Claude Shannon is one of the most influential people that you've probably never heard of. Born in 1916, he grew up as a brilliant young engineer. At the age of 21 he wrote his master's thesis that is regarded as the most important master's thesis ever written, on boolean algebra on digital logic circuits. His work made it possible for you to read this on a computer right now, and all modern computing. Later in his life though, he worked to create "a mathematical theory of communications." Far ahead of his time, he laid the ground work for the information age. The internet was able to take off like it did because we already had all the theory and the framework before we needed it. He's one of the great minds of the 20th century.

Information Theory is at a weird spot. It's too practical for most pure math people. It's too much math for most computer science people. Electrical engineering is a pretty good mix of the two, and it does help that Shannon was an electrical engineer too. That's why it currently fits somewhere between the 3. A little bit of software, a little bit of math theory, and a little bit engineering.

Apparently there has been quite a lot of work done to prove that mathematically entropy in Information Theory is the same as the entropy in thermodynamics. Entropy in thermodynamics is the tendancy of ordered systems to become disordered and random. In Information Theory, the idea for entropy is quite the same. A signal has to be carried through a physical means, whether an electro-magnetic wave like WiFi, an acoustic wave like music or anything else, information requires physical means to be communicate, and thus is subject to physical laws. Entropy means that anything communication has an inherent degree of randomness and disorder. Information Theory is mainly centered around minimizing entropy, managing entropy, or manipulating entropy (like for security).