## 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?

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.

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?

“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

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

# G0lomb

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.

## Carnival Of Mathematics 195 – July 2021

Welcome to the 195th Carnival and my second 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 in to the archive!.

Here are the entries. Enjoy!

This is a video by me discussing how crazy I get when I see crazy math memes on Facebook and Twitter. Most are not educational and further separate mathematics from would-be students. We as mathematicians must do everything we can do to get people to EMBRACE mathematics, not shy away from it.

# A 2021 problem: 20∼21 and 43×47

By: Ed Pegg
Submitted By: Lewis Baxter

Ed Pegg noticed that 2021 = 43 x 47 which are successive primes with 20 and  21 being successive integers. He asked for similar solutions and Robert Israel quickly found the next biggest solution, a number with 36 digits. I (Lewis Baxter) found more than 1500 bigger solutions, the largest having  3011 digits. This month I certified the two primes (which are  20690  apart). Unlike other “titanic” primes they are not the value of some small arithmetic expression.

# Who Needs Trig Sub?

By: Patrick Honner

Mr. Honner sent this link in, bragging about what his students came up with. “This was the coolest math my students produce this year,” Mr Honner gushed!

“I’ve taught this topic for many years and never thought of this approach. I’m grateful to have learned something new from my students, who never fail to impress me with their creativity. And I’m glad I gave them time and space to solve what I thought was an impossible problem! When I teach this next time, I’ll be sure to do it again. And I’ll be sure to share this ingenious integration.”

# When cubic polynomials have three real roots!

Holmer Breaks down how they can be solved using trigonometry. Geometrically, you can visualize it as an equilateral triangle centered directly above the inflection point, where its vertices coincide with the three roots.

# Half a year of the Liquid Tensor Experiment: Amazing developments

By: Peter Scholze
Submitted By: Robin Whitty

“Exactly half a year ago I wrote the Liquid Tensor Experiment blog post, challenging the formalization of a difficult foundational theorem from my Analytic Geometry lecture notes on joint work with Dustin Clausen. While this challenge has not been completed yet, I am excited to announce that the Experiment has verified the entire part of the argument that I was unsure about. I find it absolutely insane that interactive proof assistants are now at the level that within a very reasonable time span they can formally verify difficult original research. Congratulations to everyone involved in the formalization!!

In this Q&A-style blog post, I want to reflect on my experience watching this experiment.”

# Singmaster’s conjecture in the interior of Pascal’s triangle

By: Terence Tao
Submitted By: Robin Whitty

Kaisa MatomäkiMaksym RadziwillXuancheng ShaoJoni Teräväinen, and myself have just uploaded to the arXiv our preprint “Singmaster’s conjecture in the interior of Pascal’s triangle“. This paper leverages the theory of exponential sums over primes to make progress on a well known conjecture of Singmaster which asserts that any natural number larger than 1 appears at most a bounded number of times in Pascal’s triangle.

# #GeometrySketchbook

Submitted By: Sam Hartburn

#GeometrySketchbook is a hashtag that has been used for a daily maths art
challenge throughout June. A huge variety of media and art styles have been
used; if you’re interested in mathematical art you’re sure to find
something inspiring here.