From Euclid to Computation: Elementary Proofs in Number Theory

By Jason Earls

From Euclid to Computation: Elementary Proofs in Number Theory by Jason Earls invites readers into the timeless elegance of ancient mathematics while bridging it to modern computational curiosity. Inspired by Books VII-IX of Euclid's Elements, the book revives the clearest, most elementary proofs on divisibility, primes, parity, and the structure of integers - arguments remarkable for their simplicity, rigor, and transparency after over two millennia. These foundational demonstrations use only basic counting, multiplication, and logic, making them both accessible and deeply satisfying. Interspersed throughout are the author's original short papers on recreational number theory, which explore numerical patterns through explicit computation and concrete examples. Twin primes, Fibonacci numbers, factorials, and brilliants all make appearances, often examined through direct calculation and computational experimentation. This alternating structure - Euclidean proof followed by modern computational curiosity - highlights the continuity between ancient wisdom and contemporary discovery, creating a dialogue between Euclid's timeless logic and present-day explorations with numbers. Aimed at amateurs, non-specialists, and anyone who values clear reasoning over technical depth, the book celebrates simple proofs as chains of honest logic. With minimal algebra and an emphasis on the beauty of elementary assumptions, it avoids heavy abstraction in favor of arguments that are transparent, rigorous, and approachable. In doing so, it shows how much beauty, structure, and intellectual satisfaction can arise from the most elementary ideas-and why mathematical proofs can be profoundly rewarding, even when they remain delightfully straightforward.

• Format: Paperback
• Language: English
• ISBN: 1105668916
• ISBN13: 9781105668913
• Release Date: February 2026
• Publisher: Lulu.com
• Length: 210 Pages
• Weight: 0.63 lbs.
• Dimensions: 0.5" x 6.0" x 9.0"