80+ Best Math Projects for High School Students
Math is one of those subjects where the gap between knowing the content and being able to do something with it can feel enormous! You can ace a calculus exam and still have no real sense of what calculus is for.
However, if you’re looking for a way to close that gap, a good math project can help! A math project can take the concepts you're already learning in class and put them in a context where you have to make a modeling decision, defend an assumption, or interpret a result. Beyond the intellectual payoff, a well-executed math project is exactly the kind of independent work that distinguishes your application to competitive colleges and research programs. It shows you can operate without a rubric and are comfortable grappling with problems beyond your grade level.
What makes for a strong math project?
The most common mistake students make is treating a math project like a research report. A strong math project isn't a summary of a mathematical topic, but an original application or investigation. You're either modeling something real, proving something non-trivially, or building computational tools to explore a mathematical question.
The best math projects from what we’ve seen across cohorts have have a specific, answerable question. They use mathematics as the primary method, and produce a result you didn't know before you started. And they're honest about the limitations of the model or approach you used!
With that in mind, here are 80+ project ideas in math that you can check out in high school.
P.S. We've also put together a list of 10 math project ideas for high school students if you're looking for more ideas, a guide to free math programs for high school students, and a roundup of machine learning projects for when you're ready to bring the math and the modelling together!
Statistics and Probability Projects
Statistics is probably the most immediately applicable branch of math available to high school students. You can collect real data, apply real methods, and produce findings that are genuinely informative. That's rare in most math coursework and makes these projects particularly strong for competitions and college portfolios.
Analyzing the relationship between hours of sleep and GPA at your school using survey data you collect yourself
Studying whether home field advantage is statistically significant in your favorite sport (use a full season's data)
Examining whether Benford's Law holds across different real-world datasets (stock prices, city populations, tax returns)
Analyzing the accuracy of weather forecasts in your region over a 12-month period
Modeling the probability of college admission outcomes using publicly available acceptance rate and SAT data
Studying whether standardized test scores predict college GPA better than high school GPA does
Analyzing racial or socioeconomic disparities in school disciplinary data from a public district
Examining the birthday problem in practice: collecting birth dates from a large group and comparing to the theoretical prediction
Investigating Simpson's Paradox using a real dataset where aggregate trends reverse at the subgroup level
Modeling the spread of a rumor through a social network using a stochastic simulation
Analyzing the gambler's ruin problem with simulation vs. analytical solution
Studying regression to the mean in sports: do elite performers in year one reliably decline in year two?
Examining publication bias in academic research using funnel plot analysis on a meta-dataset
Analyzing word frequency distributions in large text corpora and testing whether Zipf's Law holds
Modeling the reliability of a complex system using fault tree analysis and probability theory
Calculus and Mathematical Modeling Projects
These projects work best when you're in or past Calculus BC. The goal is applying differentiation, integration, or differential equations to a real system and interpreting what the math tells you about how the system behaves.
Modeling population growth using logistic differential equations and fitting the model to a real population dataset
Optimizing the shape of a can to minimize material used for a fixed volume (classic but extensible)
Modeling the spread of an infectious disease using an SIR model implemented from scratch in Python
Using numerical integration to estimate the area under a measured curve (e.g., a GPS elevation profile)
Modeling heat diffusion across a metal rod using the heat equation and finite difference methods
Analyzing the brachistochrone problem and deriving the optimal curve using variational calculus
Modeling the trajectory of a projectile with air resistance and comparing it to the no-drag approximation
Using related rates to model how water level changes in a non-uniform container as it drains
Applying optimization to a real logistics problem (minimum distance delivery routing for a small set of stops)
Modeling a pendulum's motion with and without the small-angle approximation and comparing both at larger angles
Using integration to derive the moment of inertia of custom-shaped objects and verifying with physical experiments
Modeling predator-prey population dynamics using the Lotka-Volterra equations
Linear Algebra and Discrete Math Projects
These are among the highest-leverage projects for students interested in computer science, AI, or data science. Linear algebra is the mathematical backbone of machine learning, and discrete math underpins algorithms, cryptography, and network analysis.
