1st CIBio Workshop

It can be said that biomathematics is older than mathematics itself. Even before humankind could count, probably we have already started to wonder how birds fly, why some animals are faster and others stronger. The very simple practical action of making usage of colors (e.g. red and black) and pictures (e.g. eyes in the back) for defending themselves against wide animals, by indigenous, already shows a simple application of biomathematics (logic plus experimental observation). Any attempt to precisely locate when biomathematics started to exist can be a place of failure. For instance, Leonardo of Pisa (also known as Fibonacci) in 1202 wrote down an excise involving a hypothetical growing rabbit population. If at this time, one already had this mentality, it is likely that someone else tried that before, but the written evidences disappeared in the nights of time. However, we can easily identify how/when the embryo that is now on its infancy towards adulthood was fertilized. It was closer than we think, but more far away than we could have guessed. It started in the ending of the 19th century and the onset of the 20th century, with names such as Nicolas Rashevsky, John von Neumann, Jean-Baptiste Lamarck, and Alan Turing[i]; even Schrödinger, notorious physicist in quantum mechanics, presented his fascination with biomathematics in the book “what is life”, predicting things to come, e.g. what is now called protein folding. In fact, surprisingly, it was not uncommon mathematicians and physicists get involved with medical sciences, before biomathematics was recognized as field, informally, such as Leonard Euler started out in a faculty of physiology, Galileo got involved several times with biomechanics. For instance, in the history of statistics, several names got famous applying it to health insurance, which is to a certain extent biostatistics.

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Biomathematics can be found out under several names. Mathematical biology, name traditionally used in the last century, was conventionally concerned about population studies, such as birds population, cell growth and so on. Initially, skepticism was big regarding the applicability of these theories to small scale systems, e.g. cells. Nowadays it is done by areas such as systems biology, synthetic biology, and bioinformatics. Another quite similar area is mathematical physiology. Problems can overlap, such as heartbeat using molecular information can be found in both communities, mathematical biology and mathematical physiology. Others can go further, such as bioengineering and biomechanics. Biomechanics is older than mechanics itself, maybe even bioengineering. The areas differ in the level of mathematics and physics they apply. Nowadays with the age of computer science around, new areas gained momentum, e.g. systems biology and bioinformatics; they differ slightly, sometimes impossible to single out, how they treat problems, apply theories, and interpret results; for instance, synthetic biology and systems biology can be seen as twin sisters fighting for attention, systems biology is the theoretical side, whereas synthetic biology is the “mechanics side”, however it is not accepted by everyone this thumb rule to separate them, in some cases vanity and proud takes place; for synthetic biology, some says that it is the granddaughter of biomechanics, and with reasons. Some prefer to call all these “trends” theoretical biology, a name mainly applied in the 1980s and upcoming days to distinct from the “old”-fashioned biology, but nowadays, it seems not being used too much. Some likes to call them “dry” and “wet” biology, being the former the new trends based on mathematics and physics and the latter the old-styled biology, based on experiments rather than simulations and mathematics.

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The ultimate advance of biomathematics would be a unification of its ramifications, what would make it achieves its adulthood, its most important evolving step, for instance by having graduate courses, similar to any other area of knowledge. This considerable number of ramifications makes biomathematics quite similar to artificial intelligence, that in the last decades passed by a crisis of identity after years of growth and high expectations, claimed by some as being the result of an excess of “Is”; some even proposed new names, e.g. computational intelligence or synthetic intelligence; being the former now a field more focused to problem solving and the latter apparently not used. Correspondingly, if one makes a fast research in the internet, the number of materials is enormous, and so is the number of potential definitions for biomathematics. Thus, two details must be stressed about biomathematics: 1) it needs a single name to unify all the areas; 2) it needs a demarcation, boundaries, not precise, but at least easy to be explained.

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Biomathematics in general takes as granted that the laws of physics can be applied to biological systems, and it is where several issues come up. New laws are demanded, such as some claims that we need to review the concept of generality, once it was built mainly for nonliving matter, which is static and homogeneous compared to living matter. Further, in some cases biomathematics suggests that we can achieve new grounds, like it was done by physics. For centuries, physics set mathematics forward, by making it to develop new theories, such as the tensor theory developed mainly on continuum mechanics and the general theory of relativity. Furthermore, different from the theory of relativity, or even quantum mechanics, biomathematics was not neither developed by a single person or by a small group, it is a precious stone that has been cut for centuries by several scientists, most of them anonymous. The time is certainly ripe for biomathematics, due to computer developments, mathematical establishments, and mainly the current demand for complex diseases modeling; e.g., cancer modeling.  

 

[i] If we accept an “opened” mind, Gregor Mendel and Charles Darwin are examples of an interim biomathematics in practice.