Euler.
Short title, but huge Mathematical production. It's really hard to write about Euler, because you rarely do not know where you should start. He published so many things that it's even harder to summarize it in a 5 min reading text.
If we could heard drums playing for the Newton's post, now it's time to head a full orchestra. Yes, it's time to talk about a great figure — Euler. History tell us that Euler was one of that living proofs that if you really love something (in case, Math), you will do it until the end of your life. No matter if you are old, blind or so (which actually happened to him, Euler became blind).
A personal comment — Euler is probably one of the mathematicians that I most admire. Based on history books, he might have had a fascinating mind, full of original ideas and insights. Let's see some fragments of his work in this post.
Leonhard Euler (1707–1783) was a Swiss Mathematician. Influenced by his father, he studied theology, but very soon his mathematical talent got revealed. Switzerland was also Bernoulli's family home place and the young Euler studies with Johann Bernoulli. He became friends of Daniel and Nicolas Bernoulli, who soon asked Euler's father to let him move forward on his Math studies: the boy was talented. As Bernoulli's were a respectful family in the area, Euler's dad could not deny the request.
Actually by Euler's time, Math started to be a more respectful subject, given Isaac Newton's popularity. We have seen several fathers not wishing to see their kids studying math professionally, but this reality became to change by the lates ~1710.
In 1727, Euler then goes to St. Petersburg to work in the new Science Academy. During his early years in Russia, he solved problems in: Navy, Economy, Acoustics, Optics and many other areas. Then some time later he started occupying the position of Mathematician. It was when his math works productivity increased (a lot). And at the same time he became blind for the left eye :( However, this did not stop him of doing Math.
In 1741, Euler goes to Berlin. There he starts to work in a frenetic speeded up way. For example, a problem that Royal Society estimated a couple of months to be solved had it's solution delivered by Euler in… 3 days or so. He made studies in several areas: Astronomy, differential calculus, calculus of variations, number theory, algebra, physics, ballistic movement, navy theory, philosophy. There are over 500 books and articles published by Euler. Just to give you an idea, when Euler passed away, the editors still had new material made by him to publish for the next 30 years after his death.
In 1766 Euler returns to Russia and leaves his place in Berlin for Lagrange. He was becoming totally blind :( But this would not stop him of doing Math. He started to train blind write with the rest of vision that was left to him. He knew he would not be able to see anymore, so he must find a way to keep productive. He also started to dictate his ideas for his sons and they wrote it down.
Finally it happened: Euler was blind. History describes his incredible skill for mental math and complex calculations. He did not even need a paper to solve complex equations. And yes, he solved a problem related to Moons position even being blind (!!!!111 WOW).
Euler has a famous episode with Denis Diderot. Check it here.
Math symbology was also influenced by Euler:
- a, b,c for triangle sides; A, B,C for opposite angles;
- R and r for circle radius;
- f(x) for functions;
- e and ln;
- i for √-1;
- ∑ for sequence sums;
It's also incredible to analyse the set of knowledge that Euler had for various subjects:
- Mathematics
- Astronomy
- Medicine
- Physics
- Botany
- Chemistry
- Theology
- Oriental languages
- Civil history
- Literature
You might have heard about Euler in different areas. Now it's explained why we have Euler's relation, Euler's identity, Euler's constant, Euler's angles, Euler's diagram, Euler's transformation, Euler's formula, and many others. He also started initial subjects on graph theory when he was doing studies about routes.
You also might have heard about the famous 'Euler's identity'.
(this was the only time that I bought a necklace in my entire life) ^
The question is, why did Euler started studying this? Everything started with with a French mathematician, Abraham de Moivre (1667–1754). He was a Newton's friend and showed him his studies on Bombelli's complex numbers. Newton did not show interest by this subject. But this did not kill the motivation of de Moivre to keep studying the subject. He made works on series and analytics trigonometry. So he ended up creating a mathematica relation between trigonometry and complex numbers, which later became known as De Moivre's Formula. He was one of the first mathematicians to explore and document nth roots on complex numbers.
Euler knew De Moivre's works. He also knew Taylor and Maclaurin's works (which I blogged shortly here in this post). So he unified both! And then Euler's identity was made. ❤
Personal notes on this: the first time I saw Euler's identity I was like "WHAT THE HELL DOES IT MEAN? TELL ME THIS PERSON USES HEAVY DRUGS". Youngness, you know. But the time passed by and I realized that I never had seen so much love in a single equation. We have
Look at this. we have e, bringing us the idea of logarithms. We have exponentiation. We i, bringing us complex numbers (check this numbers set diagram. Complex numbers are related to the other number sets). We have π, the lord of irrational numbers. We have a plus sign, arithmetics. We have a number! One! and a equality. THIS IS ONE OF THE MOST BEAUTIFUL THINGS THAT I HAD SEEN IN MY ENTIRE LIFE. Love definition. ❤ ❤
Check this link for more information about how beautiful this equation is (there are other people sharing it's passion!)
Other works by Euler: linear equations system solution using matrixes and substitutions, topology, polar coordinates. He also tried to prove Fermat's last theorem. Euler died in 1783 after a brain haemorrhage. :(
Hope you have enjoyed this post! I try to be impartial in my writings, but it's impossible when I am talking about Euler. Same will happen when I write about Galois. Sorry about that, after all I am also a human.