Implementing principal component analysis (PCA) from scratch and applying it to a real dataset to visualize dimensionality reduction
Modeling social network structure using graph theory and computing centrality metrics (degree, betweenness, eigenvector)
Analyzing the mathematics of Google's PageRank algorithm and implementing a simplified version
Exploring the four color theorem with a computational approach on a set of real maps
Studying Markov chains by modeling a real system (weather transitions, board game outcomes, text generation)
Applying matrix transformations to image processing (rotation, shearing, scaling) and building an interactive demo
Exploring the mathematics of error-correcting codes (Hamming codes) and implementing a simple encoder/decoder
Studying the traveling salesman problem using both brute force and heuristic approaches and analyzing the computational cost tradeoff
Implementing Gaussian elimination from scratch and analyzing its numerical stability
Exploring the mathematics of RSA encryption and implementing a small-key version from number theory principles
Number Theory Projects
Number theory is deceptively accessible and produces genuinely surprising results. These projects are particularly strong for math competitions and independent research portfolios.
Investigating the distribution of prime gaps and testing whether patterns hold across large ranges
Exploring the Collatz conjecture computationally: testing stopping times for large starting values and looking for patterns
Studying the relationship between the Fibonacci sequence and the golden ratio in biological structures
Analyzing the distribution of last digits in prime numbers and testing for uniform distribution
Investigating perfect numbers, amicable numbers, and abundant numbers and searching for patterns in their structure
Exploring modular arithmetic applications in calendar systems and day-of-week computation
Studying the mathematics behind public key cryptography using Fermat's little theorem and Euler's totient function
Investigating the representation of integers as sums of squares (Lagrange's four-square theorem)
Exploring continued fraction representations of irrational numbers and testing their convergence properties
Studying the distribution of digits in pi, e, and other transcendental numbers for evidence of normality
Geometry and Topology Projects
Investigating the mathematics of origami: which geometric constructions are possible by paper folding that aren't by compass and straightedge
Studying the Euler characteristic of different polyhedra and surfaces and testing V - E + F = 2
Exploring fractal geometry by computing the Hausdorff dimension of the Sierpinski triangle and Koch snowflake
Modeling the geometry of soap bubbles and verifying Plateau's laws computationally
Investigating the mathematics of perspective drawing and projective geometry
Studying the geometry of non-Euclidean spaces using a hyperbolic plane model
Exploring the four-dimensional analog of common 3D shapes (tesseract, hyperoctahedron) using projection
Analyzing the mathematical properties of Voronoi diagrams and their applications in geography and biology
Investigating isoperimetric problems: which shapes maximize area for a fixed perimeter
Studying the mathematics of knots and exploring knot invariants
Applied and Interdisciplinary Math Projects
These are the projects most likely to be distinctive at science fairs and in college applications because they sit at the intersection of math and a domain you care about.
Modeling the acoustics of a concert hall and optimizing speaker placement using wave equations
Applying game theory to analyze a real negotiation or auction scenario (spectrum auctions, NFL draft picks)
Modeling stock price behavior using geometric Brownian motion and Monte Carlo simulation
Studying the mathematics of voting systems (Borda count, instant runoff, Condorcet) and testing for paradoxes
Modeling traffic flow using the LWR partial differential equation and simulating congestion patterns
Applying operations research to optimize a school bus route or event scheduling problem
Studying the mathematics of epidemiological compartment models and comparing predictions to real outbreak data
Modeling the physics of a roller coaster using calculus and verifying with energy conservation
Applying information theory to analyze data compression algorithms (Shannon entropy, Huffman coding)
Studying the mathematics of auction theory and bidding strategy under different auction formats
Modeling financial derivatives pricing using the Black-Scholes equation
Analyzing the mathematics of GPS triangulation and its sensitivity to measurement error
Studying the mathematical structure of the 12-tone equal temperament tuning system in music
Computational Math and Algorithm Projects
These projects are ideal for students with some programming background. The math is the point, and code is the tool you use to explore it.
