Plus.Maths.org
randomness
This article explores this most beautiful of numbers. Find out its definition, why its value can only ever be approximated, what it has to do with waves, and why it contains the history of the Universe.
If you're an artist with an interest in mathematical ideas and patterns then here's a competition for you. Enter by March 31, 2025 to win cash prizes up to £750 !
Worried about your population of bugs? A branching process can help you understand it.
You are faced with a difficult problem, it is not easily solved. How do you feel? Well, if you are Avi Wigderson, one of the winners of the 2021 Abel Prize, you are very happy!
The mathematician Martin Hairer has been awarded the 2021 Breakthrough Prize for Mathematics!
Randomness is surprisingly hard to define. Fortunately the mathematical language we use to describe it is beautifully well defined.
The second guiding principle in probability theory is more subtle – universality.
Symmetry is one of the two guiding principles in understanding probabilities – if different outcomes are equivalent they should have the same probability.
Kolmogorov complexity gives a high value to strings of symbols that are essentially random. But isn't randomness essentially meaningless? Should a measure of information assign a low value to it? The concept of sophistication addresses this question.
There are many ways of saying the same thing — you can use many words, or few. Perhaps information should be measured in terms of the shortest way of expressing it? In the 1960s this idea led to a measure of information called Kolmogorov complexity.
Most of us think that we have the capacity to act freely. Our sense of morality, our legal system, our whole culture is based on the idea that there is such a thing as free will. It's embarrassing then that classical physics seems to tell a different story. And what does quantum theory have to say about free will?