Gilbert Ames Bliss, (9 May 1876 – 8 May 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 functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

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, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

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 ( it, mandolino ; literally "small mandola") is a stringed musical instrument in the lute family and is generally plucked with a pick. It most commonly has four courses of doubled strings tuned in unison, thus giving a total of 8 ...

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 (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern mathematical analysis, analysis". Despite leaving university without a degree, ...

'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, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Tw ...

, Bliss spent the 1902–03 academic year at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

, interacting with

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

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

Hermann Minkowski Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen. He created and developed the geometry of numbers and used geometrical methods to solve problems in number t ...

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 axiomatic se ...

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 (german: link=no, Dorpat), in the Govern ...

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) t ...

, and

Constantin Carathéodory Constantin Carathéodory ( el, Κωνσταντίνος Καραθεοδωρή, Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant ...

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

and the

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

. 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 research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

, 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 lon ...

, and

Robert Lee Moore Robert Lee Moore (November 14, 1882 – October 4, 1974) was an American mathematician who taught for many years at the University of Texas. He is known for his work in general topology, for the Moore method of teaching university mathematics, ...

. 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 Eliakim Hastings Moore (; January 26, 1862 – December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, was an American mathematician. Life Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, di ...

's previous leadership, and than it would become under

Marshall Stone Marshall Harvey Stone (April 8, 1903 – January 9, 1989) was an American mathematician who contributed to real analysis, functional analysis, topology and the study of Boolean algebras. Biography Stone was the son of Harlan Fiske Stone, who wa ...

's and Saunders MacLane's direction after

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

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

Leonard Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also reme ...

. During

World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

, he worked on

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

, 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 movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

. In 1918, he and

worked together in the Range Firing Section at the

Aberdeen Proving Ground Aberdeen Proving Ground (APG) (sometimes erroneously called Aberdeen Proving ''Grounds'') 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 ...

, 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 six major influenza epidemics in the last ...

; 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, 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 Nati ...

(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, college, and high school teachers; graduate and undergraduate students; pure a ...

's first

Chauvenet Prize The Chauvenet Prize is the highest award for mathematical expository writing. It consists of a prize of $1,000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article ...

, in 1925, for his article "Algebraic functions and their divisors," which culminated in his 1933 book ''Algebraic functions''. 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, often referred to as the House of Representatives, the U.S. House, or simply the House, is the lower chamber of the United States Congress, with the Senate being the upper chamber. Together they ...

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 Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Humboldt ...

and

. Bliss also strengthened the necessary conditions of

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

, Weierstrass, Legendre, and

Jacobi Jacobi may refer to: * People with the surname Jacobi (surname), Jacobi Mathematics: * Jacobi sum, a type of character sum * Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations * Jacobi eigenva ...

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, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many ...

, 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 differentiabl ...

optimal control Optimal control theory is a branch of mathematical optimization 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 ...

, and

dynamic programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. I ...

. 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.. By 31 December 2021, it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a ty ...

External links

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