Carl Wolfgang Benjamin Goldschmidt (4 August 1807 – 15 February 1851) was a German

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

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, mathematical structure, structure, space, Mathematica ...

, and

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...

descent who was a professor of

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

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 ...

. He is also known as Benjamin Goldschmidt, C. W. B. Goldschmidt, Carl Goldschmidt, and Karl Goldschmidt.

Mathematical works

A student of

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and ...

and an assistant to Gauss at the university

observatory An observatory is a location used for observing terrestrial, marine, or celestial events. Astronomy, climatology/meteorology, geophysics, oceanography and volcanology are examples of disciplines for which observatories have been constructed. Th ...

, Goldschmidt frequently collaborated with Gauss on various mathematical and scientific works. Goldschmidt was in turn a professor of Gauss's protégé

Bernhard Riemann Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the f ...

. Data gathered by Gauss and Goldschmidt on the growth of the

logarithmic integral In mathematics, the logarithmic integral function or integral logarithm li(''x'') is a special function. It is relevant in problems of physics and has number theoretic significance. In particular, according to the prime number theorem, it is a ...

compared to the distribution of prime numbers was cited by Riemann in "

On the Number of Primes Less Than a Given Magnitude " die Anzahl der Primzahlen unter einer gegebenen " (usual English translation: "On the Number of Primes Less Than a Given Magnitude") is a seminal 9-page paper by Bernhard Riemann published in the November 1859 edition of the ''Monatsberichte ...

", Riemann's seminal paper on the

prime-counting function In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number . It is denoted by (unrelated to the number ). A symmetric variant seen sometimes is , which is equal ...

. In 1831, Goldschmidt wrote a mathematical treatise in

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

, "Determinatio superficiei minimae rotatione curvae data duo puncta jungentis circa datum axem ortae" ("Determination of the surface-minimal rotation curve given two joined points about a given axis of origin"). The paper dealt with the problem in 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 ...

of determining the minimal surface of revolution, the

surface of revolution A surface of revolution is a Surface (mathematics), surface in Euclidean space created by rotating a curve (the ''generatrix'') one full revolution (unit), revolution around an ''axis of rotation'' (normally not Intersection (geometry), intersec ...

of the planar

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

between two given

points A point is a small dot or the sharp tip of something. Point or points may refer to: Mathematics * Point (geometry), an entity that has a location in space or on a plane, but has no extent; more generally, an element of some abstract topologica ...

which minimizes

surface area The surface area (symbol ''A'') of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the d ...

Solutions Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solutio ...

to the problem exist which are not continuous; such discontinuous solutions are known as Goldschmidt solutions in honor of Goldschmidt's discovery of them.

Physics works

In 1834, Goldschmidt co-authored, in German, the textbook ''Lehrbuch der analytischen Optik'' (''Textbook of Analytical

Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

'') with J. C. Eduard Schmidt. Together with Gauss and

Wilhelm Eduard Weber Wilhelm Eduard Weber ( ; ; 24 October 1804 – 23 June 1891) was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph. Biography Early years Weber was born in Schlossstrasse in Witte ...

, Goldschmidt published in 1840 ''Atlas des Erdmagnetismus: nach den Elementen der Theorie entworfen'' (''

Atlas An atlas is a collection of maps; it is typically a bundle of world map, maps of Earth or of a continent or region of Earth. Advances in astronomy have also resulted in atlases of the celestial sphere or of other planets. Atlases have traditio ...

of Geomagnetism: According to the Elements of the Theory of Design''), a series of

magnetic Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, m ...

map A map is a symbolic depiction of interrelationships, commonly spatial, between things within a space. A map may be annotated with text and graphics. Like any graphic, a map may be fixed to paper or other durable media, or may be displayed on ...

s. In 1845, Goldschmidt published, also in German, a book on

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

, ''Untersuchungen über die magnetische Declination in Göttingen'' (''Studies of the

Magnetic Declination Magnetic declination (also called magnetic variation) is the angle between magnetic north and true north at a particular location on the Earth's surface. The angle can change over time due to polar wandering. Magnetic north is the direction th ...

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

'').

Personal life

Goldschmidt, who suffered from an enlargement of the heart, died in his sleep and was found on the morning of 15 February 1851.

References

{{DEFAULTSORT:Goldschmidt, Carl Wolfgang Benjamin 1807 births 1851 deaths 19th-century German astronomers 19th-century German mathematicians 19th-century German physicists German number theorists Academic staff of the University of Göttingen Jewish German physicists 19th-century German Jews People from the Kingdom of Hanover