Wait a minute, what? That looks very very wrong. You must be wondering if the title is some horrendous typo, right? Well, let me assure you that it's absolutely not! The sum of all natural numbers is equal to -1/12. This blog post is not just about mathematical trickery either. The equation in the title … Continue reading 1 + 2 + 3 + 4 + 5 + …. = -1/12
Category: Mathematics
What Are Confidence Intervals?
Confidence interval is a concept in statistics that is used extensively in many diverse areas like physics, chemistry, computer vision, machine learning, genetics, etc. This concept is so fundamental that any modern science would eventually end up using it. Let's say you have collected some data and you want to understand the behavior of that … Continue reading What Are Confidence Intervals?
What Are P-Values?
Let's say you are a part of the sub-atomic physics team and you are working on discovering an important effect. The thing about sub-atomic physics is that nothing is certain and you cannot say something has happened with 100% certainty. The best we can do is to say that we are x-percent sure that something interesting happened. … Continue reading What Are P-Values?
What Is Random Walk?
Consider the following situation. We have a drunkard who is clinging to a lamppost, and now he decides to start walking. He is in the middle of the street and the road runs from east to west. In his inebriated state, he is as likely to take a step towards the east as he is … Continue reading What Is Random Walk?
What Is A Galois Field?
A Galois Field is actually a corn field owned by any person named Galois! Too obvious? Alright, that was a joke. Anyway, the word 'field' is being used in the mathematical context here. Évariste Galois was a mathematical prodigy who laid strong foundations for abstract algebra. His collected works contain important ideas that have had far-reaching … Continue reading What Is A Galois Field?
Transcendental Functions
Transcendentalism refers to the philosophical movement that developed in the 1800s. It taught people to believe in the inherent goodness of people and nature. It also said that religious organizations and political parties corrupt the purity of an individual. So obviously, any ceremonies or functions attended by transcendentalists should be called transcendental functions. Right? No, … Continue reading Transcendental Functions
Asymmetric Dominance Effect
Let's consider a situation. There is a company with two products, A and B. Both these products have their own merits and demerits. Product A has relatively less features, but it's price is low. Product B, on the other hand, has more features but it's more expensive. Consumers tend to pick both these products depending … Continue reading Asymmetric Dominance Effect
Derandomization Of RANSAC
Let's say you are a clothes designer and you want to design a pair of jeans. Since you are new to all this, you go out and collect a bunch of measurements from people to see how to design your jeans as far as sizing is concerned. One aspect of this project would be to … Continue reading Derandomization Of RANSAC
What Is The Poincaré Conjecture?
Before we start, let me put something out there. Poincaré Conjecture is one of the seven millennium problems established by the Clay Mathematics Institute. Those problems are worth a million dollars each! The Poincaré conjecture depends on the mind-numbing problem of understanding the shapes of spaces. This field of study is referred to as "topology" … Continue reading What Is The Poincaré Conjecture?
Expectation Maximization
Probabilistic models are commonly used to model various forms of data, including physical, biological, seismic, etc. Much of their popularity can be attributed to the existence of efficient and robust procedures for learning parameters from observations. Often, however, the only data available for training a probabilistic model are incomplete. Missing values can occur which will … Continue reading Expectation Maximization
