Math

F1 is a sport full of complexity. Every weekend we see how teams perform various strategic actions. Commentators and viewers argue about these actions. We decide who was wrong by looking at the final results. But what if I tell you that the final results are not a good indicator…

The formula that proves the existence of the spiritual world Before we start the show, I ask you a very simple question, 1+2+3+4+ to infinity, what is his result? 1,2,3, reveal the answer, back in the 18th century, the great mathematician Euler already gave the answer equal to -1/12, and…

Things can get weird when we deal with infinity. Consider the following sum: S = 1–1 + 1–1 + 1–1 + 1–1 + 1 … It’s called Grandi’s series, after Italian mathematician, philosopher, and priest Guido Grandi (1671–1742). It is weird but grouping the series in different ways gives different…

Despite being theoretically unbreakable, the Vernam cipher seldom appears in modern encryption systems. — The Vernam cipher (also known as the One-Time Pad) is the only encryption algorithm proven to be perfectly secure. In other words, the scheme guarantees that only the key holders would ever be able to decrypt a message encrypted with it. And this property holds regardless of the capabilities of…

Neural Network architectures are evolving steadily in size and complexity like e.g. Google’s PALM or the famous language models GPT-2 and GPT-3. In this article I want to take a step backwards, to the basic concepts of Neural Networks. We will implement a neural network in a few lines of…