Polygence blog / Research Opportunities and Ideas

12 Math Project Ideas for Middle and High School Students

6 minute read

Mathematics serves as the foundation for most fields of science, such as physics, engineering, computer science, and economics. It equips you with critical problem-solving skills and the ability to break down complex problems into smaller, more manageable parts. It helps you avoid ambiguity and communicate in what is often called “the universal language,” so-called because its principles and concepts are the same worldwide. Beyond the fact that studying math can open up many career opportunities, some mathematicians also simply find beauty in the equations and proofs themselves.

In this post, we’ll give you ideas for different math research and passion projects and talk about how you can showcase your project.

How do I find my math passion project focus?

Because math is so foundational in the sciences, there are many different directions you can take with your math passion project. Decide which topics within mathematics most speak to you. Maybe you’re more interested in how math is used in sports statistics, how you can harness math to solve global problems, or perhaps you’re curious about how math manifests itself in the physical realm. Once you find a topic that interests you, then you can begin to dive deeper. 

Keep in mind that some passion projects may require more technical skills, such as computer programming, whereas others may just explore theoretical concepts. The route you take is totally up to you and what you feel comfortable with, but don’t be afraid to pursue a project if you don’t currently have the technical skills for it. You can view it as an opportunity to learn new skills while also exploring a topic you’re excited about.

Do your own research through Polygence!

Polygence pairs you with an expert mentor in your area of passion. Together, you work to create a high quality research project that is uniquely your own.

What are the best math project ideas?

1. The mathematical properties of elections

In recent years, there has been a lot of discussion about which election mechanism is most effective at achieving various goals. Proposed mechanisms in United States elections include majority elections, the electoral college, approval voting, and ranked-choice voting. All of these mechanisms have benefits and drawbacks, and it turns out that no perfect election mechanism exists. Look at the work being done by mathematicians to understand when elections fail, and what can be done to improve them. Choose the strongest mechanism and use evidence to support your claim.

Idea by math research mentor Grayson

2. Knot theory

A knot is simply a closed loop of string. Explore how mathematicians represent knots on a page. Learn how knots can be combined, and how to find knots that can't be created by combining other knots. You can learn techniques for determining whether or not two knots are distinct, in the sense that neither can be deformed to match the other. You can also study related objects, such as links and braids, and research the application of knots in the physical sciences.

Idea by math research mentor Alex

3. Bayesian basketball win prediction system

The Bayes’ Rule is crucial to modern statistics (as well as data science and machine learning). Using a Bayesian model to predict the probability distribution of basketball performance statistics, you can attempt to predict a team’s win and loss rate versus another team by drawing samples from these distributions and computing correlation to win or loss. Your project could be as simple or as complicated as you want. Based on your interest and comfort level, you could use simple normal models, mixture models, Gibbs sampling, and hidden Markov models. You can also learn how to code a fairly simple simulation in R or Python. Then, you’ll need to learn how to interpret the significance of statistical results and adjust results over time based on the success/failure of your model over time.

Idea by math research mentor Ari

4. Finding value in Major League Baseball free agency

Here’s another sports-related project idea. Every offseason, there are hundreds of professional baseball players who become free agents and can be signed by any team. This project involves determining which players might be a good "value" by deciding which statistics are most important to helping a team win relative to how players are generally paid. After deciding which stats are the most important, a ranked list of "value" can be produced based on expected salaries.

Idea by math research mentor Dante

5. Impact of climate change on drought risk

Are you interested in environmental economics, risk analysis, or water resource economics?

You can use historical data on precipitation, temperature, soil moisture, drought indicators, and meteorological models that simulate atmospheric conditions to train a machine-learning model that can assess the likelihood and intensity of droughts in different regions under different climate scenarios. You can also explore your assessments' potential adaptation strategies and policy implications. This project would require some skills in data processing, machine learning, and meteorological modeling.

Idea by math research mentor Jameson

Go beyond crunching numbers

Interested in Math? We'll match you with an expert mentor who will help you explore your next project.

6. Making machines make art 

You can program a computer to create an infinite number of images, music, video game levels, 3D objects, or text using techniques like neural style transfer, genetic algorithms, rejection sampling, Perlin noise, or Voronoi tessellation. Your challenge then is to create a functioning content generator that you could then showcase on a website, research conference, or even in a gallery exhibition.

