Math Girls 3: Godel's Incompleteness Theorems

Math Girls #3

by Hiroshi Yuki, Hiroshi Yuki

In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilbert's program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt Gödel stunned the world by proving that Hilbert's goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system. Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. Gödel's incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before. In this third book in the Math Girls series, join Miruka and friends as they tackle the basics of modern logic, learning such topics as the Peano axioms, set theory, and diagonalization, leading up to an in-depth exploration of Gödel's famous theorems. Along the way, visit other interesting and important topics such as trigonometry and the epsilon-delta definition of limits, and of course take on challenges from the enigmatic Mr. Muraki. Math Girls 3: Gödel's Incompleteness Theorems has something for anyone interested in mathematics, from advanced high school students to college math majors and educators.

Genres: Mathematics

394 pages, Hardcover

First published November 5, 2009

Reviews

[Jc · Rating 3 out of 5]

Compared to the previous books, this one felt more tedious for me. There’s not much of story going on here but there’s a lot of Maths, specifically, logic.
Being honest, Logic is not my cup of tea, so I struggled liking this book. However, Hiroshi Yuki helps you to understand the Gödel incompleteness theorems in a more comprehensive way.

[Ami Iida · Rating 4 out of 5]

The book explains incompleteness theorem easily by mathematical formula.

[Allen Kwan · Rating 4 out of 5]

An interesting introduction to Godel's Incompleteness Theorems. Starting with number theory, set theory, formal systems, and logic, the book slowly builds up the knowledge required to understand Godel's proof. It tries to avoid metaphysics and philosophical discussions by having its characters constantly dissuade each other from trying to make grandiose statements about mathematics being "incomplete", sticking mostly to an explanation of Godel's proof.

For those looking for some development to the actual Math Girls "story", there is a hint about where the main character ends up in a short epilogue, but there's more math than story. Perhaps the manga covers that in greater detail.

[sophytoeat · Rating 5 out of 5]

やっぱ不完全性定理という単語にはワクワクする。
読んでみて最終章あたりの内容は正直さっぱりだったが、数学への興奮がより深まった一冊になった。
なにかに熱中することの喜びやその時間は非常に非常に貴重なものだったのだなと今になって思う。

[Aaron · Rating 5 out of 5]

I've wanted to understand Gödel for years. Thanks to this book, I think I finally do.

[Sami · Rating 3 out of 5]

Not as entertaining as the other books in the series, in my opinion. Maybe that's due to me not being so keen on meta-mathematics that this book is all about. Also, I would have liked the plot to progress a little bit more. Still, an interesting journey to Gödel with these Japanese students.