I recently finished reading “Birth of a Theorem” by the French mathematician Cedric Villani.

It is a terrific book even if you understand only a fraction of the math in it (I certainly did not understand most of it). Villani does a great job bringing the reader along on his quest to prove a theorem that would qualify him for the coveted Fields medal. The Fields medal is the highest reward in mathematics and among its qualification requirement are that the recipient must be 40 years or younger. The book chronicles Villani’s race against this time clock.

I thoroughly enjoy mathematics and would love to learn more than I have. One of my misgivings is that there aren’t more books similar to “The Theoretical Minimum” in Physics aimed at readers who want to learn more but don’t want to slog through an undergraduate textbook. Villani’s book doesn’t solve this problem, but it does accomplish something else: it highlights many aspects of mathematical research that make it a fascinating case study in how the knowledge loop can work (you learn, you create, you share – see also World After Capital).

Villani describes in great detail how his theorem is the outcome of an intense collaboration with one of his former students and how it is informed by the work of other mathematicians, including a number of fortuitous conversations that trigger new ideas. Mathematics as a field already has a high degree of what I call “Informational Freedom” in World After Capital. Mathematical formulas cannot be patented and copyright has not been used to build up a world of expensive publications but rather previous results are widely available for free.

Villani beautifully relates how intrinsic motivation, a love for the beauty of mathematical knowledge, combines with a strong reputation system inside the mathematical community and some key prizes to drive forward the knowledge loop in mathematics. We should move other fields of knowledge to be closer to mathematics not the other way round. It is worth reading the book from this perspective alone.

I recently finished reading “Birth of a Theorem” by the French mathematician Cedric Villani.

It is a terrific book even if you understand only a fraction of the math in it (I certainly did not understand most of it). Villani does a great job bringing the reader along on his quest to prove a theorem that would qualify him for the coveted Fields medal. The Fields medal is the highest reward in mathematics and among its qualification requirement are that the recipient must be 40 years or younger. The book chronicles Villani’s race against this time clock.

I thoroughly enjoy mathematics and would love to learn more than I have. One of my misgivings is that there aren’t more books similar to “The Theoretical Minimum” in Physics aimed at readers who want to learn more but don’t want to slog through an undergraduate textbook. Villani’s book doesn’t solve this problem, but it does accomplish something else: it highlights many aspects of mathematical research that make it a fascinating case study in how the knowledge loop can work (you learn, you create, you share – see also World After Capital).

Villani describes in great detail how his theorem is the outcome of an intense collaboration with one of his former students and how it is informed by the work of other mathematicians, including a number of fortuitous conversations that trigger new ideas. Mathematics as a field already has a high degree of what I call “Informational Freedom” in World After Capital. Mathematical formulas cannot be patented and copyright has not been used to build up a world of expensive publications but rather previous results are widely available for free.

Villani beautifully relates how intrinsic motivation, a love for the beauty of mathematical knowledge, combines with a strong reputation system inside the mathematical community and some key prizes to drive forward the knowledge loop in mathematics. We should move other fields of knowledge to be closer to mathematics not the other way round. It is worth reading the book from this perspective alone.