Math Digests April 2025

Where Does Meaning Live in a Sentence? Math Might Tell Us.

Quanta Magazine, April 9, 2025

It’s often been said (by Galileo, and later by Richard Feynman) that mathematics is the language of science and nature. But human language has its own mathematical order. In fact, category theorist Tai-Danae Bradley thinks language could help mathematicians uncover new types of logical relationships. Bradley recently spoke with Quanta Magazine about her work. “I like to think of category theory as Mad Libs for mathematics,” Bradley said.

Classroom Activities: linguistics, category theory

  • (All levels) Bradley says, “There are many different ways to study language mathematically. You can think of language as having algebraic structure, for instance. When I multiply two numbers, I get another number. In the same way, I can “multiply,” or combine, two phrases in English and get another one.”
    • Write two examples of this “multiplication” in language.
  • (High level) Based on your reading, answer the following:
    • What is category theory?
    • What is an example of a “morphism”?
    • What is an example of an “enriched morphism”?
    • How does math help an algorithm decide how to fill in the blank “Curiosity killed the ___”?
  • (High level) Bradley told Quanta:

    “If you look at which words tend to come after ‘blue’—like ‘blue marble’ or ‘blue sky,’ but not ‘blue avocado’—can you get a sense of what the word ‘blue’ means? In the linguistic community, that’s not an agreed-upon fact.”

    • Write down your reaction to this quote and discuss as a class.
    • Does knowing which words do and don’t relate to each other tell you what that word means?
    • Do AI chatbots need to truly understand the meaning of their response?

—Max Levy

Why politicians manipulate statistics — and what to do about it

Nature, April 17, 2025

Between 2016 and 2021, approximately 55% and 31% of Republican and Democratic claims investigated by PolitiFact were determined to be false. While not all politicians lie, the ones that do often mislead people by manipulating statistics. “Statistics are much more than just numbers,” wrote Ole J. Forsberg for Nature. “They are numbers with concrete meaning and exist in a specific context.” In this review of a new book titled “Politicians Manipulating Statistics,” Forsberg argues that powerful people and the media must communicate statistics accurately. The article describes the book and its case studies of statistical misconduct.

Classroom Activities: statistics, misinformation

  • (Mid-level) Why do the authors write that setting targets encourages misleading statistics?
  • (Mid-level) Read this explainer about how to present health statistics. Answer the following questions:
    • What’s the difference between absolute risk and relative risk?
    • Why would a sample population that either includes or leaves out the most high-risk individuals matter for health data?
    • How can using frequencies instead of percentages be misleading?
    • How can people use images to display data misleadingly?
  • (All levels) Have you ever encountered any misleading data or statistics? Perhaps it was in the news or on social media. Discuss why you think the way it was presented may have misinformed some people.

—Max Levy

How we gamified mathematical optimization using burritos

Supply Chain Management Review, April 16, 2025

What can burritos teach you about complicated math problems? A lot, according to Lindsay Montanari, the senior director of academic programs at the technology company Gurobi. Gurobi partners with businesses to solve their optimization problems, and Montanari’s team created a new way of teaching the math of supply chain optimization: the Burrito Optimization Game. Optimization is a field of math that studies how to get the most of a good thing or the least of a bad thing. In business, supply chain optimization involves adjusting variables, like cost or modes of transport, to improve efficiency and effectiveness. Montanari wrote for Supply Chain Management Review about her team’s game, which has been played over 50,000 times. “Teaching and learning about complex concepts like optimization does not need to be, well, overly complex,” she wrote.

Classroom Activities: optimization

  • (Mid-level) Answer the following based on your reading.
    • What is optimization?
    • Give two separate examples of optimization that you’ve encountered in your life.
    • For both of those examples, describe which variables/factors are being optimized; what are your constraints; what is a trade-off in the optimization.
  • (All levels) Using the teacher’s guide, play the Burrito Optimization game. (More information is also available in the introductory slide deck and this Game Guide.)

—Max Levy

This versatile piece of maths can help you solve all kinds of problems

New Scientist, April 16, 2025

In this article for New Scientist, Katie Steckles writes about how she used math to help a friend with casting a play. She used a network called a graph to represent characters, with two characters being linked if they appeared together in a scene. Steckles used the graph to figure out whether one actor could play multiple characters, thus simplifying her friend’s job.

Classroom Activities: graph theory, networks

  • (All levels) Steckles modeled the play as a colored graph. Try coloring in the numbered nodes of the following graphs. Use the fewest number of colors possible, but make sure that two connected nodes are always different colors.
Left: Six nodes linked in a circular chain. Middle: A network with 5 nodes. Nodes 1 and 2 are connected. Node 4 is connected to both 1 & 2, as is Node 5. Node 3 is connected to Node 2. Right: An eight-node network. Nodes 2, 6, and 7 form a triangle. Nodes 4, 6, and 8 form another triangle. Nodes 1 and 5 are both connected to Node 7. Node 3 is connected to Node 4.
Graphs created by Leila Sloman using edotor.net. For the middle and right graphs, pairings were generated with numbergenerator.org.
  • (Mid-level) Read the article. Describe in your own words how Steckles used a graph to minimize the number of actors her friend needed to hire. Your description should answer the following questions:
    • What did the nodes in the graph represent?
    • What did the colors in the graph represent?
    • What did the edges in the graph represent?
    • Why was it helpful to use a graph, rather than for the friend to rely on the script and her knowledge about the play?
  • (Mid-level) Brainstorm three different situations that you can model with a colored graph. Draw out the graph and find the best coloring you can. Explain why you think the coloring has the fewest colors, and how sure you are of your solution.

—Leila Sloman

How Liverpool’s title win has completed a mysterious Fibonacci sequence

BBC, April 28, 2025

In 1992, 22 soccer clubs in England and Wales formed the Premier League, now the top soccer league in Europe. As of this year, the championship history of the Premier League exhibits a surprising mathematical pattern: List the number of times each Premier League champion has won the title, and you get the famous Fibonacci sequence—1, 1, 2, 3, 5, 8, 13. Perhaps disappointingly, it’s “nothing more than a spectacular but ultimately misleading coincidence,” writes Kit Yates for the BBC. But other scientific phenomena that seemed like coincidences have sometimes turned out to be much more. Yates takes this opportunity to explain those examples.

Classroom Activities: Fibonacci sequence, causality

  • (Mid-level) Read the article, and answer the following questions:
    • What is the Fibonacci sequence?
    • Explain in detail why the Fibonacci sequence came up for Indian mathematicians enumerating poems of length $n$ units.
    • Why is Yates convinced that the Fibonacci sequence’s appearance in the Premier League records is a coincidence? Do you agree? Why or why not?
  • (Mid-level) Imagine that the Indian mathematicians Yates mentions had been working with different length syllables. In each case below, write (1) a recursive formula for the number of poems with $n$ beats, and (2) compute the number of poems with 10 or fewer beats.
    • Short syllables have two beats, long syllables have four beats
    • Short syllables have one beat, long syllables have three beats
    • Short syllables have two beats, long syllables have three beats
    • (Bonus) Based on your reading, describe how to compute the golden ratio with the Fibonacci sequence. Does the golden ratio have a connection to the above sequences? Why or why not?
  • (All levels) Find more Fibonacci-related activities in our digests from June 2023.

—Leila Sloman

More of this month’s math headlines