Gabriel Kron (1901–1968) was a

Hungarian American Hungarian Americans (, ) are Americans of Hungarian descent. The U.S. Census Bureau has estimated that there are approximately 1.396 million Americans of Hungarian descent as of 2018. The total number of people with ethnic Hungarian backgroun ...

electrical engineer Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

who promoted the use of methods of

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

multilinear algebra Multilinear algebra is the study of Function (mathematics), functions with multiple vector space, vector-valued Argument of a function, arguments, with the functions being Linear map, linear maps with respect to each argument. It involves concept ...

, and

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

in the field. His method of system decomposition and solution called Diakoptics is still influential today. Though he published widely, his methods were slow to be assimilated. At

Union College Union College is a Private university, private liberal arts college in Schenectady, New York, United States. Founded in 1795, it was the first institution of higher learning chartered by the New York State Board of Regents, and second in the s ...

a symposium was organized by Schaffer Library on "Gabriel Kron, the Man and His Work", held October 14, 1969. H.H. Happ edited the contributed papers, which were published by Union College Press as ''Gabriel Kron and Systems Theory''.

Early life

Gabriel Kron was born in 1901 in Baia Mare in Transylvania, Hungary.Alger, P. L. (1969) ''The Life and Times of Gabriel Kron'', Mohawk Publishing In 1919 he graduated from the gymnasium. By that time Transylvania had been ceded to

Romania Romania is a country located at the crossroads of Central Europe, Central, Eastern Europe, Eastern and Southeast Europe. It borders Ukraine to the north and east, Hungary to the west, Serbia to the southwest, Bulgaria to the south, Moldova to ...

. Kron's older brother Joseph returned home, which he had left when he was ten years old. Joseph wished for a professional degree, but had no schooling after grade five. Gabriel

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ed Joseph, who passed various exams, culminating in the high-school exam in 1920. In December of that year the two left home for the United States. The brothers earned their living in

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

with odd jobs such as dish washer, bus boy, or working machines in garment factories. In the fall of 1922 the brothers had saved enough money to enter engineering school at

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

. They continued supporting themselves with casual employment. Gabriel found digging ditches more congenial than dishwashing. He coined the motto: "There are only two occupations compatible with human dignity. One is the study of atomic structure. The other is digging ditches." In 1925 Gabriel graduated and started on a trip around the world. He planned to walk and hitch hike as much as possible. He ran out of money when he reached Los Angeles, where he worked for the United States Electrical Manufacturing Company. He then transferred to the Robbins and Myers Company in Springfield, Ohio. In 1926 he set out again. From

California California () is a U.S. state, state in the Western United States that lies on the West Coast of the United States, Pacific Coast. It borders Oregon to the north, Nevada and Arizona to the east, and shares Mexico–United States border, an ...

he took passage on an oil tanker bound for

Tahiti Tahiti (; Tahitian language, Tahitian , ; ) is the largest island of the Windward Islands (Society Islands), Windward group of the Society Islands in French Polynesia, an overseas collectivity of France. It is located in the central part of t ...

. In

Sydney, Australia Sydney is the capital city of the state of New South Wales and the most populous city in Australia. Located on Australia's east coast, the metropolis surrounds Sydney Harbour and extends about 80 km (50 mi) from the Pacific Ocean ...

he ran out of money. After saving 35 pounds from work at the Electricity Metering Manufacturing Company he set out for

Northern Australia The unofficial geographic term Northern Australia includes those parts of Queensland and Western Australia north of latitude 26th parallel south, 26° and all of the Northern Territory. Those local government areas of Western Australia and Q ...

. In

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he had finished, and buried, ''Treatise on Differential Equations'' by Forsyth. In Sydney he searched for a worthy successor, settling on ''Advanced Vector Analysis with Application to Mathematical Physics'' by the Australian C.E. Weatherburn. During long hikes in Queensland, Kron saw that vector analysis would be a powerful tool in engineering. Sea voyages took him to Saigon via Borneo, Manila, and Hong Kong. Hence overland to Cairo and Alexandria by rail, supplemented by many hours of walking. In the spring of 1928 Kron arrived in Romania and stayed with his family till the fall. After his return Kron was employed as electrical engineer for brief periods with several companies the last of which was

Warner Brothers Warner Bros. Entertainment Inc. (WBEI), commonly known as Warner Bros. (WB), is an American filmed entertainment studio headquartered at the Warner Bros. Studios complex in Burbank, California and the main namesake subsidiary of Warner Bro ...

in New York. They closed his department while he was on a continuing highly paid contract. He economized by living with his family in Romania. There he studied the mathematical tools of the

general theory of relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physi ...

and conceived his method for applying

tensor analysis In mathematics and physics, a tensor field is a function (mathematics), function assigning a tensor to each point of a region (mathematics), region of a mathematical space (typically a Euclidean space or manifold) or of the physical space. Tens ...

to electrical power engineering. This was described in a paper entitled "Non-Riemannian Dynamics of Rotating Electrical Machinery" printed in Romania and distributed to friends. In 1933 Kron returned to the US where his paper had been well received. He worked at

General Electric General Electric Company (GE) was an American Multinational corporation, multinational Conglomerate (company), conglomerate founded in 1892, incorporated in the New York (state), state of New York and headquartered in Boston. Over the year ...

from 1934 until he retired in 1966. Kron was awarded the Montefiore Prize of the

University of Liège The University of Liège (), or ULiège, is a major public university of the French Community of Belgium founded in 1817 and based in Liège, Wallonia, Belgium. Its official language is French (language), French. History The university was foun ...

