This year, communities around the world are celebrating the Year of Math. It’s a chance to acknowledge the role mathematics continues to play in our lives. At COMAP, we’re sharing a series that looks at moments in history when mathematical modeling made a difference. Our goal is to really see how a mathematical modeling mindset has shaped real discussions, problem-solving, and outcomes.

Before math modeling was something students learned in the classroom, through their local Math Circle, or in contests like HiMCM®/MidMCM and MCM®/ICM®, society was using similar thinking to solve some pretty big real-world challenges. 

During World War II, many of the ideas behind math modeling began to take shape. The problems couldn’t be solved with guesswork, and the consequences of getting those decisions wrong were very real.

Everyday Logic Just Wasn’t Enough

People had to make huge decisions without really knowing if they were right. Deciding on challenges like how to protect ships from submarine attacks, figuring out where radar would help most, and making the best use of limited resources. 

When it came to figuring out the best way to protect ships crossing the Atlantic from submarine attacks, some ideas sounded very reasonable at first. Like spacing out ships to avoid detection. But once they started looking more closely at what was actually happening, that strategy began to change. And they realized that escort carrier strategy mattered, too.

The common thread for this and other problems that needed to be solved during World War II was that no one had a ready-to-go formula where they could plug in values for the variables and get the answers. So people had to look at patterns and change approaches when something clearly wasn’t working, including coming up with new equations.

What’s interesting about this is how people had to decide what details mattered. They had to make assumptions and try out various approaches. Then, they often had to rethink things when the results didn’t make sense.

There wasn’t an obvious path from the question to the answer. It wasn’t a rote exercise. They did create a model for addressing similar questions in the future, though.

What Part of the Process Carried Forward

After the war, this approach continued to be used. It began to appear in fields like transportation, logistics, business, and public policy. Math modeling became a key part of what we now call operations research. More generally, it helped shape how math modeling is used today.

The tools have changed. The problems look different. But the primary core idea is still the same: when a real-world situation is complex, you build a process for thinking through solutions to problems.

All of This Still Matters

When students do math modeling today, they run into the same kinds of challenges people have been dealing with for decades. There’s usually a lot of information (not all of it is useful!), and there's no obvious path to the “right” answer.

And when there isn't a single right answer, the goal is to get close enough to make a better decision and explain why. That’s really what was happening during World War II. One could say that mathematical modeling exploded on the scene, and it helped shape how we view math modeling today.

Perhaps newer models and better decisions can prevent future war altogether – an open-ended problem if ever there was one!

For more on our math modeling impact series, read Year of Math: Katherine Johnson and Modeling to Reach the Moon.