Millions of high-paying jobs are now vacant — and millions more will become vacant — because of a lack of qualified candidates.

What will be the best career opportunities in years to come?

Based on everything I have read and heard, here are three:

o Collaborating with machines to produce more and better work — and do it faster and cheaper — than any machines or people can, working separately.

o Writing programs to do that.

o Training people to do that.

For reasons too complicated to discuss now, a liberal arts education is the best preparation to become qualified for these high-paying jobs.

To gain a much better understanding of the key issues to consider, here’s a source I highly recommend The Mathematical Corporation: Where Machine Intelligence and Human Ingenuity Achieve the Impossible, written by Josh Sullivan and Angela Zutavern and published by PublicAffairs (June 2017).