, Belgium, for the paper written in Romania."Gabriel Kron, IEEE Transactions on Circuit Theory 15(3):174, September 1968, see IEEE Xplore external link

Career

Kron's career developed within the

corporation and has been described by P.L. Alger Alger explains that Kron made a positive impression at an AIEE conference held in New York in January 1934. The behavior of an electrical network was described as a

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

confined to a Non-Riemannian space. General Electric vice president Roy C. Muir "invited Gabe to join the staff of the Advanced Engineering Program under A.R. Stevenson". Furthermore,

Philip Franklin Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis. Dr. Franklin received a B.S. in 1918 from City College of New York (who later awarded him ...

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

approved Kron's paper for publication in ''

MIT Journal of Mathematics and Physics The journal ''Studies in Applied Mathematics'' is published by Wiley–Blackwell on behalf of the Massachusetts Institute of Technology. It features scholarly articles on mathematical applications in allied fields, notably computer science, ...

'', May 1934. "The paper instantly provoked widespread discussion and controversy. Many mathematicians derided his work: it was just for show, it was needlessly complex, or it was of no practical use." According to Alger, Kron "worked with fifteen different managers while with General Electric". Alger explained, "Kron’s value was largely in the inspiration he gave to others and in distant objectives that seemed to business managers to be merely dreams." From 1936 to 1942 Kron published primarily in the ''General Electric Review''. In 1942

John Wiley & Sons John Wiley & Sons, Inc., commonly known as Wiley (), is an American Multinational corporation, multinational Publishing, publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and pr ...

published his ''A Short Course in Tensor Analysis for Electrical Engineers''. As recalled by Keith Bowden, "In the fifties, when Kron’s ideas were first introduced, controversy raged over their validity."

Banesh Hoffmann Banesh Hoffmann (6 September 1906 – 5 August 1986) was a British mathematician and physicist known for his association with Albert Einstein. Life Banesh Hoffmann was born in Richmond, Surrey, on 6 September 1906. He studied mathematics and t ...

was one academic that supported Kron's initiative. Hoffman wrote the Introduction to the second edition of Kron's book, now titled ''Tensors for Circuits'' (1959), distributed by

Dover Publications Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, book ...

. In 1945 Kron suggested an approach to the

Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...

with networks. The same year he used

equivalent circuit In electrical engineering, an equivalent circuit refers to a theoretical circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that simplifies calculation, and more broadly, that is ...

s to solve differential equations. Kron proved to be a versatile employee: He worked in the Large Steam Turbine Engineering Department (1942), contributed to the control of atomic reactor piles (1945), and collaborated with

Simon Ramo Simon "Si" Ramo (May 7, 1913 – June 27, 2016) was an American engineer, businessman, and author. He led development of microwave and missile technology and is sometimes known as the father of the intercontinental ballistic missile (ICBM). He ...

, Selden Crary, and Leon K. Kirchmayer on

power system An electric power system is a network of electrical components deployed to supply, transfer, and use electric power. An example of a power system is the electrical grid that provides power to homes and industries within an extended area. The e ...

s. Alger notes that Kron "was a pioneer, not an educator. He used to imply that hard work is necessary for the mastery of any subject, and it does no good to make the way to understanding too easy." In 1951 Kron published ''Equivalent Circuits of Electrical Machinery''. While continuing with laboratory and turbine assignments on weekdays, Kron began to prepare Diakoptics on his own. His vision realized with publication, in 1963 Kron was assigned to Analytical Engineering Division with H.H. Happ. Together they reviewed Kron's theory, and after Kron's death Happ published ''Diakoptics and Networks'' (1971). A

bibliography Bibliography (from and ), as a discipline, is traditionally the academic study of books as physical, cultural objects; in this sense, it is also known as bibliology (from ). English author and bibliographer John Carter describes ''bibliograph ...

of Kron's writings is given as an appendix to ''Gabriel Kron and Systems Theory'', pages 165 to 172. An earlier bibliography was compiled in 1959 and appeared in pages xiii to xviii of his book ''Tensors for Circuits''.

Awards and honors

Kron received the following awards and honors: * Doctor of Science ''honoris causa'', University of Nottingham, 1961 * Montefiore Prize, University of the Liège, Belgium, 1935 * Coffin Award, General Electric Company, 1942 * Master of Science in electrical engineering, Honorary, University of Michigan, 1936 * Patron and Honorary Member of the Tensor Club of Great Britain * Honorary Member, Research Association of Applied Geometry, Tokyo

Books by Kron

* * 2nd edn. 1965. * * * Dover reprint 1967. * (Dover 2nd edition of the book formerly entitled ''A short course in tensor analysis for electrical engineers'') *

Notes

External links

Early Ideas in the History of Quantum Chemistry - Gabriel Kron 1901-1968
contains excerpts from Alger, P., (ed), 1969, ''The Life and Times of Gabriel Kron''. Mohawk Development Publ., Schenectady, NY. LCCN 70-99590, and other sources.

from Quantum-chemistry-history.com by Udo Anders.
Gabriel Kron 1901–1968
from

IEEE Xplore IEEE Xplore (stylized as IEEE ''Xplore'') digital library is a research database for discovery and access to journal articles, conference proceedings, technical standards, and related materials on computer science, electrical engineering and elec ...