{"id":17181,"date":"2026-08-23T15:15:36","date_gmt":"2026-08-23T20:15:36","guid":{"rendered":"https:\/\/ericsiegmund.com\/fireant\/?p=17181"},"modified":"2026-08-23T15:15:40","modified_gmt":"2026-08-23T20:15:40","slug":"fun-with-math","status":"publish","type":"post","link":"https:\/\/ericsiegmund.com\/fireant\/2026\/08\/23\/fun-with-math\/","title":{"rendered":"Fun with Math"},"content":{"rendered":"\n

Look*, I know the post title is an oxymoron, at least for people like me (and, possibly, you \u2014 I hope for at least some of you, which will make me feel better, albeit at your expense). I don’t understand advanced math, which I define as essentially anything that’s not basic algebra (or simple arithmetic; I like<\/em> arithmetic). I managed to get a C in undergrad calculus and I was ecstatic at that achievement, and I’m sure I can run a three minute mile before I can solve a quadratic equation.<\/p>\n\n\n\n

\"Meme:
This pretty much captures my experience with college-level calculus<\/figcaption><\/figure>\n\n\n\n

So you should be as puzzled as I am as to why I googled hardest math problems in the world<\/em><\/a> yesterday.<\/p>\n\n\n\n

*Irrelevant aside \u2014<\/strong> Have you noticed that many of the talking heads on TV now preface their statements with “look”? I have, and it’s annoying. Psychologists say that it’s an attempt to force the listener to accept as fact an unproven premise, and to make us think the speaker is normal and “no-nonsense.” Thanks to its overuse, it achieves none of those things. But, look, there are exceptions.<\/em><\/p>\n\n\n\n\n\n\n\n

That led me to this web page with the creative title of What’s The Hardest Math Problem in the World?<\/a><\/em>. Google is nothing if not literal. This site ranks nine famous (to somebody<\/em>, I guess) and as yet unsolved problems, starting with the Riemann Hypothesis<\/a>. <\/p>\n\n\n\n

As far as I can tell, the main reason this problem needs to be solved is so that some things involving prime numbers that are believed<\/em> to be true will then be known<\/em> to be true. I don’t know; it sounds like we need to solve this problem so we can say we solved this problem. Anyway, as soon as I hit the reference to the Riemann zeta function<\/em>, my eyes refused to focus until I moved to #2.<\/p>\n\n\n\n

Number two on the list is the P vs. NP Problem<\/a>, which has real world implications because it might help us get better at Sudoku. According to this website, it would also help us to determine the shortest path on a graph; I guess using a ruler is considered unsophisticated. Unfortunately, this is another problem that nobody seems to be able to get a handle on so we’ll continue to be bedeviled by those wily Japanese gamesters, and suffer the embarrassing consequences of eyeballing lines on our graphs.<\/p>\n\n\n\n

Having stumbled past the first two, I landed on number three, and found myself shouting (in my head, of course) Eureka!<\/em> because the Collatz Conjecture<\/a> \u2014 named after a German mathematician, Lothar Collatz<\/a> (1910-1990) \u2014 is a problem that (a) I can’t solve, but (2) I can test it, and at least understand the process behind it.<\/p>\n\n\n\n

Simply put, the Collatz Conjecture works like this (from the How Stuff Works<\/em> website):<\/p>\n\n\n\n

Start with any positive integer. If it\u2019s even, divide by 2. If it\u2019s odd, multiply by 3 and add 1. Repeat with the result of the previous calculation. The Collatz Conjecture posits that no matter what number you start with, you\u2019ll eventually reach 1.<\/p>\n\n\n\n

I decided to try this out for myself, and I chose to start simply, with the number 3. I opened a blank Excel spreadsheet, entered 3 on the first row, and got to work. Second row (or first iteration) is 10 (3 x 3 + 1). Third is 5 (10 \u00f7 2)…and so on. The seventh iteration yielded \u2014 wait for it \u2014 1. So far, so good…the Collatz Conjecture is true for the number 3.<\/p>\n\n\n\n

I felt cocky, so I picked another number at random. This time it was 27. First iteration: 82 (27 x 3 + 1). Second iteration: 41 (82 \u00f7 2). Third…well, let’s just say that things got out of hand quickly. By the time I got to the 77th iteration, we were up to 9,232, and I was beginning to doubt my commitment to the exercise.<\/p>\n\n\n\n

\"Meme:
That feeling when you try to manually solve the Collatz Conjecture using Excel<\/figcaption><\/figure>\n\n\n\n

However, as I recently said, I have time as a retiree to watch lizards, so surely I can also carve out a few more minutes (I hope) to help mankind by proving the Collatz Conjecture…at least with respect to the number 27. I trudged onward and reached my final destination (i.e., the number 1) at iteration #111. That 77th iteration proved to be the maximum value in the entire sequence.<\/p>\n\n\n\n

Now, I did those two computations manually in Excel, but I figured there had to be an easier way. I was sure there was a way to use Excel’s powerful functions to create an equation that would test each preceding result to determine whether it was even or odd, and then apply the proper calculation of the next number in the sequence. <\/p>\n\n\n\n

\"Meme
This applies even if A.I. does it for me…<\/figcaption><\/figure>\n\n\n\n

So I determined to figure that out in the simplest possible way: I cheated \u2014 I asked ChatGPT to do it for me. Turns out that Excel has a one-trick pony function called MOD() whose sole purpose in life is to test a number and decide if it’s even or odd. I had no idea of MOD’s existence, despite having used Excel for decades \u2014 since it kicked Lotus 1-2-3 to the curb (so, almost forty years, for you youngsters). And not once during that time did I ever need a spreadsheet function to distinguish even from odd. As ChatGPT put it, you’ve now encountered one of my favorite categories of Excel functions: the ones that are completely unremarkable until suddenly you realize, \u201cWait a minute…this is exactly what I need.\u201d<\/em><\/p>\n\n\n\n

\"Meme:
Fortunately (and surprisingly), it did turn out to be easy, but I can’t resist a good meme.<\/figcaption><\/figure>\n\n\n\n

If you’re wondering just how the MOD() function works \u2014 and I know you are, inquisitive Gazetter \u2014 it’s really quite simple. The function returns the remainder when a number is divided by 2. If the remainder is 1, the number is odd; if the remainder is 0, it’s even. Thus (the numbers being tested are bolded)…<\/p>