Six books that have shaped my mathematical worldview
It’s that time of year when my social media feeds are plastered with reading lists. I want to play too. So here are six books about mathematics that have profoundly shaped my thinking and practice:
I owe Simon Singh a huge debt. This is the book that introduced me to a world of mathematics far more illuminating than anything I encountered in the curriculum. It was the forceful nudge I needed to study mathematics at university. If I had based my decision on schooling experiences alone, I would surely have opted for History instead. The joy of Fermat’s Last Theorem is that it cuts across artificial subject boundaries, showcasing mathematics in all its interdisciplinary glory.
The book rifles through the 350 years of toil that mathematicians endured in search of a solution to Fermat’s conjecture. It only became a theorem when Andrew Wiles presented his proof in 1994.
Simon Singh does not concern the reader with technical detail. At its core, Fermat’s Last Theorem is a story about how mathematicians cope with struggle. At times, it reads like a thriller. Singh presents the true form of mathematics: a subject that is wrapped in uncertainty, demands the deepest reserves of our resilience and rewards its players with truths that are as beautiful as they are eternal.
The underground hit that deserves to be in the hands of every educator. In this extended essay, mathematician and teacher Paul Lockhart exposes school mathematics for the soul-destroying experience that it is. In its place, he calls for a recognition that mathematics is an art form, and that it should be taught as such. Lockhart does not shy away from painting a vivid picture of this beautified version of mathematics. He gives the reader a taste the addictive brand of mathematics that so many (but still too few) are drawn to. Lockhart has since served up the main course with books devoted to Geometry and Arithmetic.
I’d heard of Ramanujan. I knew that he was born in India, raised in poverty, and called over to Cambridge to collaborate with G H Hardy. I had read about the famous taxi number incident between the two. I had even peeked at his outrageous formulations of infite series. But it was only through Robert Kanigel’s biography (which has been made into a biopic) that I uncovered the essence of Srinivisa Ramanujan: the man, his short but remarkable life, and his mathematics.
The main takeaway from Ramanujan’s story gradually dawned on me over time: it is that our mathematical identities are deeply shaped by our environment and cultural underpinnings. Ramanujan’s obsession with formulas owes much to the specific text that inspired his early works. Ramanujan also attributed his ingenious findings to the Hindu goddess Namagiri, who he believed quite literally placed formulas on his tongue. The contrast between Ramanujan’s holistic approach to mathematics and the cold, rigorous objectivity of Hardy is proof enough that there is no universal profile of mathematician.
We cannot understand mathematics without historical context. The same is true of mathematicians.
In 2010, Cedric Villani was awarded the Fields Medal, the highest prize in mathematics and equal in stature to the Nobel Prize. This memoir shows us how he did it. Birth of a theorem is a wonderful juxtaposition of highly complex mathematics (he devotes several pages to samples of his research; an artistic flourish more than anything) and deeply human moments of vulnerability. Villani can be found pacing around in the dark as he searches for inspiration. His email exchanges with collaborator Clement Mouhout bring to the fore the volatility of mathematical research; the pair were stunningly close to throwing in the towel before the key breakthrough revealed itself. Once again, it is the humanity of Villani’s journey that defines his mathematical achievement. I suspect the medal is a welcome bonus.
Mindstorms is EdTech as it should be. Papert was a champion of student-centred learning. His core edict is that the child should program the computer, not the other way around. Papert understood that mathematics is to be explored, and saw vast potential in the thousands of forms and functions afforded by computers to give students agency over their mathematical development. With the dominance of half-baked apps that consign students to mindless consumers of prescribed knowledge, Papert’s vision hangs in the balance. I keep Mindstorms close as a reminder of technology’s unfulfilled potential.
The most recent addition to my list (and the reason I refuse to settle for a Top Five). I discovered Sunil’s writing on Medium a year ago and have since earned the privilege of co-founding Q.E.D. with him. Sunil is the best writer I know, so I am pleased and grateful that he has directed his gifts towards an extended love letter to mathematics. Pi of Life reads as a romance, complete with pop culture references and captivating problems that will have you hooked to the end. I wrote a more detailed review here.
That’s my lot, for now. All worth devouring if you want to broaden your mathematical horizons.
I am a research mathematician turned educator working at the nexus of mathematics, education and innovation.
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