The field of mathematics is very expansive and involves quantifying the world around us. As such, there are a number of areas where mathematics and various quantitative methods are useful for both analyzing biological data and making predictions about biological processes. The following are just a sampling of these areas where mathematics serves as a powerful tool for biological research.

1) Computational biology. It is a rapidly expanding and cutting edge field that seeks to apply computer science, statistics and applied mathematics to biological problems. Many of the other uses listed below are examples of computational biology, but it was worth mentioning the field as a whole, because its very basis is in the use of mathematics and mathematical modeling.

2) Bioinformatics. Statistics, probability and applied mathematics have been used to a huge degree in molecular biology and proteomics. One of the most famous examples was the human genome project, which took advantage of great computer processing power to sequence the human genome. Sequence alignments allow scientists to compare DNA, RNA and protein sequences to find homology and predict the presences of motifs, genes, structures and even build phylogeny trees that model evolutionary trends.

3) Biophysics. The realms of biochemistry, biophysics and structural biology have seen huge gains thanks to mathematical techniques. Molecular dynamics is the use of Newtonian physics to simulate the movement and interactions of molecules. This allows scientists with just a crystal structure of their molecule to try to gather some information on some of the physical properties of the molecule. The derivation of these forcefields and how to quantify and analyze the resulting simulations are all topics of debate for theorists, physicists and mathematicians alike.

4) Modeling and Visualization. One of the most important aspects of scientific research is the ability to relate information to others. Being able to visualize systems or model molecules is rapidly growing field. Many times, this visualization work is related to similar fields that are trying to predict the structure of RNA or protein molecules. The mathematics involved in developing models and refining them is laborious, but it provides great insight into the function of important biological macromolecules.

5) Disease modeling. A whole field of mathematics has developed that seeks to understand infection rates and how diseases spread from one region to another. These disease models are the basis for choosing the strains that will be used in the yearly flu vaccinations. It also allows governments and other organizations to plan for potentially devastating pandemics or epidemics.

6) Systems biology. Computational biology and statistical analysis are being use more every year to create system models to show the flux of important molecules in a biological system. Metabolomics and proteomics researchers use these techniques to estimate how the body or more specific organ systems take raw materials and produce important system intermediates.

7) Biological chemistry. Math plays a huge role in the field of chemistry and, in turn, is useful for understanding the chemistry of biological reactions. Calculating reaction rates, determining chemical pathways, and even using quantum chemistry to make predictions about the states of certain compounds are all ways that mathematics has been used in biological chemistry.

8) Basic data analysis. Beyond the more specific applications of bioinformatics and quantum chemistry, math is very useful for analyzing data and making predictions from this data. Given a set of data, scientists can use basic statistical analyses to make predictions and draw conclusions about their research. Without the ability to fit lines to data or calculate statistical uncertainty, it would be impossible to determine the validity of scientific data.

9) Clinical research. Without mathematics, determining the success of new therapies or drugs would be impossible. Statistical analyses allow researchers to make claims about their products and back it up with quantitative data. It also allows researchers to challenge claims by providing a measure of statistical accuracy. Researchers also need to determine the amount of a given substance necessary for an effect and how many participants are necessary to make a trial valid, all of which need mathematical procedures.

Mathematics is a critical component of biological research. It gives it validity, allows it to make predictions, and provides a mean for analysis. Without mathematics, biological research would simply be a set of qualitative observations that couldn’t provide any real benefit to society.