Christian Goldbach (; ; 18 March 1690 – 20 November 1764) was a German
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 ...
connected with some important research mainly in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...
; he also studied
law
Law is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior,Robertson, ''Crimes against humanity'', 90. with its precise definition a matter of longstanding debate. It has been vario ...
and took an interest in and a role in the Russian court.
After traveling around Europe in his early life, he landed in Russia in 1725 as a professor at the newly founded
Saint Petersburg Academy of Sciences
The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...
.
Goldbach jointly led the Academy in 1737.
However, he relinquished duties in the Academy in 1742 and worked in the Russian
Ministry of Foreign Affairs until his death in 1764.
He is remembered today for
Goldbach's conjecture and the
Goldbach–Euler Theorem
In mathematics, the Goldbach–Euler theorem (also known as Goldbach's theorem), states that the sum of 1/(''p'' − 1) over the set of perfect powers ''p'', excluding 1 and omitting repetitions, converges to 1:
:\sum_^\frac= + \cd ...
.
He had a close friendship with famous mathematician
Leonard 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 ...
, serving as inspiration for Euler's mathematical pursuits.
Biography
Early life
Born in the
Duchy of Prussia
The Duchy of Prussia (german: Herzogtum Preußen, pl, Księstwo Pruskie, lt, Prūsijos kunigaikštystė) or Ducal Prussia (german: Herzogliches Preußen, link=no; pl, Prusy Książęce, link=no) was a duchy in the region of Prussia establish ...
's capital
Königsberg
Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was name ...
, part of
Brandenburg-Prussia, Goldbach was the son of a pastor.
He studied at the
Royal Albertus University.
After finishing his studies he went on long educational voyages from 1710 to 1724 through Europe, visiting other German states, England, The Netherlands, Italy, and France, meeting with many famous mathematicians, such as
Gottfried Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...
,
Leonhard 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 ...
, and
Nicholas I Bernoulli
Nicolaus Bernoulli (also spelled Nicolas or Nikolas; 21 October 1687, Basel – 29 November 1759, Basel) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.
Biography
He was the son of Nicolaus Berno ...
. These acquaintances started Goldbach's interest in mathematics.
He briefly attended
Oxford University
Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to th ...
in 1713 and, while he was there, Goldbach learned mathematics from mathematical scholars
John Wallis and
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the grea ...
.
Also, Goldbach's travels fostered his interest in philology, archaeology, metaphysics, ballistics, and medicine.
Between 1717 and 1724, Goldbach published his first few papers which, while minor, credited his mathematical ability. Back in Königsberg he got acquainted with
Georg Bernhard Bilfinger
Georg Bernhard Bilfinger (23 January 1693 – 18 February 1750), German philosopher, mathematician and statesman, son of a Lutheran minister.
Life
He was born at Cannstatt in the Duchy of Württemberg.
As a boy he showed great aptitude for stu ...
and
Jakob Hermann
Jakob Hermann (16 July 1678 – 11 July 1733) was a mathematician who worked on problems in classical mechanics. He is the author of ''Phoronomia'', an early treatise on Mechanics in Latin, which has been translated by Ian Bruce in 2015-16. In 172 ...
.
Saint Petersburg Academy of Sciences
![Russian Academy of Sciences SPB](https://upload.wikimedia.org/wikipedia/commons/4/40/Russian_Academy_of_Sciences_SPB.jpg)
Goldbach followed Bilfinger and Hermann to the newly opened St. Petersburg Academy of Sciences in 1725.
Christian Wolff had invited and had written recommendations for all the Germans who traveled to Saint Petersburg for the academy except Goldbach.
Goldbach wrote to the president-designate of the academy, petitioning for a position in the academy, using his past publications and knowledge in medicine and law as qualifications.
Goldbach was then hired to a five-year contract as a professor of mathematics and historian of the academy.
As historian of the academy, he recorded each academy meeting from the opening of the school in 1725 until January 1728.
Goldbach worked with famous mathematicians like
Leonhard 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 ...
,
Daniel Bernoulli,
Johann Bernoulli
Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educating Le ...
, and
Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the '' Encyclopéd ...
.
Goldbach also played a part in Euler's decision to academically pursue mathematics instead of medicine, cementing mathematics as the premier research field of the academy in the 1730's.
Russian Government Work
In 1728, when
Peter II became
Tsar
Tsar ( or ), also spelled ''czar'', ''tzar'', or ''csar'', is a title used by East and South Slavic monarchs. The term is derived from the Latin word ''caesar'', which was intended to mean "emperor" in the European medieval sense of the ter ...
of Russia, Goldbach became Peter II and
Anna
Anna may refer to:
People Surname and given name
* Anna (name)
Mononym
* Anna the Prophetess, in the Gospel of Luke
* Anna (wife of Artabasdos) (fl. 715–773)
* Anna (daughter of Boris I) (9th–10th century)
* Anna (Anisia) (fl. 1218 to 12 ...
's, Peter II's cousin, tutor.
Peter II moved the Russian court from St. Petersburg to Moscow in 1729, so Goldbach followed him to Moscow.
Goldbach started a correspondence with
Euler in 1729, in which some of Goldbach's most important mathematics contributions can be found.
Upon
Peter II's death in 1730, Goldbach stopped teaching but continued to assist
Empress Anna
Anna Ioannovna (russian: Анна Иоанновна; ), also russified as Anna Ivanovna and sometimes anglicized as Anne, served as regent of the duchy of Courland from 1711 until 1730 and then ruled as Empress of Russia from 1730 to 1740. Much ...
.
In 1732, Goldbach returned to the St. Petersburg Academy of Sciences and stayed in the Russian government when Anna moved the court back to St. Petersburg.
