Arezoo Islami, Giuseppe Longo. Marriages of Mathematics and Physics: a challenge for Biology, Invited Paper, in The Necessary Western Conjunction to the Eastern Philosophy of Exploring the Nature of Mind and Life (K. Matsuno et al., eds), Special Issue of Progress in Biophysics and Molecular Biology, Vol 131, Pages 179¬192, December 2017.
Abstract: The human attempts to access, measure and organize physical phenomena haveled toamanifoldconstruction of mathematical and physicalspaces. We will survey the evolution ofgeometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/ArabicAlgebra in this transitionand its Western symbolic developmentis emphasized.In this relation, wewill also discuss changes in the ontological attitudes toward mathematics and its applications.Historically, the encounter of geometric and algebraic perspectives enriched the mathematicalpractices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and thecrisis in the mathematical analysis of the 19th century, led to the exclusion of « geometric judgments »from the foundations of Mathematics.After the success and the limits of the logicoformal analysis, itis necessary to broaden our foundational tools and reexamine the interactions with natural sciences.In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as acrossdisciplinary and crosscultural issue and will be examined in Mathematical Physics and Biology.We finally discuss how the current notions of mathematical (phase) “space” should be revisited for thepurposes of life sciences