theory - Discover and Developer

The Map Of Mathematics

Unless you were a total pro at mathematics in high school, you probably only have a vague recollection of things like geometry, algebra, and some guy called Isosceles

And that sucks, because mathematics is one of the most fascinating languages humanity has ever devised, but without university-level expertise, you’re going to have a very bad time trying to figure out how things like chaos theoryand fractal geometry tie in with machine learning and all those crazy prime numbers we keep finding.

Enter YouTuber Dominic Walliman, who last December delivered this incredible Map of Physics, and is now back to help us find – or reclaim – a passion for all things numbers.

“The mathematics we learn in school doesn’t quite do the field of mathematics justice – we only get a glimpse of one corner of it, but mathematics as a whole is a huge, and wonderfully diverse subject,” Walliman says in the video below.

To navigate this complex and busting Map of Mathematics, the best place to start is in the middle, where the orangey brown circle depicts the origins of human interest into how numbers explain our Universe:

We’ve then got two main sections that represent the two major fields in mathematics today – Pure Mathematics (an appreciation of the language of numbers itself) and Applied Mathematics (how that language can be used to solve real-world problems).

You can mess around with and download a high-res, zoomable version here, and print it on a throw pillow here, because we all need something to look at on the couch when Taboo is getting a little too weird.

To fully appreciate Walliman’s Map of Mathematics, you should definitely watch the video below to get the proper walkthrough.

All those names of things – topology, complex analysis, and differential geometry – might not sound like much to you now, but you’ll soon learn that they’re really just describing the shapes of things in our Universe, and the way those shapes change in time and space are explained by things like calculus and chaos theory.

Now that you’ve made it through the trickiest theoretical stuff, it’s on to applied Mathematics, which applies to the disciplines of physics, chemistry, and biology, where number systems are integral to understanding how the Universe and everything in it behaves.

You’ve also got engineering, economics, and game theory, and probability, cryptography, and computer science – all of which simply wouldn’t exist had our very cluey ancestors not laid the foundations of number-sleuthing for us centuries ago.

What’s that? Mathematics literally applies to everything in life and the Universe? [Internal cheering by maths teachers intensifies]

If all of this sounds all too basic for you, don’t worry, there’s more to this map than just pure and applied mathematics.

It even covers what could be the biggest mystery of the entire discipline – how researchers examining the foundations of maths have failed to find a complete set of fundamental rules, called axioms, that are provably consistent across every little nook and cranny of the mathematical universe.

The Map of Physics

Physics is a huge, complex field. It also happens to be one of the most fascinating, dealing with everything from black holes and wormholes to quantum teleportation and gravitational waves.

But unless you have an innate knowledge of the field, it’s pretty hard to figure out how all these concepts actually fit together – and how they tie in with the stuff like the physics of inertia and circuits that we learnt in high school.

After all, everyone is constantly trying to prove Einstein wrong, and Stephen Hawking famously struggled to come up with a ‘theory of everything’, so it’s easy to get confused about how things do actually fit together in physics (if at all).

To straighten that out once and for all, YouTuber Dominic Walliman has created a map that shows how the many branches of physics link together, from the earliest days of classical physics and Isaac Newton, all the way through to Einstein’s relativity and quantum physics (with a little bit of philosophy thrown in there for good measure).

It takes you all the way from Newton’s falling apple to today’s scientists trying to peer inside black holes and find a theory to unify gravity with quantum mechanics.

The video shows that there’s a gaping “chasm of ignorance” that physicists need to fill in before we can truly understand how the Universe works. This includes things like dark matter and energy, which work in theory, but so far have never been directly observed or explained.

The bottom line in all of this is that, the more we learn, the more we realise how much we have left to discover, and that’s one of the things we love the most about science.

So, for anyone who’s ever hurt their brain by trying to think about what the Universe is expanding into, or what exactly space-time is made of, this is for you. Because when the history of physics is broken down into a palatable 8 minutes, it suddenly doesn’t seem so scary after all.