Upon return to the academy, Goldbach was named corresponding secretary.
With Goldbach's return, his friend Euler continued his teaching and research at the academy as well.
Then, in 1737, Goldbach and J.D. Schumacher took over the administration of the academy.
Also, Goldbach took on duty in Russian court under Empress Anna.
He managed to retained his influence in court after the death of Anna and the rule of
Empress Elizabeth
Elizabeth Petrovna (russian: Елизаве́та (Елисаве́та) Петро́вна) (), also known as Yelisaveta or Elizaveta, reigned as Empress of Russia from 1741 until her death in 1762. She remains one of the most popular List of ...
.
In 1742 he entered the
Russian Ministry of Foreign Affairs
The Ministry of Foreign Affairs of the Russian Federation (MFA Russia; russian: Министерство иностранных дел Российской Федерации, МИД РФ) is the central government institution charged with lea ...
, stepping way from the academy once more.
Goldbach was gifted land and increased salary for his good work and rise in the Russian government.
In 1760, Goldbach created new guidelines for the education of the royal children which would remain for 100 years.
He died on 20 November 1764, at age of 74, in
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 millio ...
.
Christian Goldbach was
multilingual
Multilingualism is the use of more than one language, either by an individual speaker or by a group of speakers. It is believed that multilingual speakers outnumber monolingual speakers in the world's population. More than half of all E ...
– he wrote a diary in
German
German(s) may refer to:
* Germany (of or related to)
** Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ge ...
and
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 ...
, his letters were written in German, Latin,
French, and
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
and for official documents he used Russian, German and Latin.
Contributions
![Letter Goldbach-Euler](https://upload.wikimedia.org/wikipedia/commons/5/5f/Letter_Goldbach-Euler.jpg)
Goldbach is most noted for his correspondence with
Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of ma ...
,
Euler, and
Bernoulli Bernoulli can refer to:
People
*Bernoulli family of 17th and 18th century Swiss mathematicians:
** Daniel Bernoulli (1700–1782), developer of Bernoulli's principle
**Jacob Bernoulli (1654–1705), also known as Jacques, after whom Bernoulli numbe ...
, especially in his 1742 letter to Euler stating his
Goldbach's conjecture. He also studied and proved some theorems on
perfect power
In mathematics, a perfect power is a natural number that is a product of equal natural factors, or, in other words, an integer that can be expressed as a square or a higher integer power of another integer greater than one. More formally, ''n'' ...
s, such as the
Goldbach–Euler theorem
In mathematics, the Goldbach–Euler theorem (also known as Goldbach's theorem), states that the sum of 1/(''p'' − 1) over the set of perfect powers ''p'', excluding 1 and omitting repetitions, converges to 1:
:\sum_^\frac= + \cd ...
, and made several notable contributions to
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 ...
.
He also proved a
result
A result (also called upshot) is the final consequence of a sequence of actions or events expressed qualitatively or quantitatively. Possible results include advantage, disadvantage, gain, injury, loss, value and victory. There may be a range ...
concerning
Fermat number
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form
:F_ = 2^ + 1,
where ''n'' is a non-negative integer. The first few Fermat numbers are:
: 3, 5, 17, 257, 65537, 42949672 ...
s that is called Goldbach's theorem.
Impact on Euler
It is Goldbach and Euler's correspondence that contains some of Goldbach's most important contributions to mathematics, specifically number theory.
Goldbach and Euler's friendship survived Goldbach's move to Moscow in 1728 and communication ensued.
Their correspondence spanned 196 letters over 35 years written in Latin, German, and French.
These letters spanned a wide range of topics, including various mathematics topics.
Goldbach was the leading influence on Euler's interest and work in number theory.
Most of the letters discuss Euler's research in number theory as well as differential calculus.
Until the late 1750's, Euler's correspondence on his number theory research was almost exclusively with Goldbach.
![Leonhard Euler - edit1](https://upload.wikimedia.org/wikipedia/commons/c/c2/Leonhard_Euler_-_edit1.jpg)
Goldbach's earlier mathematical work and ideas in letters to Euler directly influenced some of Euler's work. In 1729, Euler solved two problems pertaining to sequences which had stumped Goldbach.
Ensuingly, Euler outlined the solutions to Goldbach.
Also, in 1729 Goldbach closely approximated the
Basel problem
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 ...
, which prompted Euler's interest and concurring breakthrough solution.
Goldbach, through his letters, kept Euler focused on number theory in the 1730's by discussing
Fermat's conjecture with Euler.
Euler subsequently offered a proof to the conjecture, crediting Goldbach with introducing him to the subfield.
Euler proceeded to write 560 writings, published posthumously in four volumes of
Opera omnia
The complete works of an artist, writer, musician, group, etc., is a collection of all of their cultural works. For example, ''Complete Works of Shakespeare'' is an edition containing all the plays and poems of William Shakespeare. A ''Complete W ...
, with Goldbach's influence guiding some of the writings.
Goldbach's famous conjecture and his writings with Euler prove him to be one of a handful of mathematics who understood complex number theory in light of Fermat's revolutionary ideas on the topic.
Works
* (1729) ''De transformatione serierum''
* (1732) ''De terminis generalibus serierum''
References
External links
*
*
Electronic copies of Euler's correspondence with Goldbach''Neuester Himmels-Atlas'', 1799- Full digital facsimile,
Linda Hall Library
The Linda Hall Library is a privately endowed American library of science, engineering and technology located in Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest independently funded public library of scien ...
.
{{DEFAULTSORT:Goldbach, Christian
1690 births
1764 deaths
University of Königsberg alumni
Full members of the Saint Petersburg Academy of Sciences
18th-century German mathematicians
Number theorists
Scientists from Königsberg
People from the Duchy of Prussia