5-Minute Mathematics

Dive into the extraordinary life of Évariste Galois—a mathematical genius who revolutionized algebra before his untimely death at 20. 📚✨

Évariste Galois: A Brilliant Flame Extinguished Too Soon Évariste Galois was born on October 25, 1811, in the small village of Bourg-la-Reine, just south of Paris, France. His father…

Did you know there is a conjecture that has been unsolved for over 150 years? It’s called the Riemann hypothesis, and it’s related to the distribution of prime numbers.

The Riemann hypothesis states that all the non-trivial zeros of the Riemann zeta function, which is a complex function that encodes information about prime numbers, have a real part equal to 1/2.

The Riemann hypothesis is one of the most important and difficult problems in mathematics, and it has many implications for number theory, cryptography, and physics. The Clay Mathematics Institute has offered a prize of $1 million for anyone who can prove or disprove the Riemann hypothesis.

Did you know there is a sequence of numbers that appears everywhere in nature? It’s called the Fibonacci sequence, and it’s made by adding the previous two terms to get the next term: 1, 1, 2, 3, 5, 8, 13,… 

The Fibonacci sequence can be found in many natural phenomena, such as the arrangement of petals on a flower, the spiral of a snail shell, the branching of a tree, and the growth of a pineapple. 

The Fibonacci sequence also has a close connection to the golden ratio, which is another mathematical constant that appears in art and architecture.

Did you know there is a paradox that shows that some infinities are bigger than others? It’s called Cantor’s diagonal argument, and it was devised by Georg Cantor, a pioneer of set theory. Cantor showed that the set of all natural numbers (1, 2, 3,…) is smaller than the set of all real numbers (numbers with decimals). 

He did this by assuming that there is a one-to-one correspondence between the two sets, and then constructing a new real number that is not in the correspondence by changing one digit in each decimal place. This new number contradicts the assumption, and therefore proves that there are more real numbers than natural numbers.

Did you know there is a number that contains every possible combination of digits? It’s called Champernowne’s number, and it’s made by concatenating all the natural numbers in order: 0.12345678910111213141516…

Champernowne’s number is an irrational number, meaning it can’t be expressed as a fraction of two integers. It also has the property that any finite sequence of digits can be found somewhere in its decimal expansion. For example, your birthday, phone number, and social security number are all hidden in Champernowne’s number.

Did you know there is a shape that has only one side and one edge? It’s called a Möbius strip, and it’s made by taking a rectangular strip of paper, giving it a half-twist, and joining the ends together.

If you trace your finger along the surface of a Möbius strip, you will go around both sides without crossing an edge. A Möbius strip can also be cut in half along its center line, and instead of getting two separate pieces, you will get one longer Möbius strip.

On this day in 1633, Galileo, at age 68, left his home in Florence, Italy, to face the Inquisition in Rome. By 22 Jun 1633, he buckled under the threats and interrogation by the Inquisition, and renounced his belief that the Earth revolved around the Sun.

Did you know there is a number so big that it can’t be written down or even imagined? It’s called Graham’s number, and it’s related to a problem in geometry.

Graham’s number is so huge that even if you tried to write down each digit in the smallest possible font, you would run out of space in the observable universe. Even the number of digits in Graham’s number is too big to write down.

Mathematics is the queen of the sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations, she is entitled to the first rank.

Born 28 January 1540
Hildesheim, Germany
Died 31 December 1610
Leiden, Netherlands
Ludolph van Ceulen, who computed the value of pi to 35 decimal places, born in Hildesheim, Germany. Pi is still sometimes referred to as Ludolph's number.

On this day, Janos Bolyai died in what is now Tirgu-Mures, Romania, and was then part of Hungary. Of his discoveries in non-Euclidean geometry, he wrote to his father Farkas, "From nothing I have created another entirely new world."

"Mathematics is the language with which God has written the universe "
~Galileo Galilei