Okay, I usually hate “year in review” type stuff, but this is offbeat enough to appeal. Political Calculations: The Biggest Math Story of 2019. And my degree is in Mathematics, even if it was a geologic age ago…
I have a difference of opinion with Political Calculations on what is the biggest story, but we will start with the one they selected, on Long Division.
Suppose that you need to multiply two really, really big numbers together using the long multiplication method you learned back in grade school. The one where you systematically multiply each individual digit in one number by every digit in another, keeping a rolling tally where you carry numbers to be added to the next digit as you work your way from right to left in performing, pardon the pun, a multitude of multiplications. Wouldn’t it be nice if you could get to the product with less work?
David Harvey and Joris van der Hoeven have developed a method using multidimensional Fast Fourier Transforms, which have practical application in the digital signal processing used to support modern telecommunications, including the compression methods used for digital images, audio, and video files that make it possible for millions to enjoy the millions of cat videos on the Internet.
Click the link above for more details and links to the source material.
Now the story that caught my attention…
Perhaps the most extraordinary math story of the year came when a team of particle physicists, Stephen Parke, Xining Zhang, and Peter Denton, had a question about linear algebra they asked on Reddit roughly five months ago, after they found a simple relationship between eigenvalues and eigenvectors that seemed to allow them to use relatively easy-to-work-with eigenvalues in place of eigenvectors in their analysis of neutrino behavior, which they were looking to validate.
Linear transformations were once the bane of my existence. (Or why a topologist can’t tell the difference between a doughnut and a cup-of-coffee.) Anything that makes that easier would be a beautiful thing.
For a more in-depth article on the discovery of the relationship between eigenvectors and eigenvalues in Hermitian matrices, see Neutrinos Lead to Unexpected Discovery in Basic Math