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Finding good 'maps' to mathematical answers - Printable Version

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Finding good 'maps' to mathematical answers - Kyng - 06-01-2020

https://www.quantamagazine.org/in-math-it-often-takes-a-good-map-to-find-answers-20200601/

In the late 15th century, Leonardo da Vinci sketched plans for a flying machine that resembled a modern-day helicopter. Today, da Vinci’s “aerial screw” appears fanciful and poignantly ahead of its time. While the device itself was too heavy to fly, the ideas behind it were sound, and those same ideas eventually allowed modern helicopters to take flight. Technology just had to advance over many centuries first.

Mathematicians are often in the same situation as da Vinci: They have big dreams, but mathematical knowledge may not be advanced enough to fulfill them.

Depending on who you ask, for example, present-day mathematicians have nearly as much chance of solving the Riemann hypothesis — the most famous unsolved problem in math — as da Vinci had of building a machine that could actually fly.

“As of yet there’s not been a proposed strategy for handling the Riemann hypothesis that’s even semi-plausible,” said Jacob Tsimerman of the University of Toronto.


Yeah, this is certainly an important skill in mathematics. It's one of the reasons why Fermat's Last Theorem took so long to solve: people tried hundreds of methods to solve it, and when Andrew Wiles finally did find a solution, he took a route through completely different areas of mathematics, that absolutely nobody was expecting :O . Likewise, we have the famous "3n+1 problem": not only do we still have no solution, but we don't even have any idea of what a solution might look like (people have tried the obvious lines of attack, without much success).

Still, it'd be nice to see this skill being taught more in school maths lessons - even if it was only in later years. It'd help students to understand the reasoning and the insight that goes into solving a mathematical problem - and I believe it'd make for a much more intellectually stimulating experience than the mechanical 'rote learning' that one often associates with school mathematics.