I believe that mathematics (including computer science and statitics) are very important for understanding biological systems. The complexity of biological systems is extraordinary and researching into the fundamental laws in such a complex field is a very difficult task. Through my experience in data science I have a firm belief that mathematics is a basic tool of understanding a system or its behaviour under various circumstances. If we consider the living organism as a complex system (or a living machine) we can leverage many methods and tools developed in mathematics and allied sciences to understand it through various ways.
We can use mathematics while designing an experiment, seeking interesting patterns, and in the search for most basic laws that govern the system we are studying. Some of the use cases where mathematics find direct application :
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Creating mathematical models that describe biological phenomenon or are able to express relation between entities.
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Using statistical methods we can deny or confirm initial hypothesis.
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Tracking changes in basic measurements in living organisms that show us changes over time.
Thus mathematics can be a bridge to the experimental data that we observe and theoretical models. Theory construction can be seen as an ever-developing entity, interwoven with data and hypotheses. And overtime we can use this models to investigate and study scenarios that are not amenable to experiments.
In some areas of application such as dynamics of infectious diseases or neuroscience, mathematics has already helped give some promising results that were both interesting and important. Moreover historically investigations into biological phenomena have contributed to the development of new ideas in statistics itself. For eg linear discrimant analysis is merely a generalization of Fisher’s linear discrimant and Robert Fisher’s work also led to advancements in the maximum likelihood estimation theory which today is somewhat default method to estimate parameters in a model for someone working in machine learning. A quantitative approach to biology allows traditional interaction diagrams in biology to be extended to mechanistic mathematical models. These models can serve as working hypotheses: they will further help us to understand and predict the behaviour of complex systems.
Currently Dr. Brendan Frey’s work to develop predictive models in genomic sciences and applying deep learning models to study human diseases is inspiring. Such work among many others also help to ignite interest to study biological systems from people of various backgrounds. Mathematics is a language and tool understood by people across the spectrum of science and engineering. Hence using mathematics allows people of different backgrounds an entry into the research of biology.
“The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them” - Sir William Henri Bragg