While Logicomix focuses on the great mathematician Bertrand Russell, his work, and his association with other great mathematicians of the early 20th Century, 'Uncle Petros' is about a more obscure mathematician, and explores his path from early promise to obscurity.
The narrator is fascinated by his somewhat reclusive but kind uncle, labelled rather cruelly by his businessman father and his other uncle as 'one of life's failures'. He learns that his uncle was a promising young mathematician who became so obsessed with proving Goldbach's Conjecture (still unproved as of this writing!) that his career went off the rails.
This 'most favored nephew' develops his own interest in mathematics, and tells his uncle of his plans to become a mathematician. His uncle tells him that very few people can become mathematicians, and that he doubts his nephew has what it takes. His nephew persists, so Petros challenges him to solve this problem over the summer:
Prove that every even number greater than 2 is the sum of 2 primes.
Our narrator struggles with the problem all summer long, but fails. He then finds out what some readers will already have recognized - Uncle Petros asked him to prove Goldbach's Conjecture.
At this point we wouldn't blame him for never wanting to have anything to do with his uncle again, but his interest in mathematics and in his uncle's story persists.
Gradually we learn about Petros' early career: a very useful technique he developed as a Ph.D. student which he dismisses as 'Calculation of the grocery bill variety', his work with the great G.H. Hardy and Ramanujan, and his long and ultimately futile struggle to solve the Conjecture. His isolation and his fear of revealing any of his early results lest his competitors use it to beat him to the proof causes him to miss some great opportunities to publish, and gradually his career disintegrates.
Petros is a fascinating character, flawed but with a wisdom and a sort of contentment with his lot in life, spending his days with gardening and chess. His nephew develops an obsession of his own, trying to get at the true reason Petros ultimately gave up, and to understand the course of Petros' life and career.
In my favorite quote from the book, Petros explains his preference for obscurity over minor but forgettable successes:
'I, Petros Papachristos, never having published anything of value, will go down in mathematical history - or rather will not go down in mathematical history - as having achieved nothing. This suits me fine, you know. I have no regrets. Mediocrity would never have satisfied me. To an ersatz, footnote kind of immortality, I prefer my flowers, my orchard, my chessboard, the conversation I'm having with you today. Total obscurity!'
While I don't agree with that sort of 'all or nothing' thinking, being more of an incremental and a 'set attainable goals' guy like the narrator's father, it is rather romantic in its way and I can respect his attitude. I do very much agree that obscurity is underrated (or at least that's what I tell myself here in this comment-free blog).
Being in the over 40 phase of my life, I find myself reviewing my own past successes and failures, identifying along the way regrets and things I could have done differently, trying to come to an acceptance of the things that didn't go as well as hoped. There's no sense in wallowing in failures or regrets, but I'd also say it's essential to be (sometimes painfully) honest in your assessment of your past and yourself, and that's a lot of what this book is about. There's also a kindness and empathy in the book, the book has, for lack of a better word, 'heart'.
I'd strongly recommend the book (and Logicomix) even to the non-mathematicians. Mathematicians are interesting characters, and while many struggled with mental illness, there was so much more to them as people.
As for my own mathematical pursuits (which fizzled out early) I can say with complete honesty that I have no regrets. In retrospect I can see the value of realizing it wasn't 'in me' to be a great mathematician and changing course, as painful as it was at the time. And for a while, I truly loved math, and it was all I wanted to do, and it was almost all I did. I can understand the appeal and I know there is a joy in being obsessed.