by Jonathan Kujawa
In a miracle we neither understand nor deserve, some of the most outlandish inventions of mathematicians’ fevered imaginations have later prove eminently useful in the real world. We’ve talked about some of these here at 3QD. From using the stretchy math of topology to identify data clusters in medicine, to using exotic measures of distance to fill in large amounts of missing data, to using number systems coming from elliptic curves to create strong encryption systems. These are only a few of the gifts we’ve received over the years from mathematics. Several years ago the mathematicians who congregate at mathoverflow compiled a list of applications for each of the main areas of modern mathematics.
Many of these applications contribute billions of dollars of value to our modern world, and yet in nearly every case the mathematics underpinning these were developed years, decades, or even centuries earlier. Bringing a little math to things often pays off bigly.
Plus, doing math is just plain fun! I may be biased, but I say the (fun + value)/cost ratio of math is pretty close to unbeatable. To quote Steve Earle, “I’ll stand on Bob Dylan’s coffee table in my cowboy boots and say that”.
Last month I asserted one explanation for the “unreasonable effectiveness” of mathematics is its insistence on precision in our language and thought. There is a real power in the mere act of mathematization. Even if you can’t solve the problem using actual mathematics, thinking mathematically often lays bare the real questions, the real obstacles, and the possible paths to a solution.
That’s easier said than done. As any calculus student will tell you, one of the most difficult parts of using mathematics on a real-world problem is turning the messy, ambiguous chaos of the real world into something on which you can try to do math. Read more »