*novel*? Our terminology may need an update.)

Seeking an escape from his authoritarian religious upbringing, young Bertrand turned to mathematics as the one source of absolute certainty in his life. But the more he studied mathematics, the more he realized that underlying all the sophisticated theories of the time were arguments based more on intuition than full rigor. Driven by his quest for absolute truth, Russell embarked on a project to rebuild mathematics from the foundations up, and thereby establish its status as absolute truth.

Unfortunately, his project ran into major difficulties of the mathematical/philosophical variety (to say nothing of his equally great personal difficulties) including the famous paradox of Russell's own invention, the arguments of his student Wittigstein that logic was merely a tool for generating tautologies, and finally, Godel's proof that even in the self-consistent world of mathematics, there must always be true statements that cannot be proven.

In the end, though Russell and his contemporaries eventually succeeded in placing mathematics on a rigorous footing, the dream of a logically grounded "universal truth" had to be abandoned. Mathematics is only as true as the assumptions it rests on, and cannot even prove all that is true in its domain.

While the mathematical and philosophical ideas are well-illustrated for a lay audience, the heart of LOGICOMIX is Russell's personal struggle, first to find the universal truths in mathematics and then to accept their nonexistence. Like others engaged in this project, Russell's struggle with logic occasionally veered into a struggle with sanity. Through a meta-narrative of the book's creation, the authors debate the "logic and madness" theme, and ask whether some amount of detachment from reality a prerequisite for one who spends his or her life searching for its foundations.

This narrative of Russell's quest had personal resonance for me: I went through my own late-high-school/early-college phase of viewing mathematics as a bastion of truth in an illogical world. I wonder if many of my mathematical colleagues' careers had their genesis in the same yearning for certainty. I imagine we all eventually come to the same realization as Russell: that mathematics is a powerful tool for clear thinking, but the only "truth" it contains is ultimately tautological.

Disillusioned by his self-described "failure" but ultimately freed from his need for unblemished truth, Russell turns to more worldly concerns, including pacifist activism and the founding of a school with no rules (spoiler: it doesn't go well). The book ends on a bittersweet note as Russell encourages students to accept their lives in an uncertain world.

I had great pleasure following Russell's journey, and the many ideas and people encountered along the way. If anyone is interested in what really drives mathematicians, this book is heartily recommended.

I rather liked

ReplyDeleteThe Manga Guide to Statistics, and have been meaning to check out the other titles in the series, but somehow I haven't managed it just yet.