VanGogh, Perfect Numbers, and how to annoy a mathematician

One branch of mathematics, Number Theory, boasts the rare quality that many of its theories are

Solve for x

simple enough that even a lay person with no exposure to advanced math can understand them. For example, one theory states that any and every set of positive integers (1,2,3...) has one number that's smaller than all the rest. In the set {1,2,3,4} the smallest number is 1 (easy, right?). Even infinitely large sets have a smallest number. So, the set of all positive even integers {2,4,6,8,...} has a smallest number (and that number is?).

It's a no brainer, right? What's fun, though, is that there are also theories that, easy as they are to understand, no mathematician has yet been able to prove. For example, there is this number creature called the perfect number. It is a number equal to the sum of its proper divisors (numbers that divide evenly into it, excluding the number itself). So, the divisors of 6 are 1, 2, and 3, and 1+2+3=6. Another is 28, because 1+2+4+7+14=28. The next perfect number is 496, and I will leave it up to you to verify that it is perfect. So, the unsolved theory states that there is no such thing as an odd perfect number. Mathematicians think this is true, and no computer has been able to find an odd perfect number, but so far no one has been able to prove that there are no odd perfect numbers.

What's so cool about mathematicians, though, is that they fully believe that someday, someone will come up with a proof. This is the playground for mathematicians- trying to solve centuries old puzzles while also hoping to discover new puzzles.

So, really, math belongs in the philosophy department. Or maybe the art department.

It also helps explain why mathematicians sometimes get touchy when someone asks, "but is it useful?" No one would dare ask that of VanGogh, though they might say to him "I don't get it," and that's ok.

I like Byron. I give him a 42, but I can't dance to it!

I started a post about baseball stats, and you'll never believe what happened next!

This past week has brought with it plenty of late, late nights, thanks to our Kansas City Royals bringing more baseball joy than our city has seen in decades. After nearly 30 years of playoff desert, our beloved team has so far made it to the third round. The city has turned blue: banners on the plaza, seas of blue shirts at work and play, and even blue dyed water in our fountains.

Of course, it's impossible to think about baseball without thinking about math. Statistics abound in baseball perhaps more than in any other sport. Respected statisticians have devoted years of research to the numbers of baseball. There are batting averages, home runs, runs batted in, earned run averages, and hits allowed, just to name a few. With so much data and so much history, statisticians have come up with accurate, albeit complicated, formulas that not only quantify players' performance, but also predict future performance.

With such a powerful tool for measuring performance, it should be a simple matter to correlate compensation with performance, so one would expect players' salaries to reflect past and predicted performance. One would be wrong.

Without going into the complicated data, research has shown that baseball players' salaries are not necessarily directly tied to future or past performance, or even to their importance to a team's success. For complex reasons, determining players' salaries purely on stats just hasn't proven viable.

Which brings us to teachers. Specifically, teachers in Missouri. There is a proposed constitutional amendment on this November's ballot that would use student performance on standardized tests to determine salaries of teachers. It's like the idea of tying baseball players' salaries to performance. Except that there are the added variables by measuring student performance and making the leap in logic that this is a direct result of teacher performance, while ignoring other factors that affect student performance. Except that the data for student performance is not nearly as rich or deep as the data for player performance. Except that, unlike the research into stats and player performance, the current research on the link between student performance and teacher effectiveness is murky at best. Except that unlike baseball stats, which have a long history of accurately predicting future performance, student performance versus teacher effectiveness has only been measured a short time, and even the early data is suggesting that there is not a clear, direct relation. Furthermore, no one yet has successfully predicted the future effectiveness of teachers.

So, even though math can accurately assess and predict player performance, the powers that be have decided that best practice takes much more into account than stats alone. But ironically,  some want to correlate salaries directly to stats in a case where the math can not accurately assess performance.

Good reason and good math lead to a no vote on amendment 3.

My Clementine (or, the value of a peel)

Browsing grocery ads over my Saturday morning latte, I noticed a big, bold citrus sale advertised on the front page. Yum! Contemplating the tangy possibilities, I saw that I could buy a 5 pound box of clementines for $4.88. What a deal!

On the opposite corner of the page was advertised peeled clementines for $3.99/lb.

My eyes darted back and forth. The markup was extraordinary. By the box, clementines were a little less than $1/lb, but peeled, they were about $4/lb. Of course, you're not paying for the weight of the peel in the second scenario. Ok, so estimating that the peel makes up 20% of the weight of the fruit (I googled the question to ensure accuracy), the 5 pound box would yield 4 pounds of peeled fruit, so that brings the price up to $1.22/lb.

Still, hat's a 330% markup. For what? There are about 5 clementines/lb. I, an untrained peeler, can peel a clementine in about a minute. That's one pound in 5 minutes, or 12 lb/hr. So, for an hour's labor, the price of 12 pounds jumps from $14.64 to $48, which means that hour's labor earned about $33. Whoa! That much for peeling fruit? If the store is paying $10/hr to an employee to peel, they're still making $23/hr on the labor (minus overhead, I know).

So, this is why grocery stores sell peeled fruit. It's also why I'll be buying my clementines by the box.

Would you like me to peel one for you?

Math Almost Killed Me

One warm, spring day in 19... found me lying on my back on the asphalt, staring into a sky made blurry by my tears, halfway between biology class and math class. My friend Paris, startled but not phased, lay down next to me. "How long are we going to be here?" he asked.

I was 17 and my life was dramatic. I mean no, not really. I lived a fairly normal life in an average family in the northeast heights of Albuquerque. I had good grades, loyal friends, and a violin. But I was 17, so life was dramatic.

"I can't do it," I sobbed, "I can't go back to Calculus class."

"Hm," suggested Paris.

"I don't get it. It makes no sense. It's like they're just making stuff* up."

"Yep." Paris was not taking Calculus. Paris was wiser than I.

"I'll NEVER understand it! NEVER!!! What the heck* is it even about?!"

"I think that was the late bell." Paris acutely observed.

I eventually made it to class, even managed to pass at the end of the semester. I went on to major in chemical engineering because someone told me I should. This, as it turned out, required several more math classes. After my last math class (partial differential equations, which, counter-intuitively, are more complex than full-fledged differential equations and totally ridiculous, really) I sighed and promised myself that I would never ever again take another math course. I had survived, yes, but it wasn't pretty.

So here I am, teaching math at a local college and finishing up a graduate degree in mathematics. Because life is ironic and fate has a malicious sense of humor. But I have discovered at least three things:

1. Math is unavoidable. You can love it, hate it, fight it, or ignore it, but it will not go away. It surrounds our every living and dying moment.

2. Most people hate math, which is unfortunate, and produces much more angst in life than necessary.

3. There is an actual branch of mathematics called knot theory that studies, yep, knots. I kid you not (haha!)

And so this space is for all those who fear, flirt with, dislike, celebrate, or deny math, so that together we can embrace it, laugh at it, or at least learn to tolerate it. Because it's not going away. It's stubborn like that.




*language edited for the sake of the children