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the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)

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Examples of research on how people perceive mathematical objects

The golden ratio is often cited in research on pleasing shapes to the human eye in art and architecture. For example, see http://plus.maths.org/content/os/issue22/features/golden/index
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Mathematics and cancer research

The Center for Mathematical Medicine at the Fields Institute at the University of Toronto does much mathematical research related to cancer. For example, see http://www.fields.utoronto.ca/programs/sc …