Math Files

When E = mc² was first written down by Albert Einstein

If your idea of math is boring, you're in for a surprise with François Viète. This 16th-century French genius revolutionized algebra. Before Viète, algebra was written out in long, confusing sentences. He introduced the use of letters to represent unknowns, laying the foundation for modern algebraic notation. But wait—there’s more! He was also a cryptanalyst, cracking secret codes during the French Wars of Religion. Talk about a versatile mind! Viète’s work didn’t stop at algebra or cryptography. He made significant contributions to trigonometry, geometry, and even astronomy. His methods were so groundbreaking that he was nicknamed the Father of Modern Algebra. So next time you solve for x, give a nod to François Viète for making it all possible.

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Certain cicadas display a startling behavior: their emergence from the soil is synchronized with periods that are usually prime numbers, such as 13 and 17. Sometimes, more than 1.5 million individuals emerge within a single acre over a short interval of time.

The following little-known formula yields the correct decimal digits of π to an astonishing 42 billion places; however, it is not an exact formula for π. In other words, it is only a very high-precision approximation. The symbol ≈ denotes an approximation (Borwein and Borwein, Strange Series and High Precision Fraud, 1992).

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Spherical Volume Element

If it feels like your friends have more friends than you, you’re not imagining it—it’s actually true. A group of scientists explored this idea in the late 1990s. Using concepts from network theory, they showed that networks—including social ones—often lead to paradoxical situations. And honestly, when you look at it, it makes a lot of sense. We all know someone who has a lot of friends—someone who is easy to like and liked by many people. You probably consider that person a friend of yours, but most people in your network—whether at school, work, or elsewhere—also consider that person their friend. So imagine you’re in a group of 100 people and you have five friends. One of your friends, Bob, is liked by everyone and considers half the group his friends. Another friend, Morgan, has about ten friends. These highly connected individuals significantly raise the average of your network, making it more likely that you’ll feel closer to the bottom by comparison.

3¹² ≅ 2¹⁹ That may seem trivial and stupid, but it gives rise to practically the entire corpus of Western music, by establishing an approximate residue class of 12 half-steps per octave.

“Somewhere, something incredible is waiting to be known.” – Carl Sagan 😂

Ever seen the film A Beautiful Mind? The mathematician that film was based on, John Nash, has one of the shortest PhD dissertations ever published: ‘Non-Cooperative Games’. It has a grand total of 26 pages, and only cites two references. That thesis went on to found the basis for his paper on the development of game theory, for which he won the 1994 Nobel Prize in Economics.

Boiling water

A visual proof that 666 is a triangular number.

Why should a mathematician keep a mistress as well as a wife? because when the wife thinks you’re with the mistress, and the mistress thinks you’re with the wife, you have time to get on with your mathematics. This Joke fits with Leonhard Euler who was the most prolific mathematician of all time. He was born in 1707 in Basel, Switzerland, and died in 1783 in St Petersburg, Russia. He wrote more than 800 research papers, along with a long list of books. Euler had 13 children and often worked on his mathematics while one of them sat on his knee. He lost the sight of one eye in 1735, probably because of a cataract; the other eye failed in 1766. Going blind seems to have had no effect on his productivity. His family took notes for him, and he had astonishing mental powers—once performing a calculation to fifty decimal places in his head to decide which of two students had the correct answer. Euler spent many years at the court of Queen Catherine the Great. It has been suggested that, to avoid becoming embroiled in court politics—which could easily prove fatal—Euler spent nearly all of his time working on mathematics, except when he was asleep. That way, it was obvious that he had no time for intrigue.