Information Theory: Three Theorems by Claude Shannon

The mathematical theory of communication studies in a mathematical way the conditions under which one can transmit data, in particular at which speed, and with what reliability. We owe this expression to Claude Shannon (1916–2001), and a variant of it gave rise to a scientific field, information theory.
Mathematician, electrical engineer, computer scientist, cryptologist, Shannon’s scientific activity encompassed all these fields, be it during his PhD Thesis at MIT, within the US Army during the World War II, or at the MIT of which he became a professor in 1956.
One can recognize many sources of inspiration of Shannon’s works, such as those of the mathematicians Norbert Wiener and Andrey Kolmogorov, but his direct motivation seems related to the military effort of WorldWar II.
Writing these notes made me more aware of the way the mathematical and physical sciences, information theory in particular, are intimately linked with military efforts, more generally to the military-industrial complex. At a time of history where mathematics and computer science play an important role, by their handling of enormous amounts of digital data or encryption of communications, to the point that one can talk of “surveillance capitalism”, if that awareness reaches the readers of this book then this meager effort shall not have been made in vain.