Christian Goldbach

Christian Goldbach (March 18, 1690 - November 20, 1764) was a Prussian mathematician, born in Königsberg, Prussia (now Kaliningrad, Russia), the son of a pastor. He studied law, languages and mathematics. He made several trips through Europe and met several famous mathematicians, such as Gottfried Leibniz, Leonhard Euler, and Daniel Bernoulli.

In 1725 he became a historian and professor of mathematics in Saint Petersburg. Three years later he moved to Moscow to work for Tsar Peter II of Russia.

Contributions

He made a proof regarding the infinite number of prime numbers. Today he is known for the so-called Goldbach conjecture or Goldbach's strong conjecture, which states that all even numbers greater than 2 can be represented as the sum of two prime numbers. This is now known to be true for all numbers less than a trillion, ie 10¹⁸. This conjecture was found in a letter Goldbach sent to Euler in 1742. The great Swiss mathematician Euler failed to prove or disprove the result of this theorem, and today, almost 300 years later, no one has given a fully conclusive formal proof of it. the veracity of the result and no counterexample has been found (that is, an even number that cannot be written as the sum of two prime numbers).^{[citation required]}

Goldbach also studied and proved several theorems about perfect powers.

Goldbach's Weak Conjecture

There is another Goldbach conjecture, called the weak Goldbach conjecture, which says the following:

Every odd number greater than 7 can be written as a sum of three odd prime numbers.

Therefore, the statement can be written as follows:

Every odd number greater than 5 can be written as the sum of three prime numbers.

This conjecture was solved in 2013 by the Peruvian mathematician Harald Andrés Helfgott, who managed to prove that for any odd number greater than 10³⁰ the conjecture is true. Then, using a computer, he verified that every odd number less than 10 ³⁰ (or even 8.8x10 ³⁰ ) could be expressed as the sum of three primes. His work is still being peer reviewed.