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, structure, space, models, and change. History On ...

. 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. Charte ...

. 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 wrote an expository article "What is a Sheaf". The paper showed that a

sheaf Sheaf may refer to: * Sheaf (agriculture), a bundle of harvested cereal stems * Sheaf (mathematics), a mathematical tool * Sheaf toss, a Scottish sport * River Sheaf, a tributary of River Don in England * ''The Sheaf'', a student-run newspaper se ...

is useful in analysis, algebra, and geometry when considering

germ Germ or germs may refer to: Science * Germ (microorganism), an informal word for a pathogen * Germ cell, cell that gives rise to the gametes of an organism that reproduces sexually * Germ layer, a primary layer of cells that forms during embryo ...

s of holomorphic functions,

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 n ...

s, and differential forms. 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 Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent an ...

, In 1971 Seebach and Steen took over the Book Reviews section of American Mathematical Monthly, 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 te ...

s. Telegraphic Reviews, in telegraphic style, 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) h ...

(1978). In 1975 Seebach and Steen became co-editors of

Mathematics Magazine ''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a j ...

. 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, viewed as radical at the time, has since been emulated... Seebach welcomed the rise of computers when he assembled a

Heathkit H8 Heathkit's H8 is an Intel 8080A-based microcomputer sold in kit form starting in 1977. The H8 is similar to the S-100 bus computers of the era, and like those machines is often used with the CP/M operating system on floppy disk. The main diffe ...

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

(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