Beautiful mathematics can be found in unlikely places. Building upon this premise, Power-up tries to address a marketing problem: Why is mathematics far from engaging for most people? Mathematics is not as engaging as, for instance, playing video games. However, video games offer plenty of interesting examples for motivating mathematical thinking. Matthew Lane collects some of them in his book, which is written to be accessible to a general audience and leaves some interesting technical details as a handful of endnotes.

Actually, the book starts with physics rather than mathematics, from two opposite directions. On the one side, the lack of realism in video games might reinforce students’ misconceptions (for example, changing trajectories in the middle of a jump). On the other side, carefully designed games can help understand unintuitive subjects such as relativity or a four-dimensional world.

Each chapter delves into some aspect of games that is amenable to mathematical modeling, from the intrinsic problems of games that offer a limited set of options and, hence, poor replay value to voting systems and scoring mechanics. The former addresses duplication problems, whereas the latter correspond to selection and ranking (from a mathematical perspective, the proper stage for discussing the birthday problem, the coupon collector’s problem (also known as the completionist’s dilemma), Arrow’s impossibility theorem, alternative voting schemes such as approval voting, Wilson’s confidence intervals, or even logistic regression (for predicting high scores and their limits).

Later chapters on chasing games, game complexity, friendships, and autopilots serve as the basis for discussing geometry (for example, how to hit moving targets and intercept missiles), the appeal of seemingly simple games such as Tetris or Minesweeper (the P versus NP problem), differential equations (to model social relationships, as in Strogatz’s famous book on nonlinear systems [1]), and chaos (a truly reliable autopilot mode is only possible when randomness is limited and no chaotic behavior is allowed).

Since interesting mathematics is at the heart of many popular video games, Lane advocates for the use of games to support educational goals, making mathematical topics more appealing to students. In fact, players are always learning when they play. The true educational value of games is, therefore, in “game-enhanced learning” rather than in educational games, which too often are games “in name only” (yet not always, fortunately).

Power-up is a very readable book based on examples taken from popular video games. As a matter of fact, the connection of mathematics with video games is even deeper. There is a profound similarity between playing games and doing mathematics that is often overlooked. Both are human activities based on a quest for understanding: understanding virtual worlds in the case of video games, those virtual worlds and everything else in the case of mathematics. It is a pity that too many people are deprived of the pleasure of finding things out via the intellectual game of mathematics. Hopefully, the effort of the likes of Matthew Lane will someday solve the severe marketing problem of mathematics.

More reviews about this item: Amazon