George William Hill (March 3, 1838 – April 16, 1914) was an American

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...

and

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, structure, space, models, and change. History On ...

. Working independently and largely in isolation from the wider scientific community, he made major contributions to

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, ...

and to the theory of

ordinary differential equations In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast ...

. The importance of his work was explicitly acknowledged by

Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "Th ...

in 1905. In 1909 Hill was awarded the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

Copley Medal The Copley Medal is an award given by the Royal Society, for "outstanding achievements in research in any branch of science". It alternates between the physical sciences or mathematics and the biological sciences. Given every year, the medal is t ...

, "on the ground of his researches in mathematical astronomy". Today, he is chiefly remembered for the

Hill differential equation In mathematics, the Hill equation or Hill differential equation is the second-order linear ordinary differential equation : \frac + f(t) y = 0, where f(t) is a periodic function by minimal period \pi . By these we mean that for all t :f(t+\ ...

Early life and education

Hill was born in

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

to painter and engraver

John William Hill John William Hill or often J.W. Hill (January 13, 1812 – September 24, 1879) was a British-born American artist working in watercolor, gouache, lithography, and engraving. Hill's work focused primarily upon natural subjects including landsc ...

and his wife, Catherine Smith. He moved to

West Nyack West or Occident is one of the four cardinal directions or points of the compass. It is the opposite direction from east and is the direction in which the Sun sets on the Earth. Etymology The word "west" is a Germanic word passed into some R ...

with his family when he was eight years old. After high school, Hill attended

Rutgers College Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and was a ...

, where he became interested in mathematics. At Rutgers, Hill came under the influence of professor Theodore Strong, who was a friend of pioneering US mathematician and astronomer

Nathaniel Bowditch Nathaniel Bowditch (March 26, 1773 – March 16, 1838) was an early American mathematician remembered for his work on ocean navigation. He is often credited as the founder of modern maritime navigation; his book '' The New American Practical Navi ...

. Strong encouraged Hill to read the great works on

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

Sylvestre Lacroix Sylvestre can refer to: People Surname Given name Middle name * Carlos Sylvestre Begnis (1903–1980), Argentine medical doctor and politician * Philippe Sylvestre Dufour (1622–1687), French Protestant apothecary, banker, collector, an ...

and Adrien-Marie Legendre, as well as the treatises on

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objec ...

and mathematical astronomy by

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaPierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarize ...

, Siméon Denis Poisson, and Gustave de Pontécoulant. Hill graduated from Rutgers College in 1859, with a

Bachelor of Arts Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

degree. In that same year he published his first scientific paper, on the geometrical curve of a

drawbridge A drawbridge or draw-bridge is a type of moveable bridge typically at the entrance to a castle or tower surrounded by a moat. In some forms of English, including American English, the word ''drawbridge'' commonly refers to all types of movea ...

. Two years later he earned a prize from the ''Runkle Mathematical Monthly'' for his work on the mathematical theory of the

figure of the Earth Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxim ...

. In the early 1860s, Hill began studying the works on

lunar theory Lunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbations) in the Moon's motion, and many attempts have been made to account for them. After centuries of being problematic, lunar motion can now ...

by Charles-Eugène Delaunay and Peter Andreas Hansen, which would inspire and motivate most of Hill's subsequent research. In 1861, Hill was hired by John Daniel Runkle to work in the

United States Naval Observatory United States Naval Observatory (USNO) is a scientific and military facility that produces geopositioning, navigation and timekeeping data for the United States Navy and the United States Department of Defense. Established in 1830 as the Depo ...

's Nautical Almanac Office, based in

Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston, ...

. In 1862 Rutgers awarded Hill a

Master of Arts A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Tho ...

degree. Hill lived for a while in Cambridge and later in Washington, D.C., but he preferred to carry out his mathematical work in his family farm in West Nyack, to which he retired for good after 1892.

Work on mathematical astronomy

Hill's mature work focused on the mathematics of the three-body problem, and later the four-body problem, to calculate the orbits of the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

around the

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...

, as well as that of

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...

s around the Sun. Hill was able to quantify the gravitational sphere of influence of an astronomical body in the presence of other heavy bodies, by introducing the concept of the zero-velocity surface. The space within this surface is now known as the Hill sphere and it corresponds to the region around a body within which it may capture satellites. In 1878, Hill provided the first complete mathematical solution to the problem of the apsidal precession of the Moon's orbit around the Earth, a difficult problem in

first raised in

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...

's '' Principia Mathematica'' of 1687. This same work also introduced what is now known in physics and mathematics as the "

", which describes the behavior of a parametric oscillator and which made an important contribution to the mathematical

Floquet theory Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form :\dot = A(t) x, with \displaystyle A(t) a piecewise continuous periodic function ...

Influence and recognition

Hill's work attracted the attention of the international scientific community, and in 1894 he was chosen as president of 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, meeting ...

, serving for two years. Hill lectured at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

from 1898 to 1901, but he attracted few students and he ultimately chose to return his salary and to continue working alone in his home in West Nyack, rather than within academia. Hill's ''Collected Works'' were published in 1905-07 by the Carnegie Institution for Science, with a 12-page introduction by the eminent French mathematician and theoretical physicist

. In that introduction, Poincaré said that, in Hill's 1878 article titled "Researches in the lunar theory", "one is allowed to perceive the germ of most of the progress that elestial mechanicshas made ever since". Of Hill's isolation from the academic community, Poincaré declared that George William Hill was elected as a foreign member of the

of London in 1902. He also became a member of the

Royal Society of Edinburgh The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

in 1908, and of the scientific academies of Belgium (1909), Norway (1910), Sweden (1913), and

the Netherlands ) , anthem = ( en, "William of Nassau") , image_map = , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of the Netherlands , established_title = Before independence , established_date = Spanish Netherl ...

(1914). His later years were marked by poor health, and he died in West Nyack in 1914. He never married and had no children.

Honors

* Gold Medal of the Royal Astronomical Society (1887) * Damoiseau Prize from the

Institut de France The (; ) is a French learned society, grouping five , including the Académie Française. It was established in 1795 at the direction of the National Convention. Located on the Quai de Conti in the 6th arrondissement of Paris, the institut ...

(1898) *

of the

of London (1909) * Bruce Medal of the Astronomical Society of the Pacific (1909) * Hill crater on the

Asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...

1642 Hill * ''Hill Center for the Mathematical Sciences'' at Rutgers University's Busch Campus

References

Bibliography

The collected mathematical works of George William Hill vol. 1
(Carnegie Institution of Washington, 1905–1907)
The collected mathematical works of George William Hill vol. 2
(Carnegie Institution of Washington, 1905–1907)
The collected mathematical works of George William Hill vol. 3
entitled ''A New Theory of Jupiter and Saturn'', (Carnegie Institution of Washington, 1905–1907)
The collected mathematical works of George William Hill vol. 4
(Carnegie Institution of Washington, 1905–1907)

External links

* *
National Academy of Sciences Biographical Memoir
{{DEFAULTSORT:Hill, George William 1838 births 1914 deaths American astronomers 19th-century American mathematicians 20th-century American mathematicians Recipients of the Bruce Medal Recipients of the Copley Medal Members of the Royal Netherlands Academy of Arts and Sciences Members of the Royal Swedish Academy of Sciences Recipients of the Gold Medal of the Royal Astronomical Society Foreign Members of the Royal Society Presidents of the American Mathematical Society Rutgers University alumni