"Philosophically, the reason research in math matters is that by pursuing math ideas that are deep and interesting for their own sake, you will get real-world applications in the future," Hofmann said.
"It is like making investments."
When I decide to indulge my students when they whine, "When are we ever gonna have to use this?", sometimes I point to my "When are we ever gonna have to use this" poster which lists dozens of jobs and the math knowledge necessary for those jobs. Other times I tell them about the laser--a device that had no practical application when it was invented in the 50s but now allows us to correct eyesight and listen to music.
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Maybe I'm weird. OK. I'm weird. But I am grateful to have studied algebra and trig enough to know that if I find the right formula I can figure the dimensions of the octagonal wing on my house (7'2"/side) or how long to make the support legs for my photo-voltaic panels to maximize their output (27").
Now tell me how you use sentence diagrams...
I wonder if the count of 120 words counts the amount of equations and mathematical notation that must be in the paper. If it doesn't, then the paper might be 120 words long and still be pretty extensive... ten lines of equations for every line of text, or something.
My students balk -- especially the education majors -- at learning theory in their math classes because they don't think they'll ever "need to know" it. I counter by saying that you just can't predict the future, and we have no clue what we're going to "need" to know ten years or ten days from now.
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