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 (, ; , ) is an Indo-European languages, Indo-European language, constituting an independent Hellenic languages, Hellenic branch within the Indo-European language family. It is native to Greece, Cyprus, Italy (in Calabria and Salento), south ...

as an undergraduate, making it a second

major Major most commonly refers to: * Major (rank), a military rank * Academic major, an academic discipline to which an undergraduate student formally commits * People named Major, including given names, surnames, nicknames * Major and minor in musi ...

with mathematics. Seebach studied with A. I. Weinzweig at

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

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

Saint Olaf College St. Olaf College is a private liberal arts college in Northfield, Minnesota, United States. It was founded in 1874 by a group of Norwegian-American pastors and farmers led by Pastor Bernt Julius Muus. The college is named after the King and the ...

Northfield, Minnesota Northfield is a city in Dakota County, Minnesota, Dakota and Rice County, Minnesota, Rice counties in the U.S. state, state of Minnesota. It is mostly in Rice County, with a small portion in Dakota County. The population was 20,790 at the 2020 U ...

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) In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open s ...

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 embry ...

s 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 mathematics, more specifically in 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 algebraic varieties or manifolds, or of ...

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 applications ...

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 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 a ...

, In 1971 Seebach and Steen took over the Book Reviews section of

American Mathematical Monthly ''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an exposi ...

, 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, United States. Founded in 1874, Macalester is exclusively an undergraduate institution with an enrollment of 2,142 students in the fall of 2023. The college ha ...

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 Independence is a condition of a nation, country, or state, in which residents and population, or some portion thereof, exercise self-government, and usually sovereignty, over its territory. The opposite of independence is the status of ...

of conditions on

topological space In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a to ...

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 ''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 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 ar ...

, 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 Man ...

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 The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

when they began their own newsletter. Seebach died in 1996 from complications of

diabetes Diabetes mellitus, commonly known as diabetes, is a group of common endocrine diseases characterized by sustained high blood sugar levels. Diabetes is due to either the pancreas not producing enough of the hormone insulin, or the cells of th ...

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