Lebesgue measure

I spent most of the day today with my brother. One of the things he and I share is a deep love of mathematics.

There was a point over coffee during the afternoon when we were in excited discussion about various mathematical topics. To me, the best part was when we were talking about the theory of Lebesgue measure.

Henri Lebesgue was a french mathematician who, while still in his twenties, wrote one of the most important Ph.D. dissertations in the history of mathematics. He basically created, for the first time ever, a truly general foundation for answering the question “What is the actual size of a shape — even an incredibly weird and gnarly looking shape?”

Being able to provide a good answer to this question touches on pretty much every scientific field, including biology, chemistry, physics, robotics, statistics. His insights pretty much opened the floodgates of early twentieth century math, ushering in a whole string of exciting intellectual discoveries by many brilliant people.

The way Lebesgue approaches and develops a proof of his theory is one of the most beautiful things in all of mathematics. Alas, I am not sure there is a good way for me to properly share his thinking within the limits of a blog post.

But I can definitely share a measure of my excitement.