Editing Christian Goldbach (section)

==Contributions==
[[File:Letter Goldbach-Euler.jpg|300px|thumb|right|Letter from Goldbach to [[Euler]], 1742]]
Goldbach is most noted for his correspondence with [[Leibniz]], [[Euler]], and [[Daniel Bernoulli|Bernoulli]], especially in his 1742 letter to Euler stating his [[Goldbach's conjecture]]. He also studied and proved some theorems on [[perfect power]]s, such as the [[Goldbach–Euler theorem]], and made several notable contributions to [[mathematical analysis|analysis]].<ref name="element">{{cite book |last=Rosen |first=Kenneth H. |title=Elementary Number Theory, Fifth Edition |publisher=Addison-Wesley |year=2004 |isbn=0-321-23707-2}}</ref> He also proved a [[Fermat number#Basic properties|result]] concerning [[Fermat number]]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.<ref name=":3" /> Goldbach and Euler's friendship survived Goldbach's move to Moscow in 1728 and communication ensued.<ref name=":4" /> Their correspondence spanned 196 letters over 35 years written in Latin, German, and French.<ref name=":2" /> These letters spanned a wide range of topics, including various mathematics topics.<ref name=":3" /> Goldbach was the leading influence on Euler's interest and work in number theory.<ref name=":4" /> Most of the letters discuss Euler's research in number theory as well as differential calculus.<ref name=":4" /> Until the late 1750s, Euler's correspondence on his number theory research was almost exclusively with Goldbach.<ref name=":4" />
[[File:Leonhard Euler - Jakob Emanuel Handmann (Kunstmuseum Basel).jpg|thumb|Portrait of Leonhard Euler, one of the premier mathematicians ever]]
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.<ref name=":4" /> Ensuingly, Euler outlined the solutions to Goldbach.<ref name=":4" /> Also, in 1729 Goldbach closely approximated the [[Basel problem]], which prompted Euler's interest and concurring breakthrough solution.<ref name=":4" /> Goldbach, through his letters, kept Euler focused on number theory in the 1730s by discussing [[Fermat's conjecture]] with Euler.<ref name=":4" /> Euler subsequently offered a proof to the conjecture, crediting Goldbach with introducing him to the subfield.<ref name=":4" /> Euler proceeded to write 560 writings, published posthumously in four volumes of [[Opera Omnia Leonhard Euler|Opera omnia]], with Goldbach's influence guiding some of the writings.<ref name=":4" /> 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.<ref>{{Cite web |title=Goldbach, Christian|work=Complete Dictionary of Scientific Biography|volume=5|publisher=Charles Scribner's Sons|year=2008|pages=448–451|via=Gale In Context: U.S. History|url=https://link.gale.com/apps/doc/CX2830901675/UHIC?u=mlin_oweb&sid=bookmark-UHIC&xid=a018c1f5|access-date=2022-10-20 }}</ref>