If you’re a high school student interested in math, math research is a great way to explore math in a more flexible, interesting way. You’ll explore subject areas like algebra, statistics, calculus, and number theory, and learn how they connect to real-world problems. You’ll also get to choose research topics like patterns in prime numbers, probability in games, geometry in art, or how math is used in fields like data science and cryptography. As you work on your project, you’ll develop logical thinking, problem-solving, and clear mathematical writing skills. You’ll even get to work independently or with a mentor and learn how mathematics is used across different fields.
Why should you conduct math research?
Math research helps you go beyond “getting the right answer” and start thinking about how and why things work. You will explore how math is used in various fields like economics, computer science, and engineering, as well as learn to ask your own questions, break complex ideas into manageable parts, and try different approaches when you get stuck. If you’re thinking about college applications, research can also demonstrate your interest in a subject and your ability to work independently, especially if you write a paper or present your findings somewhere.
With that, here are 40 math research topics for high school students that you can consider.
If you’re looking for math research programs for high school students, you can find them here. You can also check out our blog on STEM research topics here.
Statistics & Data Science
In this field, you’ll analyze data to find patterns, relationships, and possible predictions. You will work with datasets, statistical models, and visualization tools, often using software like Excel, Python, or R.
1. Predicting Academic Performance Using Study Habits
Research Question: Which study habits best predict academic success?
Difficulty Level: Beginner
Here, you can design and distribute surveys to gather data on study routines. You’ll analyze relationships using correlation and regression techniques. Tools like Excel, Google Forms, or SPSS can help you with data collection and analysis. Through this project, you’ll learn about psychology, education, and statistics, and build skills in survey design, statistical reasoning, and interpretation.
2. Detecting Bias in Survey Design
Research Question: How does question phrasing influence survey responses?
Difficulty Level: Beginner
For this project, you can create multiple versions of a survey with slight wording changes and compare the responses statistically. You’ll measure differences and test significance by using tools like Google Forms and Excel. You’ll build skills in experimental design, bias detection, and data interpretation, and learn about psychology, statistics, and research methodology.
3. Analyzing Income Inequality Using Public Data
Research Question: How do you measure and compare income inequality across regions?
Difficulty Level: Intermediate
You can use publicly available datasets from government or global sources and apply statistical measures like the Gini coefficient to evaluate inequality. Using tools like Excel or Python, you’ll visualize distributions and trends. You’ll sharpen your data-handling and interpretation skills and learn about economics, statistics, and public policy.
4. Evaluating the Accuracy of Election Polls
Research Question: How closely do election polls match final results, and what affects how reliable they are?
Difficulty Level: Intermediate
In this project, you can compare polling data with real election results and analyze sampling methods, margins of error, and bias. You can use probability and statistical inference tools, such as Poll Aggregators or SPSS, to assess the reliability of election polls. This will help you build critical thinking and analytical skills, and learn about political science, statistics, and social research methods.
5. Time Series Analysis of Weather Data
Research Question: What can local weather data reveal about patterns and trends over time?
Difficulty Level: Intermediate
Here, you can collect historical weather data and analyze it using time series graphs, moving averages, and trend lines. Tools like Excel or Python can help you visualize patterns and make basic forecasts. This project will help you build skills in trend analysis and data visualization, and learn about environmental science, climatology, and statistics.
6. Sports Performance Analytics
Research Question: Which statistical metrics best predict the success of a team or player?
Difficulty Level: Intermediate
In this project, you can analyze sports datasets, calculate averages and efficiency metrics, and build regression models to evaluate performance. You’ll visualize trends and compare variables by using Excel or Python. You’ll build analytical and data-interpreting skills and explore sports science, statistics, and performance analytics.
7. Predicting Stock Trends from Historical Data
Research Question: Can historical stock prices tell us where the market is headed?
Difficulty Level: Intermediate
For this project, you can analyze stock datasets using regression, moving averages, or time series models. You’ll visualize trends and test predictions by using tools like Python or Excel. You will build financial analysis and coding skills and learn about economics, finance, and data science.
