November digests:
Moon Duchin on the Math of Gerrymandering
The New York Times, November 3, 2025
American democracy depends on the geometry of local maps. The boundaries of congressional districts are redrawn every decade, often by politicians whose reelection hinges on running in a favorable district. This encourages politicians to draw maps that benefit their political party, a practice called gerrymandering. In 2023, the Supreme Court found that Republicans illegally gerrymandered in North Carolina, eroding the voting power of Black communities. In this New York Times article, mathematician Moon Duchin speaks about how math can demonstrate more fair redistricting and alternative voting systems. “The whole world should be paying particular attention to this class of problem, which I’ll call the problem of democracy,” Duchin said.
Classroom Activities: graph theory, algebra
- (Mid-level) In the article, Duchin explains an approach to redistricting with an analogy about shuffling cards. Explain in your own words why Duchin prefers the spanning-tree method to randomization.
- (High level) Read this AMS article for more information about the mathematics of gerrymandering. The math depends on calculating the distances between points in a space, which represents how far voters in the same district live from one another. We can measure this by summing the distance between each pair of points (or voters). Below are voter locations for two congressional districts, one in state A and the other in state B.
Voter locations for two districts. - What is the cumulative distance between voters in each of these imaginary districts?
- What is the average distance between voters in each?
- Plot the points on the same graph, using one color for voters from District A and another for voters from District B.
- Which district do you believe may have resulted from gerrymandering? Why?
—Max Levy
Smooth Earth
The Rest is Science (TikTok), November 20, 2025
How deep would the oceans be if you shrunk Earth down to the size of a classroom globe? Earth’s radius is 4,000 miles but the highest mountain peak is only 12 miles above the deepest undersea trench. This means Earth is actually “unimaginably smooth,” as mathematician Hannah Fry noted in this video. If you shrink our planet’s 42 million foot diameter to 12 inches, you could fill all the Earth’s oceans with less than one tablespoon of water.
Classroom Activities: ratios, unit conversion, geography
- (Mid-level) Using the data in the table below, calculate the following and show your work. (Sources: USGS Water Science School; NOAA; “The Physical Environment: The Earth System” by Michael Ritter; NPR Short Wave.)
- If Earth measured only 1 foot across, how high would Mount Everest’s peak reach above sea level?
- How far would the Mariana Trench reach below sea level?
- What volume of liquid water would Earth contain?
- How tall would your school be on this shrunken surface in inches?
- Convert the height of your shrunken school into meters and millimeters and write the measurements in scientific notation.
- What metric system unit best matches that order of magnitude? (e.g. 10-3 = millimeters)
- (All levels) Complete this 30-minute activity from NASA about the relative distances in the solar system.
—Max Levy
The 19th-century maths that can help you deal with horrible coffee
New Scientist, November 12, 2025
If you’re picking teams, or playing Connect 4, going first gives you an advantage. To mitigate that, you can “take turns at taking turns,” writes Katie Steckles for New Scientist. In this article, Steckles unpacks the technique.
Classroom Activities: calculus, algebra
- (All levels) Read the article. If you recognize the tactic of “taking turns taking turns,” share where you’ve seen it before.
- If there are 3 people sharing the badly brewed pot of coffee, how would you suggest they share it? Explain why.
- What if there are 3 captains picking players ranked 1-10 for sports teams? Calculate the total ranking of each team if your solution is followed.
- (High level, Calculus) Imagine the pot of coffee is a perfect cylinder, and the coffee reaches a height of 10 cm. Now imagine that at a height $h$ centimeters from the bottom of the pot, the strength of the coffee is $1 – h/10$.
- What is the average strength of the coffee in the pot?
- If two people share the coffee normally (the first half of the pot in one cup, the second half in another) what is the average strength of the coffee in the two cups?
- What is the average strength if the two people follow Steckles’ proposed solution?
- What is the average strength for 3 people sharing (1) normally, and (2) according to the solution you proposed earlier?
- Why is it important that the pot is a perfect cylinder?
- (Hard) Suppose the strength of the coffee at height $h$ is $1 – (h/10)^2$. For ten minutes, try to figure out whether it’s possible for two people to both get the same amount of coffee, and the same average strength. After the 10 minutes are up, make your best guess, and explain your reasoning.
—Leila Sloman
How to Identify a Prime Number without a Computer
Scientific American, November 12, 2025
Two centuries ago, long before digital computers or calculators, one mathematician named Édouard Lucas proved that a 39-digit number was prime. To do so, he relied on advanced mathematical theories—but in the end, his procedure was relatively simple. (That doesn’t mean easy!) In this article, Manon Bischoff explains Lucas’s strategy.
Classroom Activities: prime numbers, sequences, arithmetic
- (Mid-level) Read the article. What are the two methods the article gives for deciding whether $2^p – 1$ is prime?
- Prove in two different ways that 127 is prime. Show your work. (Consult the Online Encyclopedia of Integer Sequences to find the elements of the Lucas-Lehmer sequence.)
- Based on the article, how else can you deduce that 127 is prime?
- (High level) Prove that if $n$ is not prime, then $2^n – 1$ is not prime either.
- (High level) This sequence tells you the remainder when you divide the entries of the Lucas-Lehmer sequence by the corresponding Mersenne number.
- Explain in your own words how you can use this sequence to find prime numbers.
- Are the following numbers prime? Explain how you know.
- 2,047
- 8,191
- 32,767
- 131,071
- 524,287
- 4,294,967,295
—Leila Sloman
What to know about Trump’s plan to give Americans a $2,000 tariff dividend
AP News, November 11, 2025
In November, President Trump suggested that the government could write Americans checks for “at least $2,000” with funds raised from his administration’s controversial tariffs. But there may be a problem. “The numbers just don’t check out,” one policy expert told the Associated Press. This article describes Trump’s proposal and uses math to analyze whether it makes sense.
Classroom Activities: economics, arithmetic, algebra
- (All levels) Answer the following questions based on your reading:
- How much money had the tariffs raised by the end of the fiscal year? (September)
- How much more money was raised in that fiscal year compared to the previous year?
- If a \$2000 dividend to every eligible American would cost \$600 billion, then how many Americans are eligible?
- How much more would this dividend program cost than the money raised by tariffs?
- What dividend payment amount would total the money raised by tariffs in the fiscal year? (Assume the same number of eligible recipients.)
- (Mid-level) Economists have argued that tariffs ultimately hurt consumers, as they cause prices to increase.
- Suppose your annual shopping expenses sum to \$12,000. If tariffs raise prices by 20%, then how much do your expenses rise in one year? If the government promises a \$2000 dividend, how much money would you gain from a tariff program overall?
—Max Levy
More of this month’s math headlines
- AI doesn’t add up if you neglect the mathematicians
Financial Times, November 30, 2025 - Mathematicians Just Figured Out How to Better Predict the Future
Popular Mechanics, November 25, 2025 - The Sydney mathematician finding a better way to keep your data safe
The Sydney Morning Herald, November 19, 2025 - Welsh mathematician helps unlock new model that could transform medical treatments
Cymru, November 15, 2025 - New Proofs Probe Soap-Film Singularities
Quanta Magazine, November 12, 2025