the universe in zero words

The universe in zero words: The story of mathematics as told through equations is a book with a very nice cover: in case you cannot see the details on the picture, what looks like stars on a bright night sky are actually equations discussed in the book (plus actual stars!)…

The universe in zero words is written by Dana Mackenzie (check his website!) and published by Princeton University Press. (I received it in the mail from John Wiley for review, prior to its publication on May 16, nice!) It reads well and quick: I took it with me in the métro one morning and was half-way through it the same evening, as the universe in zero words remains on the light side, esp. for readers with a high-school training in math. The book strongly reminded me (at times) of my high school years and of my fascination for Cardano’s formula and the non-Euclidean geometries. I was also reminded of studying quaternions for a short while as an undergraduate by the (arguably superfluous) chapter on Hamilton. So a pleasant if unsurprising read, with a writing style that is not always at its best, esp. after reading Bill Bryson’s “Seeing Further: The Story of Science, Discovery, and the Genius of the Royal Society“, and a book unlikely to bring major epiphanies to the mathematically inclined. If well-documented, free of typos, and engaging into some mathematical details (accepting to go against the folk rule that “For every equation you put in, you will lose half of your audience.” already mentioned in Diaconis and Graham’s book). With alas a fundamental omission: no trace is found therein of Bayes’ formula! (The very opposite of Bryson’s introduction, who could have arguably stayed away from it.) The closest connection with statistics is the final chapter on the Black-Scholes equation, which does not say much about probability…. It is of course the major difficulty with the exercise of picking 24 equations out of the history of maths and physics that some major and influential equations had to be set aside… Maybe the error was in covering (or trying to cover) formulas from physics as well as from maths. Now, rather paradoxically (?) I learned more from the physics chapters: for instance, the chapters on Maxwell’s, Einstein’s, and Dirac’s formulae are very well done. The chapter on the fundamental theorem of calculus is also appreciable.

“On Babylonian mathematical tablets, the solution to a problem was never complete until the solver wrote, “Praise Nisaba!” at the end.” Dana Mackenzie, page 8

The book is very well-versed in the ancient history of mathematics, from Babylonian to Chinese mathematicians, in addition to the more well-known Greeks. (It clearly borrowed from the extensive bibliography on the history of mathematics provided at the end.) This led to one of the most exciting discoveries in the book namely that for Chinese mathematicians, the Pythagorean theorem is called the gou-gu theorem (勾股定理) [no surprise with an alternative name!], but also that the hypotenuse is called xian, meaning “lute string”! I am very pleased that my pseudonym has a mathematical meaning as well!!

While the illustrations in universe in zero words are numerous (no word but many pictures!) and to the point, I have two issues: the main one is the choice of using handwritten representations of the equations motivating each chapter. This is pretty and has an historical feel, but it makes some of the equations harder to read (some symbols were actually ambiguous enough to make me go back to the text to make sure I understood!) and it somehow looks less rigorous. My second issue is that the book did not make use of the mathematicians’ wordprocessing LaTeX for composing equations, hence resulting in a rougher and less satisfying typographic outcome. (This may only appeal to the professional mathematician, but since the book is rightly preoccupied with the beauty of equations, using a proper mathematical software should have mattered! This remark is also apologetic towards the future rendering of this review in CHANCE since the editor of the journal also refrains from using LaTeX!!!)

“A great equation tells us something that we did not know before (…) A great equation has the spare aesthetic of Japanese calligraphy.” Dana Mackenzie, page 6

If you can bear with me a wee longer, I would like to get over the various formulae proposed through the book. Some of those are definitions, like 1+1=2, 1-1=0, π=3.1415926535…, exp(ix)=cos(x)+i sin(x), which, despite providing natural entries to a wealth of mathematical concepts and discoveries, do no necessary “tell us something new”. Others are approximations like the definition of π, or Gauss’ prime number theorem. Or conjectures, like Riemann’s and the Continuum Hypotheses, now that Fermat’s Theorem is out of the way! And, as mentioned above, (too) many are physics equations: Archimedes’ lever law, Kepler’s planet laws, Newton’s gravitational laws, Maxwell’s, Einstein’s, and Dirac’s formulae, Lorentz’s equations. There are many good stories arising from those, but the book still make a choice of the most standard characters, from Newton, to Fermat, to Galois, to Einstein, and of the most popular stories, with the apparently unavoidable Gödel (and Whitehead and Russell) appearing twice.  (I prefer the introduction provided by Logicomix, obviously, even though all formulae are botched in the drawings! And I am not highly excited by the Continuum Hypothesis, I must say…) The absence of Laplace, even more than of Bayes, is felt in the book. Anyway, enough grumbling: the universe in zero word: The story of mathematics as told through equations makes for an easy and pleasant read, as well as a wonderful gift for mathematically inclined (and English speaking) teenagers.