Current Digests: January & February 2026
Gladys West, mathematician whose work paved the way for GPS, dies at 95
NPR, January 23, 2026
Gladys West, a former mathematician with the U.S. Navy, died in January at age 95. West pioneered models of Earth’s shape. Global positioning systems (GPS) still use her findings today. “Despite the struggles of her childhood and the effects of racism on her career, West said she believes she accomplished all she could,” NPR’s Bill Chappell wrote in an obituary for West.
Classroom Activities: geometry, trigonometry, trilateralization
- (Mid-level) To determine a receiver’s location, GPS calculates its distance to satellites orbiting Earth.
- If a GPS satellite is 12,000 miles overhead and its signal moves at the speed of light (~186,000 miles/second), calculate the signal’s travel time.
- Calculate the distances between a receiver and each of three satellites (A, B, and C) if the signals travel for 71 milliseconds, 68 milliseconds, and 72 milliseconds respectively.
- GPS requires at least 3 satellites to determine a receiver’s longitude, latitude, and altitude. Why do you think three satellites are necessary to provide enough information? (Hint: Think of position on Earth as $(x,y,z)$ coordinates.)
- (Mid-level) Consider a simplified GPS that measures a receiver’s location in two dimensions. Suppose Satellite 1 is positioned at the coordinates (0,0), Satellite 2 is at coordinates (8,6), and Satellite 3 is at coordinates (13,4). Determine the coordinates of the following objects. If you are unable to determine the object’s unique coordinates based on the information provided, explain why.
- Object A is 5 units away from Satellite 1 and 5 units away from Satellite 2.
- Object B is equidistant from Satellites 1 and 3.
- Object C is 16 units away from Satellite 1, 6√2 units away from Satellite 2, and 5 units from Satellite 3.
- Object D is equidistant from all three satellites.
— Max Levy
The Math behind a Perfect Poker Deck
Scientific American, January 12, 2026
To play poker successfully, it helps to understand probability. To win, players must find the best five-card hand they can, and hands that display rarer patterns are worth more. Calculating the odds is complicated—but a recent preprint argues that the traditional 52-card deck actually simplifies those calculations. It’s a happy coincidence, writes Emma Hasson: “The usual number of cards in a deck is purely historical.” Perhaps mathematics had something to do with why the 52-card deck has lasted.
Classroom Activities: probability
- (High level) Read the article and answer the following questions.
- Examine the graphic “A Guide to Poker Hands.” If you pull five cards from a four suit, 52-card deck, what is the probability of getting each type of hand? What is the probability that you get none of the hands listed?
- What is the probability that the best hand among five cards is a straight flush? A three of a kind? A high card?
- What is the “showdown probability”? Why is it different from the probability of getting a particular hand?
- What is special about a 52-card deck, according to Williamson’s preprint?
- (Bonus) Try Scientific American’s tie-in poker puzzle.
- (Mid-level) After calculating the probabilities above, play Texas Hold’em in small groups. As you play, identify an odds calculation that would help your game. As homework, write down how you came up with your question, solve it, and explain how the answer would have affected the game.
—Leila Sloman
Math trick speeds up seismic calculations to transform earthquake preparedness
Earth.com, February 15, 2026
Earthquake simulation is slow and expensive. Right now, accurate models require many rounds of computation. “When a single run can take hours on a cluster, teams cannot afford the thousands of repeats they need,” writes Raquel Brandao for Earth.com. But a recent study could change that. In this article, Brandao covers the study, which could reduce the computations need by a factor of 1,000.
Classroom Activities: Fourier transform, simulation
- (Mid-level) Read the first three sections of the article (“Speed meets shaking,” “New models for earthquake simulations,” and “The slow loop”). Answer the following questions.
- What is the goal of earthquake simulation?
- What difficulty is the new work addressing?
- Read this explanation of a seismogram. Describe what a seismogram is in your own words. Using an educated guess, describe how a seismogram can help scientists study earthquakes.
- (Mid-level) A useful tool in seismology is the Fourier transform. Read about the Fourier transform here. Why do you think it might be useful to apply the Fourier transform to a seismogram?
