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.
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.
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 very 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.
If you haven’t already heard, Strava provide a powerful API that allows users to access their data using code. This gives us the ability to create interesting visualisations, analyse progress, and create custom trackers and planners, all with just a few lines of code.
The Travelling Salesman Problem, TSP, describes a scenario where a salesman wishes to visit a number of cities, while taking the shortest possible route, before returning home to the start point. While it may appear simple, this problem not only has no known polynomial time solution, but there is also no time-efficient way to prove that a given solution is in fact optimal.
Imagine you want to travel around Europe. You want to see the sights, and visit as many European capital cities as possible, but you’re on a budget; flights can get expensive, so you plan to travel by rail and bus. To make your funds stretch as far as possible, you need to plan a route that will take you to all of the cities on your list for the cheapest price, before heading home again.
In the ever-expanding field of artificial intelligence, some of the most fascinating advancements come from mimicking the natural world. One such breakthrough is the Genetic Algorithm, a powerful machine learning technique inspired by Charles Darwin’s theory of natural selection. Just as organisms evolve over time, honing their adaptations to thrive in their environments, Genetic Algorithms evolve solutions to complex problems, becoming increasingly effective with each iteration.
