by Jonathan Kujawa
While considering topics for this month's 3QD essay, the US Senate voted to approve a tax bill which not only dramatically reshapes US tax law, but says a great deal about our society's values. We're in an era where research and education are dramatically underfunded and underappreciated, to be knowledgeable about a subject is an automatic disqualification, and where what things which should be a question of fact and evidence are being dragged down into the political muck. I thought about writing about the Dark Ages and how the advancement of knowledge is not guaranteed. About the danger of eating our seed corn. About how it feels like we are truly living in the darkest timeline [1]. But here at 3QD this is preaching to the choir. I'd rather light a candle which can be shared with others. I'd rather talk about Exploding Dots.
In math even the most innocuous ideas can lead to undiscovered worlds. All we need is equal doses of creativity and bravery. The creativity to ask crazy questions and the bravery to try crazy things. As I tell my students, bravery in math should be easy to come by. There is no harm in trying. After all, this isn't brain surgery or nuclear engineering — nobody will die if we screw up! — just erase and try again.
The really scarce commodity is creativity. After 18+ years of schools drilling the creativity right out of your skull, it's awfully hard to let your mathematical freak flag fly. As David Hilbert said when he heard one of his students had dropped out to study poetry, "Good, he did not have enough imagination to become a mathematician". But, with some practice, we can undo the damage of our early years and start to see the wonders of the mathematical universe. Sometimes all it takes is a new perspective.