Is mathematics science or art? Mathematics resembles science. In math, data and examples are collected and hypotheses made. There is a difference in the hypotheses of math versus science: in the former they can be proved, but that could be considered a small point. But I have met mathematicians who don't consider themselves scientists, and I think most mathematicians could probably understand this point of view. The underlying motivation of mathematics is often more artistic than scientific: that practitioners may seek out results they find elegant and beautiful, and not yield to justifications about understanding the world. However, mathematics sometimes struggles against its artistic roots and I have a feeling this is becoming a problem.

Science is beneficial to mathematics in numerous ways. But there is also a dangerous aspect to this relationship as well. If mathematics is too closely viewed as a science, it is treated as such in practical ways: how new results are supported, funded, and published. This danger is perhaps more relevant to pure mathematics, but it has serious implications for applied mathematics as well.

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