Final answer:
The difference between science and mathematics arises from their different subject matters and methods of inquiry, with science relying on empirical evidence and the scientific method, while mathematics is based on logical deduction and reasoning.
Step-by-step explanation:
The difference between science and mathematics arises primarily from the nature of their subject matter and their methods of inquiry. Science is an empirical way of knowing about the world, heavily relying on observation, experimentation, and the scientific method. This method involves repeated cycles of making observations, formulating hypotheses, designing experiments, and then making further observations. On the other hand, mathematics is not a natural science; it is more abstract, focusing on the study of patterns, structures, and relationships independent of empirical observations. Mathematics uses deductive reasoning to prove theorems and establish truths based on logical deduction from axioms and definitions, without the need for experimental verification.
While both disciplines seek to understand and describe aspects of the universe and our existence within it, science strives to explain natural phenomena through the laws of nature and scientific theories that are validated or refuted by empirical evidence. Mathematics aids in the formulation of scientific laws and models but is distinct in that its principles are discovered through logic and reasoning, not experimentation. Furthermore, the historical development of both fields and their applications has been influenced by their inherent methods. As science has progressed, technology has advanced with many technological revolutions that have been grounded in scientific discovery. Similarly, mathematical theorems and discoveries have played a crucial role in these advancements but have evolved through a logical progression rather than empirical discovery. This separation is evident in how these subjects have developed over time, and how they continue to impact our understanding of the world.