Math

Prime numbers are among the most intriguing puzzles in mathematics — seemingly random yet deeply significant. 

Their elusive pattern defies easy detection, making them both a source of fascination and frustration. The challenge grows exponentially with larger numbers, where determining if a number is prime becomes immensely time-consuming.

However, some clever shortcuts can speed up the search and help us swiftly eliminate impostors.

Before we can uncover the hidden mysteries behind prime numbers, we must first face the challenge of finding them…

You’ve probably seen this puzzle before.

You could probably solve it without too much hassle.

But let’s ask a more interesting question…

What is the fewest number of moves required to solve the puzzle? 

Can we prove we’re correct?

Luckily, studying for a degree in mathematics is different from high school.

Math class didn’t exactly get the best reputation in school — and I can see why. It tells students to learn about seemingly pointless techniques and memorise different formulas that 99% of them will never use again — unless they go on to become math teachers.

Things change, however, when you decide to study maths at a higher level.

Mathematics becomes much more precise, and more transparent, and emphasises problem-solving over performing the same laborious calculations you’ve done hundreds of times before from a textbook.

It becomes a transferrable skill that you can build and develop and will serve you in many different areas of work. You also start studying more advanced concepts that are useful in engineering, economics, computer science, or pretty much any STEM subject.

But it’s also a big adjustment, and if you don’t know what you’re getting in for, it can be quite a shock. So here’s a list of things I wish I’d known before arriving at my first lecture.

Have you ever climbed a staircase that just didn’t seem to be made for human legs?

The steps are too small to comfortably take one at a time, but too large for an easy double-stair.

You either end up shuffling along with baby-steps, or stretching so far that it feels like you’re trying out for the gymnastics team.

In situations like these, you might start to wonder (or maybe it’s just me?): how many different ways could you actually climb this staircase, taking just one or two stairs at a time?

Suppose you’ve just been hired as the new manager of Hilbert’s Infinite Hotel. 

On your first day you arrive at work only to be greeted by an infinitely long line of people in the lobby each expecting a room.

The Problem? All of the infinite number of rooms are already occupied by an infinite number of guests. The Infinite Hotel is full.

Turning them all away is out of the question — you’d get an infinite number of complaints and that would take literally forever to deal with.

You also can’t ask the current guests to leave to make room for the new ones as then you’d get an infinite number of 1 star reviews, and that would probably bring the average rating down a little.