Christian Goldbach ( , ; 18 March 1690 – 20 November 1764) was a Prussian
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 ...
connected with some important research mainly in
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
; he also studied
law
Law is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior, with its precise definition a matter of longstanding debate. It has been variously described as a science and as the ar ...
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.
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
In many countries, the ministry of foreign affairs (abbreviated as MFA or MOFA) is the highest government department exclusively or primarily responsible for the state's foreign policy and relations, diplomacy, bilateral, and multilateral r ...
until his death in 1764.
He is remembered today for
Goldbach's conjecture
Goldbach's conjecture is one of the oldest and best-known list of unsolved problems in mathematics, unsolved problems in number theory and all of mathematics. It states that every even and odd numbers, even natural number greater than 2 is the ...
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= + \c ...
.
He had a close friendship with famous mathematician
Leonhard Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
, serving as inspiration for Euler's mathematical pursuits.
Biography
Early life
Born in the
Duchy of Prussia
The Duchy of Prussia (, , ) or Ducal Prussia (; ) was a duchy in the region of Prussia established as a result of secularization of the Monastic Prussia, the territory that remained under the control of the State of the Teutonic Order until t ...
's capital
Königsberg
Königsberg (; ; ; ; ; ; , ) is the historic Germany, German and Prussian name of the city now called Kaliningrad, Russia. The city was founded in 1255 on the site of the small Old Prussians, Old Prussian settlement ''Twangste'' by the Teuton ...
, 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 trips 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 Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...
,
Leonhard Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
, and
Nicholas I Bernoulli. These acquaintances started Goldbach's interest in mathematics.
He briefly attended
Oxford University
The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...
in 1713 and, while he was there, Goldbach studied mathematics with
John Wallis
John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
Between 1643 and 1689 Wallis served as chief cryptographer for Parliament and, later, the royal court. ...
and
Isaac Newton
Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
.
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 became acquainted with
Georg Bernhard Bilfinger 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

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 polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
,
Daniel Bernoulli
Daniel Bernoulli ( ; ; – 27 March 1782) was a Swiss people, Swiss-France, French mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applicati ...
,
Johann Bernoulli
Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...
, 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 ''Encyclopé ...
.
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 1730s.
Russian government work
In 1728, when
Peter II became
Tsar
Tsar (; also spelled ''czar'', ''tzar'', or ''csar''; ; ; sr-Cyrl-Latn, цар, car) is a title historically used by Slavic monarchs. The term is derived from the Latin word '' caesar'', which was intended to mean ''emperor'' in the Euro ...
of Russia, Goldbach became Peter II and
Anna'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
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
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.
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 retain his influence in court after the death of Anna and the rule of
Empress Elizabeth.
In 1742 he entered the
Russian Ministry of Foreign Affairs, stepping away 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 in place for 100 years.
He died on 20 November 1764, aged 74, in
Moscow
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...
.
Christian Goldbach was
multilingual
Multilingualism is the use of more than one language, either by an individual speaker or by a group of speakers. When the languages are just two, it is usually called bilingualism. It is believed that multilingual speakers outnumber monolin ...
– he wrote a diary in
German
German(s) may refer to:
* Germany, the country of the Germans and German things
**Germania (Roman era)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizenship in Germany, see also Ge ...
and
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 ...
, 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, a Romance ethnic group related to or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance languag ...
and for official documents he used Russian, German and Latin.
Contributions

Goldbach is most noted for his correspondence with
Leibniz
Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many ...
,
Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
, and
Bernoulli, especially in his 1742 letter to Euler stating his
Goldbach's conjecture
Goldbach's conjecture is one of the oldest and best-known list of unsolved problems in mathematics, unsolved problems in number theory and all of mathematics. It states that every even and odd numbers, even natural number greater than 2 is the ...
. 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= + \c ...
, 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 (38 ...
.
He also proved a
result
A result (also called upshot) is the outcome or consequence of a sequence of actions or events. Possible results include gain, injury, value, and victory. Some types of results include the outcome of an action, the final value of a calculation ...
concerning
Fermat number
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a natural number, positive integer of the form:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers ...
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 1750s, Euler's correspondence on his number theory research was almost exclusively with Goldbach.
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 1730s by discussing
Fermat's conjecture
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than . The cases and have been ...
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, 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 mathematicians 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''
See also
*
Goldbach's comet
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, on the grounds of a urban arboretum. It claims to be the "largest independently funded public library of sc ...
.
{{DEFAULTSORT:Goldbach, Christian
1690 births
1764 deaths
University of Königsberg alumni
Full members of the Saint Petersburg Academy of Sciences
18th-century German mathematicians
German number theorists
Scientists from Königsberg
People from the Duchy of Prussia
Mathematicians from the Kingdom of Prussia