And the discovery of a new operator with amazing properties — In this article, we will define an interesting operation and use it to define a new operator S which has some interesting properties just like the differential operator d/dx. Then we will look at all the properties of the theory. It turns out, for example, that this operator obeys rules…

A graph containing structured knowledge from more than 120 articles on mathematics and data science — In this article, I will show how you can structure and explore the content of your own articles using graph technology and some programming. The idea of using NLP techniques for structuring unstructured data is not new, however, the latest progress in LLMs (Large Language Models) has sparked countless opportunities…

Convergence and series explained — This is one of the questions I get asked a lot by non-mathematicians. If, in a discussion about interesting mathematical facts, I by mistake mention the term “infinite series” or “infinite sum”, then, of course, they will immediately ask “What do you mean by an infinite sum?”. “Isn’t that always…

Rediscovering the complex numbers from first principles — I want you to forget everything you think you know about numbers and common operations like addition and multiplication. In this article we will start over by thinking of things a little differently but as you will soon see, by this way of thinking, the real and complex numbers will…

A story of an extreme commitment to mathematics — I think this story is important to tell for many reasons. I will elaborate on what I mean by this near the end of the article. For now just hang on to your hat! This is a story of a mathematician with a mind-blowing devotion to mathematics. A man with…

And a beautiful formula for a generalized version of the Möbius function — What is your favorite version of the Riemann hypothesis? In this rather short article, we will see a curious but easy-to-understand version of the Riemann hypothesis that clearly shows the connection between that and the distribution of the prime numbers. …

What is mathematics and is there a “best” one? — Math is math, right? 1+1 is always 2 and the angles in any triangle always add up to 180 degrees, right?… Right? Well… No, actually… Or rather, it is not that simple at least. We mathematicians have a little-known secret that we usually don’t like to talk about. Let’s talk…

What does it mean to raise a number to the power of an operator and can we view it as a matrix? — The other day I had an exciting thought and couldn’t really let go of it. I guess this is my way of doing that. By writing about it and hopefully inspiring someone to take this further. It all started with a simple question. Is there a way to view differentiation…

Applications of the theory of shapes to the real world and beyond — Did you know that at any point in time, there is at least one place on Earth where the wind is standing completely still? Or how about this: at any point in time there exist two diametrically opposite points on Earth’s surface with exactly the same temperature and exactly the…