Math Digests March & April 2026

March & April digests:

The math of March Madness brackets

Scientific American, March 19, 2026

Predicting the outcomes of every game in college basketball’s March Madness tournament is virtually impossible. With 64 teams and 63 games, there are about 9 quintillion distinct possibilities. That’s why most people’s brackets—predictions of the outcome of each March Madness game—score less than perfectly. Mathematician Sam Spiro wants to know: Can I reconstruct the tournament from a collection of imperfect brackets and their scores? In an article for Scientific American, writer Emma Hasson explains what the mathematician found.

Classroom Activities: probability, combinatorics

    • (Mid-level) Suppose that three of your friends create brackets for a four-team tournament. Based on their brackets and scores, what was the outcome of the matches?
Semifinals are worth 1 point, and championship is worth 5 points.Friend 1's bracket: In semifinals, Team A wins against Team B, and Team C wins against Team D. In championship, Team A wins against Team C. Score: 6 points. Friend 2's bracket: In semifinals, Team B wins against Team A and Team C wins against Team D. In championship, Team C wins against Team B. Score: 0. Friend 3's bracket: In semifinals, Team A wins against Team B and Team D wins against Team C. In championship, Team D wins against Team A. Score: 2 points.
Drawn in Google docs by Max Levy.
  • (Mid-level) Repeat this exercise with 8 teams and 7 matches. Based on their brackets and scores, what was the outcome of the three matches?

    Quarterfinals are worth 1 point each. Semifinals are worth 2 points each. Championship is worth 4 points.Quarterfinals games are: T1 vs. T2, T3 vs. T4, T5 vs. T6, T7 vs. T8. Friend A's bracket: Quarterfinal winners are T1, T4, T5, T7. Seminals: T1 wins against T4, T7 wins against T5. Champion: T1. 9 points. Friend B's bracket: Quarterfinal winners are T1, T3, T6, T8. Semifinals: T1 wins against T3. T6 wins against T8. Champion is T1. 8 points. Friend C's bracket: Quarterfinal winners are T1, T4, T5, T7. Semifinals: T4 wins against T1, and T7 wins against T5. Champion is T4. 5 points. Friend D's bracket: Quarterfinal winners are T2, T4, T6, T7. Semifinals: T4 wins against T2, and T7 wins against T6. Champion is T4. 3 points.
    Drawn in Google docs by Max Levy.

—Max Levy

Huge Numbers tackles mathematics at its most incomprehensibly large

Science News, April 3, 2026

For Science News, Emily Conover reviews a book about big numbers in math, science, and modern life. The book is (appropriately) titled “Huge Numbers” and written by Richard Elwes, a mathematician at the University of Leeds. “The patient reader willing to stick with Elwes will be rewarded with a new appreciation for numbers and a vastly expanded frame of reference for what it means to be truly, unfathomably, large,” Conover writes.

Classroom Activities: integers, numbers, exponentiation

  • (All levels) Read the article and answer the following questions.
    • What is scientific notation? Why is it useful?
    • Why does Elwes say that “small numbers are the exceptions; big numbers are the rule”?
    • What do you think of Elwes’ statement? When does it apply?
  • (Mid-level) Convert the following numbers into scientific notation:
    • 2,000
    • four hundred
    • one trillion
    • one googol
    • two googolplex
  • (Mid-level) Convert the following numbers out of scientific notation:
    • $4 \times 10^4$
    • $4.6 \times 10^2$
    • $3 \uparrow \uparrow 2$
    • $3 \uparrow \uparrow 3$
    • $2 \uparrow \uparrow 4$
  • (Mid-level) Calculate the following:
    • $(3 \uparrow \uparrow 2) \div 3^2$
    • $(2 \uparrow \uparrow 4) \div 2^4$

—Leila Sloman

Mathematicians figured out the perfect espresso

Popular Science, April 6, 2026

You probably know, roughly, how brewing coffee works: Water percolates through a bed, or “puck,” of coffee grounds, picking up flavor and caffeine along the way. But did you know that there’s an active area of mathematical research called percolation theory? In this article for Popular Science, Andrew Paul covers a new paper that simulated 22 different coffee brews. In each case, the authors calculated how easy it was for water to pass through the coffee grounds. The easier it is, the weaker the coffee. “The short answer is that it’s all about puck size,” Paul writes.

