Book Review: Blueprints: How Mathematics Shapes Creativity

Today, I resume posting from a hiatus because I was moving across the country and relocating to my new job at the University of Tulsa College of Law. I announced yesterday on LinkedIn that I have a new pre-print that is close to done of an article that I plan to submit to Nature. But I'm looking for readers to vet this, and for a senior co-author because I don't have a PhD, though I'd characterize myself as a "savant" in math.

I'm reading a wonderful new book by Oxford mathematician Marcus du Sautoy, and my strong recommendation is "buy it, immediately!" Du Sautoy's book has relevance to law and economics because mathematics is relevant to so many disciplines, including architecture. I'm also looking into this topic right now for a law review version of the pre-print I'm writing. But one fact that du Sautoy relates is that brutalist buildings designed in a minimalist style, often premised on efficiency (think John Nash) instead of belonging (think Freeman Dyson/Bill Press/me), have horrible acoustics. This is due to the architecture not naturally "reflecting" the values that are inscribed in certain styles of math. 

Now, du Sautoy and I agree when he says, effectively, than math must be beautiful if one is doing it right. Good math papers (or physics papers) should be so overwhelming they make a reader cry, just as once a paper on wetness and the incredible optics properties of water made me shed actual tears, or when I learned the wave equation I wept in class. So good math, like good music, should be able to educe emotions, and provoke a strong emotional response. But I postulate, unlike du Sautoy, that there is also ugly math, and that ugly math is the reason brutalist architecture exists. 

What is ugly math? I tend to think John Nash's approach to the Prisoner's Dilemma, and people who believe in the (D,D) equilibrium, are ugly. And I mean that literally. This form of math brings out the ugly side of humans: kill or be killed, eat or be eaten. Kind of like cannibalism, and the scenarios of hunter gatherers fighting for basic survival. But assuming basic needs are met, math and communities should be beautiful, and there should be no need to defect, or to design ugly buildings in the brutalist style. I will confess I find these buildings hideous, and could not understand anyone who loves them, though I do love minimalism, and I think minimalism in art is gorgeous. 

So my main critique of du Sautoy is that he seems to romanticize or homogenous all aspects of math and mathematicians, and paint them through a very starry-eyed lens. And that's not necessarily bad because I'm a starry-eyed dreamer and my math includes sacred images, and is ultimately about peace, and even compassion and mercy. These are the values my Prisoner's Dilemma new answer stands for.

To bring this back to du Sautoy, who I hope contacts me because I worship him or think his book is incredible, the brutalist buildings he describes had to be "rescued" with a different form of math that he characterizes as encapsulating randomness: i.e., prime numbers. Now, I'm no expert in prime numbers, though I'm interested in them, but I would suggest that nothing is random, even though I'm not a determinist, and there are mathematicians who devote their lives to primes attempting to find patterns, and some people indeed have found patterns, even if these patterns don't fully describe all primes. But prime numbers in the book were used to create structures that were used in the concert halls he describes to repair the horrible acoustics, and they were used in a pragmatic way, and designed by physicists. Which means they had incredible practical applications.

I adore du Sautoy's book, and I think it has clear relevance to law and economics, even if it's essentially about art and math, and architecture is a form of law and economics, and talk to the architects at the University of Chicago. (I'll save this anecdote for a law review article.) 

One sad thing: there's a basic mistake, and I'll give brownie points to any reader who can point out my error, or to du Sautoy himself if he can explain himself better. In my print copy of this book, on page 34, du Sautoy describes a pattern and says if one takes the first six numbers of a clock, and then squares them, one should get "0,1,4,2,2,4,1." Unless I've badly misunderstood this (which is possible), I don't see that. I assume clocks count normally, so the first six numbers are "0,1,2,3,4,5." Squaring these numbers yields "0,1,4,9,16,25." Can anyone see my mistake? But even if I'm correct it doesn't diminish my love for this outstanding book, and maybe there's a longer story behind this computation in a peer-reviewed paper that he's basing this on, and I'd love to see that. 

So is du Satoy my hero? Yes! And would I like to meet him? Yes! Should others buy this book: Yes, even if you are lawyers or law professors, and there's a clear link between law and economics and law and literature as du Sautoy makes evident on his chapter on Shakespeare and patterns and numbers! 

-Cortelyou C. Kenney (8/10/25, 12:16 PM CT)

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