The Map of Mathematics – How Everything in Maths is Interconnected

The Map of Mathematics. Image Source:Dominic Walliman/Youtube

Adding up your loose change, working out how much a round of beers costs or how much change you’ll get back is probably the extent that most people think maths affects them.

“But when am I ever going to use this in real life?” – a question asked in almost every single algebra lesson by students convinced that letters belong in English classes and nowhere near maths class.

Maths is used every single day in a plethora of different ways despite its ambivalent response by a lot of disgruntled students (and adults).

In an attempt to break maths down and explain its uses (and necessity),  Dominic Walliman posted a video on YouTube entitled “The Map of Mathematics”. In just over 11 minutes, he explains how all maths is related and how it can be applied to real world problems.

Dominic starts building this complex Map of Mathematics shown below from the middle. Here the orangish brown circle traces the origins of numbers and how they began.

What are the Different Types of Mathematics?

“Modern mathematics can broadly be broken down into two areas – Pure Maths: the study of mathematics for its own sake, and Applied Maths: when you develop mathematics to help solve some real world problem”, says Dominic in his video below. Both the sections are respectively on the left and right of the orangish brown circle.

So what’s the difference? Pure maths is studying maths just for the sake of studying maths – finding out rules and equations that exist, regardless of whether they’re needed or useful. Applied maths is when these ideas are used to tackle real life problems with real life implications.

That sounds simple – Doesn’t it? Well that’s just a humble beginning to the infinite world of maths. You can play around with a downloadable high-resolution, zoomable version here.

Pure Mathematics and Its Implications

The study of numbers start with the natural numbers, these are the numbers that everyone is familiar with – 1, 2, 3, etc. This includes cardinal numbers used for counting, and ordinal numbers which are used for orders and lists based on a numerical value.

Then the map looks at other kinds of numbers like integers which contain negative numbers, rational numbers like fractions, real numbers which include numbers like pi which go off to infinite decimal points and then complex numbers and a whole bunch of others.

The video then goes on to explain how these pure maths theories have been used and applied to real world problems.

All these complex terms – complex analysis, topology, and differential geometry – might sound alien, but in practicality they’re really just used to just describe the varied shapes of things in our universe.

How those shapes change with respect to time and space are most understandable by higher order calculus and chaos theory.

Similarly, partition theory, combinatorics, linear algebra, matrices and a combination of other principles build up the entire essence of our world as we know it.

Applied Mathematics and Its Implications

Moving towards the right, we have applied mathematics, which is applied in physics, chemistry and biology. Nanotechnology (Applied physics), nuclear medicine (Applied bio-chemistry) and nano-biotechnology (Applied biology), all integrate applied mathematics within their fabric.

Game theory, optimisation, cryptography and machine learning may not mean much to the regular person, but all of them have extremely valuable and real implications in the universe.

The Map of Mathematics
Map of Mathematics
The Map of Mathematics. Image Source: Dominic Walliman/Youtube
There’s more to it

Dominic ends his video “The Map of Mathematics” talking about the foundations of maths. A brief mention goes to Gödel’s incompleteness theory, which came to the conclusion that “mathematics does not have a complete and consistent set of axioms”, meaning that “it’s all kind of made up by us humans”.

If you weren’t confused before, now is the time that you should be.

The video explains everything fairly simply and concisely, so if you’re looking to get a brief understanding then it’s definitely a good starting point.

What Else has Dominic got on his Channel?

His YouTube channel also includes a video on “The Map of Physics” which goes into the same level of detail covering classical physics, relativity, philosophy and quantum physics.

Seeing as physics uses almost all of the pure maths explained his mathematics video, the two complement each other very well.


Map Of Physics: How Different Fields In Physics Are Connected

map of physics





Source Dominic Walliman/Youtube

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