Simple Yet Unsolvable Math Problems

We all know that math is really hard. So hard, in fact, that there's literally a whole Wikipedia page dedicated to unsolved mathematical problems, despite some of the greatest minds in the world working on them around the clock. Inspired by Thompson's list, we've come up with our own list of deceptively simple maths problems.

1. Prime numbers are those magical unicorns that are only divisible by themselves and as far as we know, there's an infinite number of primes, and mathematicians are working hard to constantly find the next largest prime number.

2. This is something most of us have struggled with before - you're moving into a new apartment and trying to bring your old sofa along. But, of course, you have to maneuver it around a corner before you can get comfy on it in your living room. Thompson says, “The largest area that can fit around a corner is called - I kid you not - the sofa constant. Nobody knows for sure how big it is, but we have some pretty big sofas that do work, so we know it has to be at least as big as them. We also have some sofas that don't work, so it has to be smaller than those. All together, we know the sofa constant has to be between 2.2195 and 2.8284.”

3. The Collatz conjecture is one of the most famous unsolved mathematical problems: pick a number, any number. If it's even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat those steps again with your new number. Eventually, if you keep going, you'll eventually end up at 1 every single time (try it for yourself, we'll wait).

4. The Beal conjecture basically goes like this: If Ax + By = Cz

And A, B, C, x, y, and z are all positive integers (whole numbers greater than 0), then A, B, and C should all have a common prime factor. 

A common prime factor means that each of the numbers needs to be divisible by the same prime number. So 15, 10, and 5 all have a common prime factor of 5 (they're all divisible by the prime number 5).

So far, so simple, and it looks like something you would have solved in high school algebra.

But here's the problem. Mathematicians haven't ever been able to solve the Beale conjecture, with x, y, and z all being greater than 2.

5. Similar to the Twin Prime conjecture, Goldbach's conjecture is another seemingly simple question about primes and is famous for how deceptively easy it is. The question here is: is every even number greater than 2 the sum of two primes?

It sounds obvious that the answer would be yes, after all, 3 + 1 = 4, 5 + 1 = 6 and so on.

But, again, no one's been able to prove that this will always be the case, despite years of trying.

The reality is that, as we continue to calculate larger and larger numbers, we may eventually find one that isn't the sum of two primes... or ones that defy all the rules and logic we have so far. And you can be sure mathematicians aren't going to stop looking until they find it.

Knobull suggests further details at:

https://www.sciencealert.com/6-simple-maths-problem-that-no-one-can-solve