Classroom Activities: graph theory, percolation, geometry

  • (All levels) Mathematicians model a percolation system as a network made up of nodes and links. Here are some simplified examples:
    Left: Tree with START node at the root, and END node two layers down. Right: Tree with END node at the root, and START node five layers down.
    Drawn in TikZ by Leila Sloman.
    Connected graph with START node at top and END node at bottom.
    Drawn in TikZ by Leila Sloman.
    • Let’s say our system is permeable if you can find a path, made up of links between nodes, that reaches from the node labeled “START” to the node labeled “END”. Which of the percolation systems above are permeable?
    • What if you can only move downwards, not upwards, along the path?
  • (Mid-level) Describe how the percolation system might represent brewing coffee. What do the nodes represent? What do the links represent?
    • As a class, come up with a definition for permeability through a coffee puck. How does permeability change if the coffee is (a) packed more tightly? (b) ground more coarsely? Describe how these changes would affect the number of nodes and/or links in the mathematical system.
    • Based on the article, does low, high, or zero permeability make the strongest coffee? Justify your answer.
    • Which network above do you think corresponds to the strongest cup of coffee?
  • (High level) In the paper, the authors give a simple equation for measuring permeability $k$: $$k = \frac{\phi^3}{5s^2V},$$ where $\phi$ is the volume of empty space within the coffee puck, $s$ is the surface area of the coffee grounds, and $V$ is the volume of the coffee puck.
    • Model coffee brewing with a glass of ping-pong balls, where the balls represent the coffee grounds. Calculate the permeability of your model.
    • Draw the percolation network that represents your model. Do you notice anything interesting?

—Leila Sloman

New Strides Made on Deceptively Simple ‘Lonely Runner’ Problem | Quanta Magazine

Quanta Magazine, March 6, 2026

Imagine $N$ runners circling a mile-long track, with each runner moving at a different speed. According to the “lonely runner” conjecture, no matter what the runners’ speeds are, the group spreads out over time: Each runner will at some point be $1/N$ miles away from anyone else. This simple question relates to number theory, geometry, and network organization. “For just two or three runners, the conjecture’s proof is elementary,” writes Paulina Rowińska in this Quanta Magazine article. After decades of being stuck at seven runners, mathematicians recently settled the problem for up to ten.

Classroom Activities: rates, geometry

  • (All levels) An analog clock is an example of the lonely runner problem with three runners—the second hand, minute hand, and hour hand.
    • Suppose the circumference of the clock is 1 foot. Write down the unique speed of each “runner” in feet/s.
    • What distance between runners would count as “far” according to the conjecture?
  • (Mid-level) Give an example of times (hour:minute:second) that satisfy the conjecture for each of the following situations.
    • Only the “hour” runner is far from the pack
    • Only the “minute” runner is far from the pack
    • Only the “second” runner is far from the pack
    • Every runner is far from the pack
  • (High level) Now imagine a clock with hands that move at more similar speeds: Hand 1 takes 60 seconds to go around, Hand 2 takes 55 seconds, and Hand 3 takes 50 seconds.
    • If all the hands begin at the same point, which two runners will be furthest apart after 60 seconds?
    • What is that distance, and is it “far” according to the conjecture?
    • How long will it take for one runner to be $1/N$ distance from the rest?

—Max Levy

What to know about National Pi Day 2026

NBC Boston, March 12, 2026

Around 250 B.C.E., Greek mathematician Archimedes closed in on the true value of $\pi$. Archimedes sought the ratio between a circle’s circumference and its diameter. He first inscribed hexagons inside and just outside a circle. The hexagons’ perimeters suggested upper and lower limits for the circle’s perimeter. He gradually refined this estimate using polygons with more sides. The process led him to conclude that all circles share a common circumference-to-diameter ratio of somewhere between $3 \frac{1}{7}$ and $3 \frac{10}{71}$. This article from NBC10 Boston shares more facts about $\pi$.

Classroom Activities: pi

  • (All levels) Have a class-wide competition for who can accurately recite the most digits of $\pi$.
  • (Mid-level) Work on this brain teaser from the National Council of Teachers of Mathematics.
  • (High level) Practice converting between degrees and radians with this “Pi fight” game.
  • (All levels) See this March 2024 Digest for more activity ideas.

—Max Levy

More of this month’s math headlines: