When we think of prime numbers, the first thing that we tend to associate them with is randomness. Prime numbers are scattered all over the number line and there is no fixed formula that can tell you when the next one is going to occur. This has been used heavily by mathematicians and cryptographers to … Continue reading Underlying Pattern Governing The Prime Divisors
Category: Mathematics
The Interesting Case Of Russell’s Paradox
The picture on the left is actually a joke related the topic of discussion here. It'll make sense soon! Russian Dolls, also known as Matryoshka Dolls, are wooden dolls that are placed inside one another. You can read more about them here. Back in the late 1800s, Set Theory was really picking up pace and mathematicians … Continue reading The Interesting Case Of Russell’s Paradox
What’s So Interesting About The Prime Counting Function?
Mathematicians have obsessed over prime numbers for centuries, and will continue to do so for the foreseeable future. Prime numbers are so enigmatic and fascinating that mathematicians just can't stop thinking about them! Prime counting function is probably one of the most famous problems in this domain. This function simply counts the number of prime numbers … Continue reading What’s So Interesting About The Prime Counting Function?
What Is Bayesian Information Criterion?
Let's say you have a bunch of datapoints and you want to come up with a nice model for them. We want this model to satisfy all the points in the best possible way. If we do this, then we will be able to use a mathematical formula to extract information about unknown points. At … Continue reading What Is Bayesian Information Criterion?
Why Are They Called “Elliptic” Curves?
Have you heard of elliptic curves before? They are used extensively in number theory and cryptography. The reason elliptic curve cryptography is gaining popularity is because it's fundamentally much stronger than the RSA algorithm, the algorithm that we all love and adore. If you don't know what elliptic curves are, just google it and see what they … Continue reading Why Are They Called “Elliptic” Curves?
What Is A Holomorphic Function?
How do you feel when see the term "holomorphic function"? It just feels like we shouldn't be looking further into it, right? I mean, it looks like an esoteric mathematical concept that should remain in advanced textbooks. Interestingly enough, holomorphic functions are very useful in real life. Holomorphic functions are ubiquitous in the field of … Continue reading What Is A Holomorphic Function?
How Do We Know That There Are Infinitely Many Prime Numbers?
There is a very famous theorem which says that there are infinitely many prime numbers. For people who are new to this, a prime number is a number that doesn't have any divisors except for 1 and itself. For example, 11 is a prime number because it doesn't have any divisors apart from 1 and … Continue reading How Do We Know That There Are Infinitely Many Prime Numbers?
What Is Zeta Function Regularization?
There is a popular mathematical result which says that the sum of all natural numbers is -1/12. I have discussed it in detail here. This looks very unintuitive to a first time observer. In fact, most people would say that this is some kind of mathematical trickery. How can a bunch of positive numbers sum … Continue reading What Is Zeta Function Regularization?
What Is Relative Entropy?
In this blog post, we will be using a bit of background from my previous blog post. If you are familiar with the basics of entropy coding, you should be fine. If not, you may want to quickly read through my previous blog post. So coming to the topic at hand, let's continue our discussion … Continue reading What Is Relative Entropy?
What Is Entropy Coding?
Entropy Coding appears everywhere in modern digital systems. It is a fundamental building block of data compression, and data compression is pretty much needed everywhere, especially for internet, video, audio, communication, etc. Let's consider the following scenario. You have a stream of English alphabets coming in and you want to store them in the best … Continue reading What Is Entropy Coding?
