics at St. Olaf College, Northfield, Minnesota in the U.S. He wrote numerous books and articles on the teaching of mathematics. H ...

wrote an expository article "What is a Sheaf". The paper showed that a sheaf is useful in analysis, algebra, and geometry when considering germs of

holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex de ...

local ring In abstract algebra, more specifically ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic ...

s, and

differential form In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many application ...

s. J. Arthur also wrote "Injectives and Homotopy".J.A. Seebach (1972
Injectives and Homotopy
'Illinois Journal of Mathematics'' 16:446–53, link from Project Euclid, In 1971 Seebach and Steen took over the Book Reviews section of

American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an ...

, including Telegraphic Reviews which ran for several pages every month. The massive effort was eventually distributed over some 50 mathematicians at Saint Olaf, Carleton, and

Macalester College Macalester College () is a private liberal arts college in Saint Paul, Minnesota. Founded in 1874, Macalester is exclusively an undergraduate four-year institution and enrolled 2,174 students in the fall of 2018 from 50 U.S. states, four U.S t ...

s. Telegraphic Reviews, in

telegraphic style Telegram style, telegraph style, telegraphic style, or telegraphese is a clipped way of writing which abbreviates words and packs information into the smallest possible number of words or characters. It originated in the telegraph age when teleco ...

, was started by Kenneth O. May in 1965 and provided an American posting of new publications before the digital age. Seebach and Steen conducted research in a 1967 summer school with students investigating the independence of conditions on

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called po ...

s. They summarized their work in

Counterexamples in Topology ''Counterexamples in Topology'' (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) ...

(1978). In 1975 Seebach and Steen became co-editors of Mathematics Magazine. Steen wrote: :Arthur’s sense of whimsy, his love of puns, and his proclivity for obscure connections totally transformed the image of ''Mathematics Magazine''.

Cover art Cover art is a type of artwork presented as an illustration or photograph on the outside of a published product such as a book (often on a dust jacket), magazine, newspaper (tabloid), comic book, video game ( box art), music album ( album ...

, viewed as radical at the time, has since been emulated... Seebach welcomed the rise of computers when he assembled a Heathkit H8. In 1986 he became editor of Mathematical Notes in ''American Mathematical Monthly''. Beyond mathematics, Seebach sang with the Bach Society of Minnesota. The craftsmanship of the

Studebaker Studebaker was an American wagon and automobile manufacturer based in South Bend, Indiana, with a building at 1600 Broadway, Times Square, Midtown Manhattan, New York City. Founded in 1852 and incorporated in 1868 as the Studebaker Brothers ...

automobile appealed to Seebach and he operated a side-business in Studebaker parts, driving some, and publishing a

newsletter A newsletter is a printed or electronic report containing news concerning the activities of a business or an organization that is sent to its members, customers, employees or other subscribers. Newsletters generally contain one main topic of ...

for fellow aficionados of the car. His newsletter experience was of value to Mathematical Association of America when they began their own newsletter. Seebach died in 1996 from complications of

diabetes Diabetes, also known as diabetes mellitus, is a group of metabolic disorders characterized by a high blood sugar level (hyperglycemia) over a prolonged period of time. Symptoms often include frequent urination, increased thirst and increased ...

References

* Lynn Arthur Steen (1997) "In Memoriam: J. Arthur Seebach Jr.", ''Mathematics Magazine'' 70: 78–79.

External links

* {{DEFAULTSORT:Seebach, J. Arthur 1938 births 1996 deaths 20th-century American mathematicians 20th-century American educators St. Olaf College faculty Northwestern University alumni