Idea by math research mentor Sam

7. Measuring income inequality and social mobility

If you’re interested in the intersection of mathematics and public policy, here’s an idea. Use data from the World Bank, the Organization for Economic Co-operation and Development (OECD), and other sources to calculate the Gini coefficient and the intergenerational elasticity of income for different countries and regions over time. Explore the factors that influence these measures and their implications for economic development and social justice. You will need to have some skills in data collection, analysis, and visualization.

Idea by math research mentor Jameson

8. Rocket (fuel) science

Rockets are mainly made out of fuel. When the fuel burns, it gets heated and expelled out, producing thrust. Fuel is heavy and, for long-range space missions, we need to carry around the fuel for the rest of the mission the whole way. It is important that the fuel gives us the most bang for our buck (i.e., the most acceleration per unit of fuel). Compare the amount of fuel (weight) required to get to various celestial objects and back using current electric and chemical propulsion technologies. Then do a cost analysis and compare how long it would take.

Idea by math research mentor Derek

9. COVID-19 and the global financial crisis

It is shocking how the economic effects of COVID-19 have far outweighed the ones from the Global Financial Crisis in 2007-08. How much is the difference in terms of employment? Production? Let's go to the data!

Idea by math research mentor Alberto

10. Modeling polarization in social networks

We've all seen or heard about nasty political arguments and echo chambers on social media, but how and why do these happen? To try and find out, construct a mathematical and/or computational model of how people with different opinions interact in a social network. When do people come to a consensus, and when do they become more strongly divided? How can we design social networks with these ideas in mind?

Idea by math research mentor Emily

11. The world of mathematics

The history of mathematics dates all the way back to the very first civilizations and followed throughout history all over the globe. This development leads us to our way of living and thinking today. Rarely taught in math courses, the origins of math can provide clear insight into the necessities of learning math and the broad applications that math has in the world. Conduct research on a chosen time period, location, or figure in mathematics and describe the impacts this innovation or innovator had on the development of math as we know it today.

Idea by math research mentor Shae

12. Simulating the stock market

Here’s an idea for a beginner-to-intermediate statistics and programming project centered around Monte Carlo simulations. Monte Carlo simulations are random methods for modeling the outcome of a complicated process. These methods are used in finance all the time. How could you code a program that uses the Monte Carlo technique to "simulate" the stock market? You will need some familiarity with statistics, basic finance, and basic programming in any language to complete this project.

Idea by math research mentor Sahil

How can I showcase my math project?

After you’ve done the hard work of completing your mathematics passion project, it’s also equally important to showcase your accomplishments. You can see that in many of the project ideas above, there is a clear topic, but how you want to present the project is open-ended. You could try to publish a research paper, create a podcast or infographic, or even create a visual representation of your concept. You’ll find that although many project ideas can simply be summarized in a paper, projects can also be showcased in other creative ways.

Polygence Scholars Are Also Passionate About

What are some examples of math passion projects completed by polygence students?

There are several examples of math projects Polygence students have completed through enrolling in our programs; we’ll highlight two here.

  • Ahmet's mathematical passion project offers detailed breakdowns of the first introduced quantum algorithm Deutsch-Jozsa, and the first quantum algorithm proven to be faster than classical algorithms, Grover’s Algorithm. It also includes a side-by-side comparison of the quantum algorithms and their classical counterparts. He uploaded his paper on Github and plans to submit it to an official publication soon.

  • Anna’s finance project provides an overview of topics related to personal finance, covering tax and benefits, tax-deferred savings, interest rates, cost of living, investing, insurance, and housing to help young adults manage their savings. To further her understanding of how different areas of finance influence one's life consumption, she created a life consumption plan for a hypothetical person and produced a paper. 

How can I get guidance and support on my math project?

In this post, we covered how to find the right mathematics project for you, shared a dozen ideas for physics passion projects, and discussed how to showcase your project.

If you have a passion for math–or are generally curious about exploring mathematical concepts–and are interested in pursuing a passion project, Polygence’s programs are a great place to start. You’ll be paired with a mathematics research mentor with whom you’ll be able to meet one-on-one. Through these virtual mentorship sessions, your mentor can help you learn new concepts, troubleshoot issues you encounter along the way to bringing your math project to completion, and brainstorm with you on how to showcase your passion project.