Carnival Of Mathematics 206 – July 2022

Welcome to the 206th Carnival and my third time hosting the event.

To see past entries in the Carnival Of Mathematics and future scheduled hosts, please visit The Aperiodical.

I am honored to again host the Carnival of Mathematics! I learn so much from hosting; things I usually wouldn’t be exposed to are jam packed into every Carnival Of Mathematics post. Be sure to dig into the archive!.

Here are the entries. Enjoy!

Math Vs Culture

by Storm Bear Williams

A short little rant about all of those forgotten mathematicians from antiquity that hardly ever get the credit they deserve.

Mom Does Math

by Dr. Alyssa J Foss

I’m on the life long journey to recover from math-phobia. Which is why I have thrown myself into the math world head first! Next to momming and mathing, writing is my favorite thing. So, I’m trying to do the blog thing. This is my first post from September.


Editor’s Note: Her blog, Math Rehab, is really well written. Very worth the read!

What Is the Pascal Matrix?

By Nick Highham

In mathematics, particularly matrix theory and combinatorics, a Pascal matrix is a (possibly infinite) matrix containing the binomial coefficients as its elements. It is thus an encoding of Pascal’s triangle in matrix form. There are three natural ways to achieve this: as a lower-triangular matrix, an upper-triangular matrix, or a symmetric matrix.

Here Professor Higham steps his way through an example.

This article is part of the “What Is” series, available from and in PDF form from the GitHub repository


Editor’s Note: For more on Professor Highham; Twitter, Wiki, Google Scholar, Blog.

Ivan Guo: Financial models of the future

by Dr Ivan Guo

How can a 240-year-old logistics problem be used in quantitative finance? Dr Ivan Guo’s research lies predominantly in the areas of stochastic control and financial mathematics. In this interview with the Sydney Mathematical Research Institute, Ivan describes how stochastic transport theory applies in financial maths and how financial models are applied. He also debunks some misunderstandings about his field.

What does craiyon/DALL·E mini ‘think’ mathematics and mathematicians look like?

By Peter Rowlett

“You may have seen DALL·E mini posts appearing on social media for a little while now – it’s been viral for a couple of weeks, according to Know Your Meme. It’s an artificial intelligence model for producing images, operating as an open-source project mimicking the DALL·E system from company OpenAI but trained on a smaller dataset.”

Peter Rowlett presents a good introduction to DALL-E and offers several awesome examples.


Two Saturday Morning Breakfast Cereal Cartoons

by Zach Weinersmith

The first fun cartoon is titled “Incomplete”. LINK

The second is titled “Mathematics” and we can all feel this one down in our bones! LINK

Editor’s Note: You can find out more about the author here: Twitter, Facebook, Tumblr, Patreon


by Sneak Thief

One of my (many) interest areas is in algorithmic music composition. But it was not until @CarnivalOfMath mentioned that content didn’t need to be blogs, that I thought to submit this.

This piece is one where I use the Golomb ruler to determine the bar position, and length, of notes in a composition. I wrote a short piece of JavaScript which creates the data, incorporate it with a MIDI library which exports a MIDI file, that in turn can be loaded into a sequencer. I then assign each note to specific sound, based on their duration and what my ear tells me is good. (Being a synth-based composer, some sounds change a lot over time and are therefore better for long notes.)

The notes are always determined by me, a human, to match a particular key signature (to they sound in tune) and varied according to previous trial runs of the algorithm. So, for example, if notes of length 10 and 11 do not appear simultaneously I can assign them the notes E and F which (normally) do not sound good together. Similarly, I try to ensure that the start and end of the composition include notes which give an element of “resolution” which is prevalent in most western music. (Just because it’s based on maths, doesn’t mean it has to _sound_ that way!)

Finally, I sprinkle additional sounds generated by a different algorithm.

Click the image within the link to see a representation of the music, and 
you’ll clearly see the ruler being used.