DRAFT: Feasible Mathematics

Alexandre Harvey-Tremblay
2018 Figshare  
p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Helvetica Neue'} ***DRAFT: Please note that this paper is a draft. It's purpose is to help me collect my thought and to facilitate informal discussion about the ideas presented herein. This draft remains accessible to facilitate this conversation. For production quality publications, please instead refer to my latest research on a) geometric thermodynamic and b) axiomatic science. *** From algorithmic information theory (and using notions of
more » ... d using notions of algorithmic thermodynamics), we introduce *feasible mathematics* as distinct from *universal mathematics*. Feasible mathematics formalizes the intuition that theorems with very long proofs are unprovable within the context of limited computing resources. It is formalized by augmenting the standard construction of Omega with a conjugate-pair that suppresses programs with long runtimes. The domain of the new construction defines feasible mathematics.
doi:10.6084/m9.figshare.5747322 fatcat:yxcafebesngy3axu65cjidipae