I believe the following about mathematics
· Mathematics is an objective feature of the universe; mathematical objects are real; mathematical truth is universal, absolute, and certain.
· What human beings believe about mathematics therefore has no effect on what mathematics really is. Mathematics would be the same even if there were no human beings, or beings of any sort. Though mathematics is abstract and disembodied, it is real.
· The mathematics of physics resides in physical phenomena themselves - there are ellipses in elliptical orbits of the planets, fractals in the fractal shapes of leaves and branches, logarithms in the logarithmic spirals of snails. This means that "the book of nature is written in mathematics," which implies that the language of mathematics is the language of nature and that only those who know mathematics can truly understand nature.
I think this affects how I teach mathematics in that I am constantly trying to show students how real mathematics is and where they can find mathematics in places they never thought. When a child thinks of nature, they do not think of mathematics, so I like to show them how different things can follow different mathematical patterns. Some develop a greater appreciation for mathematics because of that.
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