The dawn of mathematical biology A aurora da biologia matemática

arXiv: History and Philosophy of Physics, 2015

In this paper I describe the early development of the so-called mathematical biophysics, as conceived by Nicolas Rashevsky back in the 1920's, as well as his latter idealization of a "relational biology". I also underline that the creation of the journal "The Bulletin of Mathematical Biophysics" was instrumental in legitimating the efforts of Rashevsky and his students, and I finally argue that his pioneering efforts, while still largely unacknowledged, were vital for the development of important scientific contributions, most notably the McCulloch-Pitts model of neural networks.

Journal of The History of Biology, 2004

This paper explores the work of Nicolas Rashevsky, a Russian émigré theoretical physicist who developed a program in “mathematical biophysics” at the University of Chicago during the 1930s. Stressing the complexity of many biological phenomena, Rashevsky argued that the methods of theoretical physics – namely mathematics – were needed to “simplify” complex biological processes such as cell division and nerve conduction. A maverick of sorts, Rashevsky was a conspicuous figure in the biological community during the 1930s and early 1940s: he participated in several Cold Spring Harbor symposia and received several years of funding from the Rockefeller Foundation. However, in contrast to many other physicists who moved into biology, Rashevsky's work was almost entirely theoretical, and he eventually faced resistance to his mathematical methods. Through an examination of the conceptual, institutional, and scientific context of Rashevsky's work, this paper seeks to understand some of the reasons behind this resistance.

The first part of this paper highlights some key aspects of the differences in the use of mathematical tools in physics and in biology. Scientific knowledge is viewed as a network of interactions, more than as a hierachically organized structure where mathematics would display the essence of phenomena. The concept of "unity" in the biological phenomenon is then discussed. In the second part, a foundational issue in mathematics is revisited, following recent perspectives in the physiology of action. The relevance of the historical formation of mathematical concepts is also emphasized.

2011

Charles Darwin’s 1859 work On the Origin of Species contained no equations. But that does not mean mathematics has no role to play in the science of life; in fact, the field of biomathematics is burgeoning and has been for several decades. Ian Stewart’s new book does an admirable job of unfolding the mathematics undergirding so much of the research being carried out today in the many fields that comprise the subject of biology. Stewart sets the context by noting five great revolutions that have changed the way scientists think about life. These five revolutions are: (i) the microscope; (ii) classification; (iii) evolution; (iv) genetics, and (v) the structure of DNA. The sixth, Stewart says, is well on its way. It is mathematics. I’m ashamed to admit it, but I did not pass my high school biology exam (in the UK it was called the “Ordinary Level” exam, or “O” Level). Reading Chapter 2 of the book (“Creatures Small and Smaller”) brought back a lot of horrible memories about, well, mem...

Keywords: Geometric vs algebraic constructions Ontological and historical differences Synthesis and applications Eastern and western traditions Measurement Space Biological evolution and mathematics a b s t r a c t The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis 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 logico-formal analysis, it is 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 a cross-disciplinary and cross-cultural 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 the purposes of life sciences.

Axiomathes, 2009

Category theory has been proposed as the ultimate algebraic model for biology. We review the Ehresmann-Vanbremeersch theory in the context of other mathematical approaches.

Progress in biophysics and molecular biology, 2013

It is rather ironical that the term used to refer to what are perhaps the most famous equations in biomathematics, the "Volterra-Lotka equations", should bring together the names of two so different scientists, so radically far apart in their backgrounds, conceptions and scientific methods.

Physics of Life Reviews, 2011

This note is motivated by various commentaries which have critically analyzed our contribution to a personal perspective on the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter, and specifically on the challenging goal of developing a mathematical theory for the evolution of living systems. The commentaries (Banasiak and

In this paper we explore the boundary between biology and the study of formal systems (logic).