Recently, a friend told me that Artificial Intelligence is solving some of the most complex problems in mathematics. Complex math problems are not something I spend a great deal of my time worrying about. My math skills ended somewhere around "quadratic equations" and "polynomials”, which I still know how to pronounce. For years, many non-geniuses like me have suspected that math beyond these two mystifying concepts is mostly made up.
"Not so," says my friend. "There are plenty of mathematical mysteries waiting to be solved, and artificial intelligence is on the task," It was good to know that at least I wouldn't be held responsible for advancing the field of math research. My seventh grade algebra teacher, Mrs. Gookins—were she alive today—would back me up on this.
Many of the math problems AI is working on involve a concept called a "paradox". Here is an example of a paradox we can all relate to. You list your monthly budget and spend only what's on it. The bank sends you an overdraft anyway. Either your math is wrong, or the bank's is. This is a paradox because what really happened is that you forgot to account for the six trips to Dutch Bros Coffee and the pair of pants you ordered from Amazon that didn't fit, but you never sent them back.
As is true of stamp collecting and gardening, solving math paradoxes arose from boredom. Years ago, when science was in its infancy, the only entertainment available on our primitive televisions was the Ed Sullivan Show and Pabst Blue Ribbon beer commercials. The beer commercial jingle was a classic and intricate piece of music in which the phrase "What'll ya have? Pabst Blue Ribbon!" was repeated over and over.
With these limited entertainment options, all of us, including math nerds, had plenty of spare time to ponder the mysteries of the universe. People who liked math and held little hope of ever dating an actual live person frequently sat around discussing puzzling math-type questions, known forever after as math paradoxes. To demonstrate how much fun these get-togethers were, I will list a couple of the more exciting paradoxes they pondered.
1. The Combinatorial Optimization Problems in Ramsey Theory
This paradox is a real problem that mathematicians have wrestled with, not something I made up. It asks the critical question: "How many people do you need at a party so that either at least six people all know each other, or at least six people all don't know each other?" Even after thinking very, very hard, our smartest math people have not solved this paradox. I think the correct answer is, "I hate parties."
2. The Riemann Hypothesis
This theory concerns prime numbers, which are numbers that can be divided only by themselves and 1. Math people have for years suspected that prime numbers are doing something strange and perhaps even sinister, but we just can't catch them at it. Personally, I spend very little time worrying that prime numbers might be misbehaving. But I think we can all agree that "The Riemann Hypothesis" would make an excellent title for a movie starring Tom Hanks.
So, artificial intelligence is tackling some of the most daunting questions troubling our scientists. Questions like how many people to invite to your birthday party or what movie project Tom Hanks should consider next.
There is one question that I think will challenge even the most sophisticated Artificial Intelligence computer. I call it the Home Depot-Heinz Paradox. This theory explores why men can find a 3/8-inch hex nut in the plastic bin of random hardware they keep in the garage but are incapable of seeing the giant bottle of ketchup in the refrigerator, even if it's plainly visible. Mathematicians and wives all over the world can only hope that artificial intelligence tackles this difficult paradox in the near future. I think the correct answer is "Because I would've had to move the jar of pickles to see it."