Numbers for Wittgenstein

Numbers for Wittgenstein by Jason Earls is a bold, unconventional fusion of rigorous computational number theory and profound philosophical reflection, inspired by one of the 20th century's most enigmatic thinkers, Ludwig Wittgenstein. This collection of articles and explorations dives deep into the "bedrock of arithmetic" through modern computation - using tools like PARI/GP to test conjectures, hunt patterns, probe divisors of exotic forms, explore aliquot chains, partition functions, repunits, and computations involving constants like π and e^π√n. Yet it is no ordinary math book. Each piece resonates with Wittgenstein's revolutionary views on mathematics as a human activity, a "language game" governed by rules and practice rather than timeless Platonic truths. Earls candidly grapples with Wittgenstein's ideas - from the Tractatus Logico-Philosophicus and Remarks on the Foundations of Mathematics - while pursuing brute-force computations that challenge traditional boundaries. He revisits foundational concepts like the successor function, Peano arithmetic, Cantor's diagonal argument, and even proofs of 1+1=2 in Principia style, all while questioning logic's limits, infinity, and the nature of "absolute truth" embodied in simple integers. Far from a dry scholarly treatise, this is an intellectual adventure blending hard number crunching with personal meditations, eccentric anecdotes (including Wittgenstein's aeronautical origins and Frege's definitions), and playful speculation. It bridges the abstract "silence" of philosophy with the vibrant "noise" of algorithms, inviting readers - whether mathematicians, philosophers, or curious minds - to engage in honest exploration and perhaps rethink their own "grammar" of the world. In a time when computation transforms how we "do" mathematics, Numbers for Wittgenstein stands as a tribute to rigorous inquiry, intellectual play, and the thrilling intersection where code meets contemplation. Discover why probing integers can feel like testing the very structures of logic itself.