Revealing the necessity for abstract math

On August 8, 1900, the German mathematician David Hilbert gave an address to the International Congress of Mathematicians in Paris, outlining 23 unsolved problems that he thought would form the program of mathematics research in the 20th century.
One hundred years later, mathematicians Sir Michael Atiya and John Tate echoed Hilbert by presenting a list of seven unsolved problems ― the “millennium problems” ― that experts had agreed formed the leading edge of modern mathematics.
Only this time there was money attached: the mutual fund magnate Landon Clay put up $7 million, $1 million for each problem, to be given to anyone who could solve the problems. (None have yet been solved.) Apparently, the project aims to do for math what the X Prize did for space travel: make it sexy again. Or at least lucrative.
But how do you catch the attention of a public that can’t even begin to understand modern math jargon?
That’s where the math popularizer Keith Devlin comes in. In his book, cunningly titled “The Millennium Problems,” he demystifies the frontiers of modern math for the dogged layperson.
Starting with the Riemann hypothesis, the only holdover from the 1900 list, the book shrewdly stacks the problems so that they become more difficult to understand as the reader proceeds. And thank God, because the final chapter is quite a strain. It concerns the Hodge hypothesis, which has something to do with ps and qs and hourglass-shaped multi-dimensional objects. Devlin devotes nearly four pages to convincing his readers that it’s OK if they don’t understand a single word of this chapter.
Which is part of why his effort is such a success. The book candidly cordons off the mathematics that aren’t essential to understanding the problem and puts them in terms a decent high school math student can understand, without being condescending. Devlin even tells his readers what to read if they want to try solving the problems (though he warns that it will probably take the rest of their lives).
Devlin also includes the practical implications of each problem, reminding the reader that math does, in fact, matter. Several of the problems, if solved, could shatter modern cryptography. One could increase industrial efficiency. Another could help explain the fabric of the universe itself. Who knew that such incredible, technical heights could be rendered so accessible?

The Millennium Problems:
The Seven Greatest Unsolved Mathematical Puzzles of Our Time
By Keith Devlin
Basic Books, 237 pp.

by Ben Applegate