Alexander Gelfond facts for kids

Alexander Osipovich Gelfond (Russian: Алекса́ндр О́сипович Ге́льфонд; October 24, 1906 – November 7, 1968) was a very smart Soviet mathematician. He is famous for a special math rule called Gelfond's theorem. This important rule is named after him.

About Alexander Gelfond

Alexander Gelfond was born in Saint Petersburg, which was part of the Russian Empire at the time. His father, Osip Gelfond, was a doctor and also loved to think about big ideas as a philosopher.

Alexander started studying at Moscow State University in 1924. He continued his advanced studies there in 1927. By 1930, he earned his Ph.D., which is a very high degree in academics. His teachers were Aleksandr Khinchin and Vyacheslav Stepanov.

In 1930, Alexander traveled to Germany for five months. He worked with famous mathematicians like Edmund Landau, Carl Ludwig Siegel, and David Hilbert in cities like Berlin and Göttingen.

When he returned in 1931, he became a professor at Moscow State University. He taught there for the rest of his life. From 1933, he also worked at the Steklov Institute of Mathematics, a top research center.

In 1939, he was chosen as a Corresponding Member of the Academy of Sciences of the Soviet Union. This was because of his important work in Cryptography, which is the science of making and breaking secret codes. During World War II, Gelfond was the main expert for secret codes in the Soviet Navy. He helped keep important information safe.

Gelfond's Amazing Math Discoveries

Alexander Gelfond made big discoveries in many areas of math. These included number theory (the study of numbers), analytic functions (special types of math equations), and integral equations. He also studied the history of mathematics.

His most famous discovery is his own theorem, called Gelfond's theorem. It's a very important rule about numbers.

What is Gelfond's Theorem?

Gelfond's theorem says: If you have two special types of numbers, called algebraic numbers, let's call them α and β. (An algebraic number is a number that can be the answer to a simple math equation using only whole numbers.)

• If α is not 0 or 1,
• And if β is not a simple fraction (a real rational number),

Then, if you calculate α raised to the power of β (like 2 to the power of 3, but with these special numbers), the answer will always be a transcendental number.

A transcendental number is a number that cannot be the answer to any simple math equation using only whole numbers. Famous examples are π (about 3.14159) and e (about 2.71828).

This theorem helped solve a very old and difficult math problem known as Hilbert's seventh problem. Gelfond first proved a part of this theorem in 1929 when he was still a student. He proved the full theorem in 1934. Another mathematician, Theodor Schneider, also proved the same theorem on his own. That's why it's often called the Gelfond–Schneider theorem.

In 1929, Gelfond also suggested an idea that went even further, called Gelfond's conjecture. Another mathematician named Alan Baker proved this idea to be true in 1966.

Before Gelfond's work, mathematicians only knew a few numbers that were transcendental, like e and π. Thanks to Gelfond's discoveries, it became much easier to find an endless number of transcendental numbers. Some of these numbers are even named in his honor:

• 2^√2 is called the Gelfond–Schneider constant.
• e^π is called Gelfond's constant.