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Poplular Maths Articles

From Here to Hensel

Here’s a nice maths problem, which I thought it would be fun to discuss. The question doesn’t involve any advanced concepts, but it leads on to a very nice result called Hensel’s lemma.

dan 2020-12-052020-12-05 Poplular Maths Articles No Comments Read more

Return of the Euler-Fermat theorem

A long long time ago, in a galaxy far away, I wrote up an account of the Euler-Fermat theorem for school students.

dan 2020-12-022020-12-02 Poplular Maths Articles No Comments Read more

Sitting out the math wars

Very few professional mathematicians have been involved in the “math wars”, and when they have, they have not always inspired confidence. I wondered why.

dan 2020-08-232020-08-23 Etc., Poplular Maths Articles No Comments Read more

Not human, but inhabited by humans: writing mathematics

Mathematics can be written in many ways. One approach, very popular with professional pure mathematicians, is to write as little as possible. But there should also be others.

dan 2020-08-172020-08-17 Poplular Maths Articles No Comments Read more

Breakthroughs in primary school arithmetic

Humans have known how to multiply natural numbers for a long time. In primary school you learn how to multiply numbers using an algorithm which is often called long multiplication, but it’s called “long” for a reason! Recently, a new paper purports to give an algorithm to multiply faster.

dan 2019-05-052020-06-17 Poplular Maths Articles No Comments Read more

From Liouville geometry to contact geometry

The standard contact structure on R^3.

(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.

dan 2019-02-032020-06-21 Notes, Poplular Maths Articles No Comments Read more

Lovely Liouville geometry

Lovely Liouville geometry

(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.

dan 2019-02-012020-09-21 Notes, Poplular Maths Articles 2 Comments Read more

Emmy had a theorem (mathematical nursery rhyme #2)

In the spirit of previous work in abstract algebra, I have, erm, adapted another nursery rhyme. To the tune of “Mary had a little lamb”, a discussion of Noether’s theorem.

dan 2019-01-272020-06-17 Poplular Maths Articles No Comments Read more

Golay Golay Golay (Top of the autocorrelation world)

In 1949, Marcel Golay was thinking about spectrometry. Here’s what happened next…

dan 2019-01-222020-06-17 Poplular Maths Articles No Comments Read more

Topological entropy: information in the limit of perfect eyesight

Entropy means many different things in different contexts, but there is a wonderful notion of entropy which is purely topological. It only requires a space, and a map on it. It is independent of geometry, or any other arbitrary features — it is a purely intrinsic concept. This notion is known as topological entropy.

dan 2019-01-162020-06-17 Poplular Maths Articles No Comments Read more
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Recent popular articles

  • From Here to Hensel
  • Return of the Euler-Fermat theorem
  • Sitting out the math wars
  • Not human, but inhabited by humans: writing mathematics
  • Breakthroughs in primary school arithmetic
  • From Liouville geometry to contact geometry
  • Lovely Liouville geometry
  • Emmy had a theorem (mathematical nursery rhyme #2)
  • Golay Golay Golay (Top of the autocorrelation world)
  • Topological entropy: information in the limit of perfect eyesight
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