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

What Is A Galois Field?

mainA 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 consequences for nearly all branches of mathematics, thus etching his name in mathematics forever. Unfortunately, he died at a tender age of 20. The work he did as a teenager is now being used by mathematicians around the world for their doctorate studies and related research work. Prodigy indeed! Just so we are clear, this blog post has nothing to do with corn fields. Well then, what else can it be about?   Continue reading