Implementing Newton's method and comparing convergence rates for different functions
Building a Runge-Kutta ODE solver from scratch and applying it to a real dynamical system
Implementing the Fast Fourier Transform and using it to analyze audio signal frequency content
Studying the numerical behavior of different sorting algorithms and analyzing time complexity empirically vs. theoretically
Implementing a cellular automaton (Conway's Game of Life) and exploring which initial conditions produce stable structures
Building a symbolic differentiation engine that takes a function as input and returns its derivative
Studying the convergence of iterative methods for solving linear systems (Jacobi, Gauss-Seidel) and comparing them
Implementing a Mandelbrot set visualizer and studying the boundary between bounded and unbounded orbits
Building a Monte Carlo estimator for pi and analyzing how error decreases with sample size
Implementing gradient descent from scratch and applying it to a simple function minimization problem
Studying the behavior of chaotic systems using the logistic map and Lyapunov exponents
Building a Bayesian inference engine for a simple probability problem and comparing results to frequentist approaches
How will I know if my math project actually works?
The students who struggle most with math projects are the ones who pick a topic instead of a question. "The mathematics of cryptography" is a topic. "Does increasing key length in RSA encryption reduce factoring vulnerability at a rate consistent with theoretical predictions?" is a question.
Good scoping means knowing what you're trying to find out before you start, what method you'll use to find it, and what result would count as an answer. This is the same scientific rigor expected in any research context, and it's exactly what math competition judges, science fair reviewers, and college admissions readers are trained to recognize.
One more thing: don't underestimate the power of computing in a math project. Tools like Python (with NumPy, SciPy, and matplotlib), Mathematica, GeoGebra, and Desmos let you explore mathematical behavior at scales and speeds that weren't available to researchers a generation ago. A student who can both derive a result analytically and verify it computationally is operating at a level that impresses people.
How can I use these math projects to do AI research?
The students who do the most interesting AI and data science work are the ones who understand the mathematics underneath the tools. Knowing why gradient descent works, where the normal equations come from, and what a covariance matrix actually represents. That's not something you pick up by running scikit-learn tutorials. It comes from spending real time with linear algebra, probability, and calculus in a context where the math has to produce a result.
Veritas AI is perfect for you if you’re interested in the above! The program pairs high school students with mentors from top universities and AI companies to work on original applied AI projects, with a curriculum that covers the mathematical foundations of machine learning alongside hands-on model development. Students who come in with strong math backgrounds tend to get the most out of the mentorship because they can engage with the "why" behind the methods, not just the implementation. If you're serious about AI research and want to apply the mathematical thinking you've been building, this is the program where that preparation pays off.
You can learn more about Veritas AI here
Frequently Asked Questions
What are good math projects for a high school science fair? The strongest science fair math projects use mathematics to investigate a real-world question with original data or a novel computational approach. Statistical studies, mathematical modeling of physical or biological systems, and computational explorations of number theory or geometry tend to perform well. The key is having a specific research question and a clear methodology, not just a demonstration of a known result.
Do math projects need to involve coding? Not necessarily, but for many of the most interesting projects, Python or another computational tool significantly expands what's possible. Computational math projects also tend to be more engaging to judges who aren't pure mathematicians because you can visualize results and show working code.
What math competitions accept independent project submissions? Competitions like Regeneron ISEF, JSHS, PRIMES (MIT), RSI (MIT), and various regional science fairs accept mathematics research projects. Programs like the Simons Student Research Competition and the Davidson Fellows also welcome original math work. These competitions typically require a formal paper and methodology, not just a demo.
How does a math project help with college applications? A well-executed math project demonstrates intellectual initiative and the ability to work independently on a sustained problem. It's particularly strong for students applying to engineering, computer science, physics, and mathematics programs, where admissions readers understand what it takes to produce original mathematical work. Pairing a strong math project with structured research experience, like the kind offered at Veritas AI, gives you both the work product and the vocabulary to talk about it credibly.
What's the difference between a math project and a math research paper? A math project is a broader term that includes modeling, computational exploration, and applied investigations. A math research paper typically involves proving or disproving a conjecture, extending a known result, or discovering something genuinely new. Most high school students produce projects rather than papers, which is completely appropriate. The distinction matters mostly if you're submitting to academic competitions that require formal proofs and citations.