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 their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

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 ...

, 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 caus ...

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

descent who was a professor of

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

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 ...

. He is also known as Benjamin Goldschmidt, C. W. B. Goldschmidt, Carl Goldschmidt, and Karl Goldschmidt. Goldschmidt, who suffered from an enlargement of the heart, died in his sleep and was found on the morning of 15 February 1851.

Mathematical works

A student of

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

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, geophysical, oceanography and volcanology are examples of disciplines for which observatories have been constructed. His ...

, 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 (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rig ...

. 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 In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying ...

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 seminal9-page paper by Bernhard Riemann published in the November 1859 edition of the ''Monatsberichte der K ...

", 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 ''x''. It is denoted by (''x'') (unrelated to the number ). History Of great interest in number theory is t ...

. In 1831, Goldschmidt wrote a mathematical treatise in

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

, "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 functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

of determining the

minimal surface of revolution In mathematics, a minimal surface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose boundary is the axis of revolution of the surface. It is generated by a curve that lies in t ...

, the

surface of revolution A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation. Examples of surfaces of revolution generated by a straight line are cylindrical and conical surfaces depending on ...

of the

planar Planar is an adjective meaning "relating to a plane (geometry)". Planar may also refer to: Science and technology * Planar (computer graphics), computer graphics pixel information from several bitplanes * Planar (transmission line technologies), ...

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

between two given points which minimizes surface area.

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 * Soluti ...

to the problem exist which are not

continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...

; such

discontinuous Continuous functions are of utmost importance in mathematics, functions and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of a ...

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 instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...

'') 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 of Wilhelm Early years Weber was born in Schlossstrasse in ...

, 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 maps of Earth or of a region of Earth. Atlases have traditionally been bound into book form, but today many atlases are in multimedia formats. In addition to presenting geographic ...

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

magnetic Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particle ...

map A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...

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. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

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

Magnetic Declination Magnetic declination, or magnetic variation, is the angle on the horizontal plane between magnetic north (the direction the north end of a magnetized compass needle points, corresponding to the direction of the Earth's magnetic field lines) and ...

Göttingen Göttingen (, , ; nds, Chöttingen) 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. At the end of 2019, t ...

'').

References

{{DEFAULTSORT:Goldschmidt, Carl Wolfgang Benjamin 1807 births 1851 deaths 19th-century German astronomers 19th-century German mathematicians 19th-century German physicists Number theorists University of Göttingen faculty Jewish physicists 19th-century German Jews