Scientists use a scientific method to investigate phenomena and acquire knowledge. They base the method on verifiable observation — i.e., on replicable empirical evidence rather than on pure logic or supposition — and on the principles of reasoning.  Scientists propose explanations — called hypotheses — for their observed phenomena, and perform experiments to determine whether the results accord with (support) the hypotheses or falsify them. They also formulate theories that encompass whole domains of inquiry, and which bind supported hypotheses together into logically coherent wholes. They refer to theories sometimes as ‘models’, which often have a mathematical or computational basis. 
- Isaac Newton (1643-1727) The Rules of Reasoning in Philosophy Excerpts in: The Mathematical Principles of Natural Philosophy. Source: Modern History Sourcebook
- Full-Text: Newton's Principia: The Mathematical Principles of Natural Philosophy (c1846), including BOOK III. RULES OF REASONING IN PHILOSOPHY
- Leng G, MacGregor DJ. (2008) Mathematical Modelling in Neuroendocrinology. Journal of Neuroendocrinology: From Molecular to Translational Neurobiology 20:713-718.
- Excerpt: Our science is not only about facts, but also about explanations; rational accounts of phenomena, embedded in a framework of theory, which include a wide range of observations and which are predictive of behaviour in circumstances as yet untested. We all seek to explain the world of observations using a set of logically interacting components, and we all simplify by recognising that some observations are important while others can be reasonably neglected. Formulating such explanations mathematically is a natural ambition, because this ensures their logical consistency, and makes them open to structured analysis; it is a stringent test of their intellectual coherence.
- Citizendium Collaborators. (2009) Biology’s Next Microscope: Mathematics. Citizendium Free Online Encyclopedia.
- Excerpt: Mathematics broadly interpreted is a more general microscope. It can reveal otherwise invisible worlds in all kinds of data, not only optical….Charles Darwin was right when he wrote that people with an understanding “of the great leading principles of mathematics... seem to have an extra sense”….Today’s biologists increasingly recognize that appropriate mathematics can help interpret any kind of data. In this sense, mathematics is biology’s next microscope, only better.