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What’s the next term in the sequence?

a) Possibly the most famous sequence in the history of maths. This is how it begins

1, 1, 2, 3, 5, 8, 13, 21, …

What number is next? And why?

b) Letters can be in sequence too. What is the next letter in this sequence and why? Incredibly simple when you see it. Seemingly impossible when you don’t.

O, T, T, F, F, S, S, …

What letter is next? And why?

c) And one of my favourites, because in many ways a small child has more chance of getting this right than a Professor of Mathematics. What is the next number in this sequence?

1, 11, 21, 1211, 111221, 312211, …

What number is next? And why?

Why the sunflower? It’s all to do with the first sequence.

Maths is all about patterns. There are some beautiful patterns hidden in even the most basic of times tables.

Times Tables, Mandelbrot and the Heart of Mathematics NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologerMathologer PayPal: paypal.me/mathologer(see the P...

❤️Tadashi's Tokieda's Toys❤️
Maybe you've heard that there's such an object as a one-sided shape. Maybe you've made a one-sided shape. Maybe you've cut one in half and seen what happens. Maybe you've cut one in thirds and seen what happens. But have you ever glued two together and then cut those in half? In this numberphile video Tadeshi Tokieda takes you through it. The result is fitting for a February.

Unexpected Shapes (Part 1) - Numberphile Tadashi Tokieda cuts various combinations of loops and Mobius loops - with surprising results.More links & stuff in full description below ↓↓↓Part 2: https:/...

Tadashi's Tokieda's Toys 2.
More marvellous Mobius manipulation.

Unexpected Shapes (Part 2) - Numberphile See part one at: https://youtu.be/wKV0GYvR2X8More links & stuff in full description below ↓↓↓Tadashi Tokieda continues to cut loops and Mobius strips...And m...

For anyone who thinks A-level integration can be a bit of a challenge - and it can - have a look at what it takes to integrate the cube root of tan x.

The Easiest Integral on YouTube He did the derivative!!! Check out Fematika https://www.youtube.com/watch?v=as1vk0IuAHA&t=0s100 integrals: https://youtu.be/dgm4-3-Iv3sshop calculus t-shir...

What does 1+2+3+4+... add up to? You might be surprised, or even astounded, by this answer.

ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12 Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-helpMore links & stuff in full description below ↓↓↓EXTRA ARTICLE BY TONY...

A very good introduction to the mathematics that LLMs/AI such as ChatGPT are built on.

But what is a neural network? | Chapter 1, Deep learning What are the neurons, why are there layers, and what is the math underlying it?Help fund future projects: https://www.patreon.com/3blue1brownWritten/interact...

How Many Seconds in a Day? A Year? And, thinking about it, What exactly is a year?
Matt Parker, talking about eclipses, gives some insight into why a year is much more complicated than it appears. A year is 365 days, surely? Or 365¼ days? “Unfortunately it’s not that simple”.

Solar Eclipse Maths and the Cosmic Coincidence of the Saros Cycle There was a solar eclipse on the 20 March 2015 and so I thought I'd make a quick video of the mathematics behind predicting eclipses. I now regret that decis...

A Christmas Puzzle:
The Hardest Easy Geometry Problem. Only requires properties of angles studied at GCSE but has defeated professional mathematicians.

How To Solve The Hardest Easy Geometry Problem In the figure, what is the value of angle x? This problem is known as Langley's Adventitious Angles. It is also known as the hardest easy geometry problem be...

Complex Numbers are often taught as pretty puzzling algebra; this series from Welch Labs is a great introduction. He tells the story with motivations, visualizations, and animations.

Imaginary Numbers Are Real [Part 1: Introduction] For early access to new videos and other perks: https://www.patreon.com/welchlabsWant to learn more or teach this series? Check out the Imaginary Numbers are...

The hour and minute hands of a clock overlap at 12:00. But what is the time when they next overlap?

A Classic Puzzle suitable for primary school children, but a challenge for an adult as well.
Once upon a time, there was a Farmer who had a tiny boat. The boat was so tiny that it could only carry the Farmer himself and one additional passenger. He wanted to move a Wolf, a Goat, and a Cabbage across a river with his tiny boat.
When the Farmer is around, everyone is safe, the Wolf will not eat the Goat, the Goat will not eat the Cabbage.
But he can’t leave the Wolf alone with the Goat because the Wolf will eat the Goat. He can’t leave the Goat alone with the Cabbage because the Goat will eat the Cabbage.
The question is: How can he safely transport the three of them to the other side of the river?
(To be clear there is no throwing of cabbages – or goats, or wolves. There are no swimming wolves – or goats, or cabbages. There’s just a Farmer with a boat, a Wolf, a Goat, a Cabbage, and a plan.)