Welcome

Hello World! My name is Juan Pablo Herrera, I'm a highschool student, I live in Santiago De Chile and I am passionate about mathematics. There sre some mathematicians I admire, Euclid, Euler, Hardy and Ramanujan, particularly the latter. Ramanujan found many interesting properties and formula, but they all remained in notebooks that only he could read. That's why I decided to open this blog, to share with the world some of the wonderful things I've found and written in my math notebooks without them ever being published.


I think what kickstarted all this, was during a day I was bored in class. I wrote all the square numbers, then wrote their differences I realized they were all the odd numbers, resulting in this:

I came to the conclusion that a squared number is the sum of all the odds until the one corresponding tho such number, like this:

n² = 1 + 3 + 5 + 7 + 9 + 11 + … + 2n – 1

That's when I met summations (without even knowing how to use the sigma notation), which is going to be something fundamental for many articles in this blog.

I had always been keen on maths at school, but it wasn't something I really enjoyed, it was boring and repetitive. However, after that point, I was really curious about, for example, could there be a formula to get all the prime numbers? What would happen if I do this to the cubed numbers? Suddenly, I started to find some useful and interesting properties and formulas.

Those formulas are what I'm going to publish here,and in a way that literallya fifteen-year-old boy can understand, good explanations, informal language, etc…