The roots of unity

Okay, so I know I was going to do a post about the Carmichael Numbers, but we went over these things called the roots of unity in maths this week and I just thought they were amazing, so – sorry Carmichael Numbers, but you’re taking a backseat this week. This is going to be good. […]

What is the uncertainty principle – really?

Okay, I know. I’m going rogue today. I’ve deviated to…applied maths. (It’ll be fun. I promise.) Today, I thought we’d check out the uncertainty principle. This principle was thought up by a man named Werner Heisenberg, one of the founders of quantum theory (the physics of, mainly, the very small). Physics at a subatomic level […]

Mersenne primes!

So I was looking around at some Numberphile videos before my Cambridge interview whilst searching for some extra, last-minute mathematical inspiration. I found out about these numbers called Mersenne primes and was struck by the strangeness of it all. A prime is a number whose only prime factor above one is itself. They have always […]

Can you randomly solve a Rubik’s cube?

It’s my first post of December and so I wish everyone a Merry Advent (or a happy whichever-holiday-you-celebrate:))! I also finished my Cambridge interview…! I’m not sure how it went, but I’m just going to go with it’s all in God’s hands:) I am glad to be able to go back to more recreational maths, […]

i to the power of i is…an infinite number of real numbers?

Hi all! I’m back after two hectic weeks. I’m tired and super busy, but looking forward to this post. I also have a Cambridge interview on December 4th so pray for me/wish me well! It’ll probably be over by the next time I post… The Euler formula So today’s maths hinges on my last post, […]

The Euler formula: when e starts drawing circles

What is e? e is the exponential factor and is often used to illustrate increasing growth. When we differentiate e^x, we get e^x; the gradient of the exponential function is itself. Growing with e Any real number can be described in terms of e, for example: We can visualise this on n Argand diagram as […]

The Bernoulli Numbers

The Bernoulli numbers were hinted at by Johann Faulhaber, simultaneously independently discovered by Jakob Bernoulli and Seki Kowa and later rediscovered by Ramanujam. They play a key part in sums and crop up in an array of different areas of maths (including many already talked about on this site!). What are Bernoulli Numbers? The Bernoulli […]

Happy Ada Lovelace Day!

So today, October 9th 2018, marks this year’s Ada Lovelace Day! It’s a day for people to get excited about programming and remember one lady who played a part in getting it all started. Who was Ada? Often referred to as ‘the first computer programmer’, Lady Augusta Ada King, Countess of Lovelace, was a tech […]

When 10 isn’t ten: base systems

A couple of years ago I read ‘Sleeping Giants’ by Sylvain Neuvel. I followed the epic journey of a girl named Rose who stumbled upon an ancient artefact buried in the earth. She grew up to become a scientist leading a team of people to study the object. She and her team find that it […]

A problem of proof: perfect cuboids

So I was at a maths lecture in London and the speaker mentioned an interesting problem that I thought was worth writing about. It goes like this: We hypothesise a cuboid. All the sides of this cuboid have integer lengths, and so do their diagonals. This makes it a Euler brick, named after mathematician Leonhard […]