Chasing Fermat’s Last Theorem

1 mainFermat’s Last Theorem is one of the most celebrated problems in mathematics. It is a problem in the field of Number Theory that’s very simple to understand, yet extremely difficult to solve. In fact, it’s so difficult that it remained unsolved for 358 years even though it got a lot of attention from some of the best mathematicians in history. Pierre de Fermat first came up with it in 1637. It remained a conjecture because he didn’t provide any proof. Let’s go ahead and explore this labyrinth, shall we?   Continue reading

Dissecting Diophantine Equations

1 mainThe word Diophantine refers to Diophantus, the third century mathematician from Alexandria. Numbers are the fundamental building blocks of mathematics, so he started thinking about problems for which we need integer solutions. For example, how many horses do we need to achieve a particular task? Even if the exact answer is 15.5, we cannot really cut the last horse into half. So he started studying these problems in order to develop a sound framework around it. This went on to become one of the most enigmatic and endearing fields in the history of mathematics. Diophantine equations have become so fundamental that we cannot imagine our world without them. Let’s go ahead and see what they are all about, shall we?   Continue reading

Understanding Catalan’s Conjecture

1 mainNumbers are deceptively simple. We use them everyday in a variety of contexts. It’s beautiful how there are so many mysteries hidden inside these numbers. Catalan’s Conjecture is a mathematical problem that’s really easy to understand, but extremely difficult to prove. In fact, it took around 158 years to come up with a mathematical proof. It was Preda Mihăilescu, the amazing Romanian mathematician, who came up with a proof in 2002. In solving these problems, mathematicians come up with profound ideas and formulations that impact many fields within mathematics. Let’s go ahead and peel this metaphorical onion, shall we?   Continue reading

1 + 2 + 3 + 4 + 5 + …. = -1/12

sum of all natural numbersWait 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 is actually a very important result used in theoretical physics, particularly in string theory. Now how can that be possible? Are physicists really that bad at mathematics? That can’t be it! What is the proof behind this? Do we ever encounter it in real life?   Continue reading

What Do You Know About Infinity?

infinityWhat do you think of the term “infinity”? In layman’s terms, infinity is something that has no end, something that is bigger than all the things we know. This is what most people think! Many people who have not seen advanced mathematics do not know about the fact that there are many different types of infinity, some of which are bigger than others. Now how is that possible? Isn’t there just one single infinity which quantifies the essence of uncountability?   Continue reading