Is Information Theory Mathematics?

Question

When I read about Information Theory, for example on Wikipedia, I can never find statements that say if Information Theory is "real" Mathematics with underlying axioms, a notion of "proof beyond doubt" and such.

On the one hand I've read it's an engineering subject with a high level of abstraction (German Wikipedia) and "entropy" is a term used in thermodynamics, but on the other hand I recall reading proofs when seeking an answer to this question (didn't understand the least bit though) and it seems like Information Theory is a branch of probability theory (also, it's part of this website about math), but I'm still confused.

So, is Information Theory Mathematics?

Thanks in advance!

Answer 1

Yes, Information Theory is a branch of mathematics, although its practitioners are often found in departments of Electrical and Computer Engineering or Computer Science.

Answer 2

Instead of mathematics, I would say it's probability/statistics. The basic idea, entropy, is defined in terms of the probability.

Answer 3

Information theory is a mathematical field that deals with the transmission, processing, and storage of information. It was developed by Claude Shannon in the late 1940s, and has become an essential part of telecommunications and data storage systems.

The basic concepts of information theory can be described in simple terms. Information is measured in units called bits, and the amount of information that can be transmitted over a communication channel is limited by the bandwidth of that channel. The efficiency of data transmission is also limited by noise interference and other factors.

Information theory is a complex and fascinating topic, but these basics provide a good introduction to this important area of mathematics.