- (High level) This Khan Academy unit explains how to calculate the Fourier transform of a periodic function (called a Fourier series). Watch the videos, and then find the Fourier series coefficients of the following functions.
- $f(x) = \sin(x) + \cos(2x)$
- $f(x) = \sin(x)^2$
- $f(x) = |\cos(x)|$
- $f(x) = \{ x \}$, the fractional part of $x$
—Leila Sloman
Two Twisty Shapes Resolve a Centuries-Old Topology Puzzle
Quanta Magazine, January 20, 2026
If you carve up a surface like a jigsaw puzzle, can you build a new shape out of the pieces? If you want the shape to be smooth and self-contained, then the answer is usually no—the pieces of a sphere can only come together as a sphere; the pieces of a flat sheet can only form a flat sheet. “A relatively small amount of local information about the surface is all you need to figure out its overall form. The part uniquely defines the whole,” wrote Elise Cutts for Quanta Magazine. A new study has finally proven an exception thanks to a series of twisty shapes resembling rhinos.
Classroom Activities: topology, geometry
- (High level) Based on your reading and the first figure in article, explain the difference between extrinsic and intrinsic curvature. Then answer the following:
- What is the mean curvature of a flat surface?
- What is the mean curvature of a cylinder where the largest curvature is 5?
- At a point where the largest curvature is 5 and the smallest curvature is 1, what does the surface look like?
- Where would there be two different mean curvatures on a donut shape (torus)?
- How do the intrinsic curvatures of the above shapes compare to each other? To the intrinsic curvature of a sphere?
- (All levels) Draw a triangle on a flat piece of paper and measure its angles. They should sum to 180 degrees.
- Roll another sheet of paper into a cylinder. With thumbtacks, identify three points to be the corners of a triangle. On a curved surface, a “straight” path means the shortest path, so mark the edges of your triangle with string, stretching the string tight to ensure it traces out the shortest possible path among the corners. Sum the angles of the triangle. Unwrap the cylinder and repeat; do the triangle’s edges change at all?
- Draw a triangle on a globe by moving directly south from the North Pole down to the equator, then moving east along the equator, then moving due north again. What is the sum of this triangle’s three angles?
—Max Levy
This Brooklyn bagel shop is saving money with plug-in batteries
Canary Media, January 19, 2026
An electricity startup called David Energy is giving large batteries away for free, claiming that it will financially benefit both their customers and them. “We’re in the game of nickels and dimes,” said the owner of a bagel shop. That shop uses one of David Energy’s batteries to power their oven during times of peak demand. This Canary article explains how battery technology may improve economics for customers, electricity companies, and renewable energy.
Classroom Activities: financial math, energy costs, algebra
- (All levels) Black Seed Bagels is testing battery technology to reduce demand charges: extra costs levied by a power company when customers use a large amount of power within a short time. According to the article, Black Seed has 10 locations across New York City, and demand charges from peak electricity can represent up to 50% of a company’s monthly utility bills.
- If Black Seed’s average monthly electricity bill is $720 per location, and demand charges make up 40% of each bill, how much are they paying in demand charges each month at that location? How much are they paying in demand charges across all of their locations?
- The article mentions that every kilowatt reduced from peak hours saves about $50 over the course of one month. If three batteries at one location help reduce their rate of demand by 3.5 kilowatts, how much money would that location save per month in demand charges?
- Each of Black Seed’s three plug-in batteries has a capacity of 2.8 kilowatt-hours (kWh). If all three batteries are fully charged and then used during peak hours, how many total kilowatt-hours of stored energy can they provide across all 10 stores? If electricity costs $0.25 per kWh during peak hours, what is the dollar value of the electricity they can provide from stored battery power?
- Suppose the batteries cost David Energy $1,200 per location to provide and install. Based on the savings-per-battery you calculated above, how many months would it take for the total savings across all 10 locations to equal the total investment David Energy made in batteries for all locations?
- Currently, David Energy provides the batteries to customers for free. Based on these savings, could David Energy charge a $20 rental fee per battery in the future? Explain why or why not.
—Max Levy
Explore coverage of the recipients of the 2022 Fields Medals in Nature, Quanta Magazine, and The New York Times.
Read more recent digests of math in the media.
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