Gilbert Ames Bliss
Encyclopedia
Gilbert Ames Bliss, was an American
mathematician, known for his work on the calculus of variations
.
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
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 calculus of variations
, via the lecture notes of Weierstrass
'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
, Bliss spent the 1902-03 academic year at the University of Göttingen, interacting with Felix Klein
, David Hilbert
, Hermann Minkowski
, Ernst Zermelo
, Erhard Schmidt
, Max Abraham
, and Constantin Carathéodory
.
Upon returning to the United States, Bliss taught one year each at the University of Chicago
and the University of Missouri
. In 1904, he published two more papers on the calculus of variations in the Transactions of the AMS. Bliss was a Preceptor at Princeton University
, 1905–08, joining a strong group of young mathematicians that included Luther P. Eisenhart
, Oswald Veblen
, 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
. A near-contemporary of Bliss's at Chicago was the algebraist Leonard Dickson.
During World War I
, he worked on ballistics
, designing new firing tables for artillery, and lectured on navigation
. In 1918, he and Oswald Veblen
worked together in the Range Firing Section at the Aberdeen Proving Ground
, 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
; their two children survived. Bliss married Olive Hunter in 1920; they had no children.
Bliss was elected to the National Academy of Sciences
(United States) in 1916. He was the American Mathematical Society
's Colloquium Lecturer (1909), Vice President (1911), and President (1921–22). He received the Mathematical Association of America
's first Chauvenet Prize
, 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 among the several states.
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 Weierstrass
. Bliss also strengthened the necessary conditions of Euler
, 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 Weierstrass
, Hilbert
, and Bolza
. Subsequent work on variational problems would strike out in new directions, such as Morse theory
, optimal control
, and dynamic programming
.
Bliss also studied singularities of real transformations in the plane.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician, known for his work on the calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
.
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 ChicagoUniversity of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
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
Mandolin
A mandolin is a musical instrument in the lute family . It descends from the mandore, a soprano member of the lute family. The mandolin soundboard comes in many shapes—but generally round or teardrop-shaped, sometimes with scrolls or other projections. A mandolin may have f-holes, or a single...
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 calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
, via the lecture notes of Weierstrass
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
's 1879 course, and Bolza
Oskar Bolza
Oskar Bolza was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Rhenish Palatinate, and his parents were Luise Koenig and Moritz 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
University of Minnesota
The University of Minnesota, Twin Cities is a public research university located in Minneapolis and St. Paul, Minnesota, United States. It is the oldest and largest part of the University of Minnesota system and has the fourth-largest main campus student body in the United States, with 52,557...
, Bliss spent the 1902-03 academic year at the University of Göttingen, interacting with Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
, David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, Hermann Minkowski
Hermann Minkowski
Hermann Minkowski was a German mathematician of Ashkenazi Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.- Life and work :Hermann Minkowski was born...
, Ernst Zermelo
Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.-Life:He graduated...
, Erhard Schmidt
Erhard Schmidt
Erhard Schmidt was a German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. He was born in Tartu, Governorate of Livonia . His advisor was David Hilbert and he was awarded his doctorate from Georg-August University of Göttingen in 1905...
, Max Abraham
Max Abraham
Max Abraham was a German physicist.Abraham was born in Danzig, Imperial Germany to a family of Jewish merchants. His father was Moritz Abraham and his mother was Selma Moritzsohn. Attending the University of Berlin, he studied under Max Planck. He graduated in 1897...
, and Constantin Carathéodory
Constantin Carathéodory
Constantin Carathéodory was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory...
.
Upon returning to the United States, Bliss taught one year each at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
and the University of Missouri
University of Missouri
The University of Missouri System is a state university system providing centralized administration for four universities, a health care system, an extension program, five research and technology parks, and a publishing press. More than 64,000 students are currently enrolled at its four campuses...
. In 1904, he published two more papers on the calculus of variations in the Transactions of the AMS. Bliss was a Preceptor at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, 1905–08, joining a strong group of young mathematicians that included Luther P. Eisenhart
Luther P. Eisenhart
Luther Pfahler Eisenhart was an American mathematician, best known today for his contributions to semi-Riemannian geometry.-Life:...
, Oswald Veblen
Oswald Veblen
Oswald Veblen 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.-Life:...
, and Robert Lee Moore
Robert Lee Moore
Robert Lee Moore was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics.-Life:...
. 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
E. H. Moore
Eliakim Hastings Moore was an American mathematician.-Life:Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at Yale University, where he was...
's previous leadership, and than it would become under Marshall Stone's and Saunders MacLane's direction after World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. A near-contemporary of Bliss's at Chicago was the algebraist Leonard Dickson.
During World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
, he worked on ballistics
Ballistics
Ballistics is the science of mechanics that deals with the flight, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.A ballistic body is a body which is...
, designing new firing tables for artillery, and lectured on navigation
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
. In 1918, he and Oswald Veblen
Oswald Veblen
Oswald Veblen 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.-Life:...
worked together in the Range Firing Section at the Aberdeen Proving Ground
Aberdeen Proving Ground
Aberdeen Proving Ground is a United States Army facility located near Aberdeen, Maryland, . Part of the facility is a census-designated place , which had a population of 3,116 at the 2000 census.- History :...
, 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
Influenza pandemic
An influenza pandemic is an epidemic of an influenza virus that spreads on a worldwide scale and infects a large proportion of the human population. In contrast to the regular seasonal epidemics of influenza, these pandemics occur irregularly, with the 1918 Spanish flu the most serious pandemic in...
; their two children survived. Bliss married Olive Hunter in 1920; they had no children.
Bliss was elected to the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
(United States) in 1916. He was the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
's Colloquium Lecturer (1909), Vice President (1911), and President (1921–22). He received the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America 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 and applied mathematicians; computer scientists;...
's first Chauvenet Prize
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 on a mathematical topic. The prize is named in...
, 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 among the several states.
Work
Bliss's work on the calculus of variationsCalculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
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
Alfred Clebsch
Rudolf Friedrich Alfred Clebsch was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Berlin. He subsequently taught in Berlin and Karlsruhe...
and Weierstrass
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
. Bliss also strengthened the necessary conditions of Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
, Weierstrass, Legendre
Adrien-Marie Legendre
Adrien-Marie Legendre was a French mathematician.The Moon crater Legendre is named after him.- Life :...
, and Jacobi into sufficient conditions. Bliss set out the canonical formulation and solution of the problem of Bolza
Oskar Bolza
Oskar Bolza was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Rhenish Palatinate, and his parents were Luise Koenig and Moritz Bolza....
with side conditions and variable end-points. Bliss's Lectures more or less constitutes the culmination of the classic calculus of variations of Weierstrass
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
, Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, and Bolza
Oskar Bolza
Oskar Bolza was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Rhenish Palatinate, and his parents were Luise Koenig and Moritz Bolza....
. Subsequent work on variational problems would strike out in new directions, such as Morse theory
Morse theory
In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a differentiable function on a manifold will, in a typical case, reflect...
, optimal control
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
, and dynamic programming
Dynamic programming
In mathematics and computer science, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems which are only slightly smaller and optimal substructure...
.
Bliss also studied singularities of real transformations in the plane.
Publications
- 1933 Algebraic Functions
- 1944 Mathematics for Exterior Ballistics
- 1946 Lectures on the Calculus of Variations