Gilbert Ames Bliss, (May, 9 1876 – May 8, 1951), was an American mathematician, known for his work on the

calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

Life

Bliss grew up in a Chicago family that eventually became affluent; in 1907, his father became president of the company supplying all of Chicago's electricity. The family was not affluent, however, when Bliss entered the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

in 1893 (its second year of operation). Hence he had to support himself while a student by winning a scholarship, and by playing in a student professional

mandolin A mandolin (, ; literally "small mandola") is a Chordophone, stringed musical instrument in the lute family and is generally Plucked string instrument, plucked with a plectrum, pick. It most commonly has four Course (music), courses of doubled St ...

quartet. After obtaining the B.Sc. in 1897, he began graduate studies at Chicago in mathematical astronomy (his first publication was in that field), switching in 1898 to mathematics. He discovered his life's work, the

, via the lecture notes of

Weierstrass Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school t ...

's 1879 course, and Bolza's teaching. Bolza went on to supervise Bliss's Ph.D. thesis, ''The Geodesic Lines on the Anchor Ring'', completed in 1900 and published in the ''Annals of Mathematics'' in 1902. After two years as an instructor at the

University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...

, Bliss spent the 1902–03 academic year at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

, interacting with

Felix Klein Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ...

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

Hermann Minkowski Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, o ...

Ernst Zermelo Ernst Friedrich Ferdinand Zermelo (; ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel set theory, Z ...

Erhard Schmidt Erhard Schmidt (13 January 1876 – 6 December 1959) was a Baltic German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. Schmidt was born in Tartu (), in the Governorate of Livonia (now ...

Max Abraham Max Abraham (; 26 March 1875 – 16 November 1922) was a German physicist known for his work on electromagnetism and his opposition to the theory of relativity. Biography Abraham was born in Danzig, Imperial Germany (now Gdańsk in Poland) ...

, and

Constantin Carathéodory Constantin Carathéodory (; 13 September 1873 – 2 February 1950) was a Greeks, Greek mathematician who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, ...

. Upon returning to the United States, Bliss taught one year each at the

and the

University of Missouri The University of Missouri (Mizzou or MU) is a public university, public Land-grant university, land-grant research university in Columbia, Missouri, United States. It is Missouri's largest university and the flagship of the four-campus Univers ...

. In 1904, he published two more papers on the calculus of variations in the ''Transactions of the American Mathematical Society''. Bliss was a Preceptor at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

, 1905–08, joining a strong group of young mathematicians that included Luther P. Eisenhart,

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lo ...

, and Robert Lee Moore. While at Princeton he was also an associate editor of the ''Annals of Mathematics''. In 1908, Chicago's Maschke died and Bliss was hired to replace him; Bliss remained at Chicago until his 1941 retirement. While at Chicago, he was an editor of the ''Transactions of the American Mathematical Society'', 1908–16, and chaired the Mathematics Department, 1927–41. That Department was less distinguished under Bliss than it had been under E. H. Moore's previous leadership, and than it would become under Marshall Stone's and Saunders MacLane's direction after

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

. A near-contemporary of Bliss's at Chicago was the algebraist Leonard Dickson. During

World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

, he worked on

ballistics Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially weapon munitions such as bullets, unguided bombs, rockets and the like; the science or art of designing and acceler ...

, designing new firing tables for artillery, and lectured on

navigation Navigation is a field of study that focuses on the process of monitoring and controlling the motion, movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navig ...

. In 1918, he and

worked together in the Range Firing Section at the

Aberdeen Proving Ground Aberdeen Proving Ground (APG) is a U.S. Army facility located adjacent to Aberdeen, Harford County, Maryland, United States. More than 7,500 civilians and 5,000 military personnel work at APG. There are 11 major commands among the tenant units, ...

, applying the calculus of variations to correct shell trajectories for the effects of wind, changes in air density, the rotation of the Earth, and other perturbations. Bliss married Helen Hurd in 1912, who died in the 1918

influenza pandemic An influenza pandemic is an epidemic of an influenza virus that spreads across a large region (either multiple continents or worldwide) and infects a large proportion of the population. There have been five major influenza pandemics in the l ...

; their two children survived. Bliss married Olive Hunter in 1920; they had no children. Bliss was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

(United States) in 1916. He was the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

's Colloquium Lecturer (1909), Vice President (1911), and President (1921–22). He received the

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 ...

's first Chauvenet Prize, in 1925, for his article "Algebraic functions and their divisors," which culminated in his 1933 book ''Algebraic functions''. He was also an elected member of the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

and the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

. Bliss once headed a government commission that devised rules for apportioning seats in the

U.S. House of Representatives The United States House of Representatives is a chamber of the bicameral United States Congress; it is the lower house, with the U.S. Senate being the upper house. Together, the House and Senate have the authority under Article One of th ...

among the several states.

Work

Bliss's work on the

culminated in his classic 1946 monograph, ''Lectures on the Calculus of Variations'', which treated the subject as an end in itself and not as an adjunct of mechanics. Here Bliss achieved a substantial simplification of the transformation theories of Clebsch and

. Bliss also strengthened the necessary conditions of

Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

, Weierstrass, Legendre, and Jacobi into sufficient conditions. Bliss set out the canonical formulation and solution of the problem of Bolza with side conditions and variable end-points. Bliss's ''Lectures'' more or less constitutes the culmination of the classic calculus of variations of

Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosophy of mathematics, philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad ...

, and Bolza. Subsequent work on variational problems would strike out in new directions, such as

Morse theory In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differenti ...

optimal control Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations ...

, and dynamic programming. Bliss also studied singularities of real transformations in the plane.

Publications

*1925 ''Calculus of Variations'' *1933 ''Algebraic Functions'' *1944 ''Mathematics for Exterior Ballistics'' *1946 ''Lectures on the Calculus of Variations''

References

*MacTutor
Gilbert Ames Bliss.
The source for most of this entry.
Ames' Students
at the

Mathematics Genealogy Project The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. it contained information on 300,152 mathematical scientists who contributed to research-level mathematics. For a typical mathematicia ...

External links

National Academy of Sciences Biographical Memoir
{{DEFAULTSORT:Bliss, Gilbert Ames 1876 births 1951 deaths 20th-century American mathematicians American mathematical analysts Ballistics experts Mathematicians from Chicago University of Chicago alumni University of Chicago faculty Members of the United States National Academy of Sciences Presidents of the American Mathematical Society University of Missouri mathematicians Members of the American Philosophical Society