Christian Goldbach: His Discovery Still Challenges Mathematicians Today

Christian Goldbach: His Discovery Still Challenges Mathematicians Today

By Jen Breitegan

Christian Goldbach was an 18th-century Russian mathematician. He famously postulated that every integer greater than 2 can be expressed as the sum of three prime numbers. 

Goldbach’s claim, first proposed in 1742 (and known today as the Goldbach conjecture), has been widely considered true for centuries. However, no mathematician has been able to prove or disprove it—to this day.

Mathematics was just one of Goldbach’s many interests. He was also multilingual and wrote letters and legal documents in German, Latin, French, Italian, and Russian. He served as a professor of mathematics and history and as an administrator at the St. Petersburg Academy of Sciences. 

He also worked in various roles within the Russian government, tutored the Russian royal family, and established an education program for Russian royalty.

Read on to learn more about Christian Goldbach’s life and contributions to mathematics!

Christian Goldbach (1690-1764): Life of a Worldly Scholar & Mathematician

Christian Goldbach was born March 18, 1690 in Königsberg, Prussia. (Today, his birthplace is known as Kaliningrad, Russia.) His father was the pastor of a local Protestant church.

Goldbach studied law, medicine, and mathematics at the Royal Albertus University in Königsberg. He then spent four years traveling throughout Europe. He met and exchanged ideas with leading scientists while visiting England, France, Italy, Holland, and the German states. 

Goldbach met and befriended several noted mathematicians during his travels. These included Nicolaus and Daniel Bernoulli, who influenced his desire to further his studies in the field.

Daniel Bernoulli's letter to Goldbach, via Wikimedia

Related: The Bernoullis: Mathematical Genius and Serious Family Drama

Goldbach returned home to Königsberg in 1724. He remained interested in the study of mathematics. He read articles written by other famous mathematicians and produced his own works. His efforts earned him a respected position as a professor of history and mathematics at the St. Petersburg Academy of Sciences a year later.

During his early years at the Academy of Sciences, Goldbach met the renowned mathematician Leonhard Euler. The two men became friends and exchanged letters for thirty-five years. Euler would later play an important role in Goldbach’s enduring mathematics legacy.

Leonhard Euler: Lifelong Curiosity

Goldbach moved to Moscow in 1729 to serve as a tutor to Tsar Peter II. He returned to the Academy of Sciences in 1732, where he was responsible for day-to-day administration. 

Goldbach’s position at the Academy and his ability to write in several languages earned him increasing importance within the Russian government. He was appointed to serve in the Ministry of Foreign Affairs in 1740, but he always remained interested in mathematics.

The Goldbach Conjecture

Letter from Christian Goldbach to Leonhard Euler, via Wikimedia

As previously mentioned, Goldbach and Euler met before Goldbach’s 1729 move to Moscow and began a decades-long correspondence. 

In 1742, Goldbach sent a letter to Euler claiming that every integer greater than 2 can be expressed as a sum of three prime numbers. (In Goldbach’s day, the number 1 was considered a prime number; it is not considered a prime number today.)

This claim became known as the Goldbach conjecture. In mathematics, a conjecture is a proposition that appears correct but lacks definitive proof.

The example 3 = 1+1+1 fits Goldbach’s original conjecture. 

The modern-day Goldbach conjecture, which does not count 1 as a prime number, states every even integer greater than 2 can be expressed as a sum of two prime numbers

For example, 4 = 2+2 

(The number 2 is a prime number.)

Euler responded to Goldbach by saying that he believed his conjecture was true, though he too was unable to prove it.

What neither of these men could have known is that Goldbach’s conjecture would continue to remain unproven. It would challenge and confound mathematicians for centuries.

Today, Goldbach’s conjecture remains one of the best-known unsolved mathematics problems. 

The first noted breakthrough occurred in 1930. Mathematician Lev Genrikhovich Shnirelman of the Soviet Union proved that every natural number can be expressed as the sum of a finite number of prime numbers.

Publisher Faber and Faber offered a million-dollar prize in 2000 to anyone who could prove the Goldbach conjecture. (The proof would also need acceptance by fellow mathematicians.) The offer remained open for two years, but no one claimed the prize.

In 2012, a professor from Portugal named Tomás Oliviera e Silva confirmed the conjecture is true for integers less than 4x1018.

Mathematician Harald Andres Helfgott proved in 2013 that all odd numbers greater than 7 can be expressed as the sum of three odd prime numbers. 

However, to date, no one has been able to prove the original conjecture using an infinite number of possibilities.

Because the Goldbach conjecture remains unproven for all numbers, it cannot be considered a theorem. It’s still widely considered to be true.

Goldbach’s Russian Royal Family Ties

Russian ruler Peter the Great and his wife Catherine were instrumental in the creation of the Academy of Sciences in St. Petersburg. Goldbach served as the recording secretary as well as professor when the Academy opened in 1725.

In 1728, Goldbach was appointed to be a tutor for Peter II. The young son of Peter the Great had just ascended the throne at the age of 11. Goldbach moved to Moscow with Peter II and the royal court.

Peter II died three years later from smallpox and Anna Ivanova became the empress of Russia. Anna moved the court from Moscow back to St. Petersburg. Goldbach moved back as well and took an administrative position at the Academy of Sciences. He also began working for the Russian government.

Goldbach ceased his work for the Academy in 1740. He then focused full-time on his position in the Ministry of Foreign Affairs. His influence and respect grew until he was awarded the position of privy counselor in 1760. (A privy counselor is part of a committee of close advisors to a monarch.)

Goldbach was tasked with establishing the guidelines for an education program for the royal family. His guidelines remained in effect for the next century.

Christian Goldbach died in 1764 in Moscow at the age of 74, but his legacy and contribution to mathematics live on.

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