2019/03/11 by Henri Lombardi, Lombardi, Henri
Computer Science · Mathematics · #01A65 #03F65 #08Axx #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1903.04200
openalex publication_date 2019/03/11 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28
The book "A Course in Constructive Algebra" (1988) shows the way of understanding classical basic algebra in a constructive style similar to Bishop's Constructive Mathematics. Classical theorems are revisited, with a new flavour, and become much more precise. We are often surprised to find proofs that are simpler and more elegant than the usual ones. In fact, when one cannot use magic tools as the law of excluded middle, it is necessary to understand what is the true content of a classical proof. Also, usual shortcuts allowed in classical proofs introduce sometimes useless detours. In order to understand clearly a problem, prescience may be a handicap.