8. Analyzing the Relationship Between Sleep and Productivity
Research Question: How does sleep duration impact productivity or academic performance?
Difficulty Level: Beginner
In this project, you can collect real survey data from students or colleagues on their sleep hours and academic performance, then use correlation and regression analysis to see whether pulling all-nighters actually hurts your grades as much as everyone says. You can visualize and interpret your findings using Excel or SPSS. You’ll learn how psychologists and health scientists study the relationship between lifestyle habits and performance.
Geometry & Topology
In this field, you’ll learn about space, shapes, and spatial relationships. You’ll explore visual patterns and abstract surfaces, often connecting math to design, physics, and engineering.
9. Finding the Shortest Paths in Networks
Research Question: How can the shortest route between points in a network be determined?
Difficulty Level: Intermediate
Here, you can apply graph-theory concepts and algorithms, such as Dijkstra’s algorithm, to solve path-finding problems. You can use coding tools like Python or visual graph software (Gephi or Neo4j Bloom). You’ll develop algorithmic thinking and learn about computer science, logistics, and optimization.
10. Geometry behind Origami Structures
Research Question: What mathematical principles govern paper folding patterns?
Difficulty Level: Beginner
For this topic, you can experiment with folding techniques and analyze crease patterns mathematically. You can document folds and model them using diagrams or software (e.g., TreeMaker or Oripa). This will allow you to build spatial reasoning and design skills, and learn about materials science, engineering, and applied geometry.
11. Knot Theory and Topology
Research Question: How can knots be classified and distinguished mathematically?
Difficulty Level: Intermediate
Here, you study different knot structures and their properties using diagrams and mathematical rules. You can use visualization tools (SnapPy or KnotInfo) or physical rope models. This project helps you build abstract reasoning skills and connects to topology, physics, and molecular biology.
12. Symmetry in Architecture
Research Question: How is symmetry used in architectural design?
Difficulty Level: Beginner
Here, you can analyze buildings or structures using geometric symmetry concepts like reflection, rotation, and translation. You can use tools like GeoGebra to overlay symmetry axes on building images, or AutoCAD to draft and measure symmetry in floor plans. This project helps you build visual and analytical skills and learn about its connections to architecture, art, and geometry.
13. Uses of Voronoi Diagrams
Research Question: How do geometric rules change in curved spaces?
Difficulty Level: Intermediate
In this project, you can create Voronoi diagrams using software tools (QGIS, MATLAB, or Wolfram Mathematica) and apply them to real-world cases like city planning or cell coverage. You can use computational tools such as SciPy or Turf.js, along with geometric reasoning. This will help you build analytical and modeling skills and learn about computational geometry, geography, and data science.
14. Exploring Non-Euclidean Geometry
Research Question: How do geometric rules change in curved spaces?
Difficulty Level: Intermediate
In this project, you can explore spherical or hyperbolic geometry and compare it to standard Euclidean rules. You can visualize these concepts by using tools like GeoGebra, SnapPy, or physical models like a ball with rubber bands tracing geodesics. This project helps you develop abstract reasoning skills and connects to physics, especially relativity, and advanced mathematics.
15. Optimizing Shapes for Maximum Area
Research Question: Which geometric shapes give you the maximum area under fixed constraints?
Difficulty Level: Beginner
In this project, you can explore how different shapes behave when perimeter or boundary conditions are fixed, comparing circles, polygons, and irregular shapes. You can use geometric formulas, graphing tools, or even simulations in Python/GeoGebra. This project will help you build spatial reasoning and optimization skills and learn about geometry, physics, calculus, and engineering design.
16. Analyzing Tessellations Using Math
Research Question: Which shapes can tile a plane without gaps or overlaps?
Difficulty Level: Beginner
In this project, you’ll investigate which shapes can tile a plane without gaps by analyzing how their interior angles must sum to exactly 360° at every vertex. You can create and test your own tessellations digitally using GeoGebra or Inkscape. You can also explore more complex irregular tilings, such as Penrose patterns, which never repeat. You’ll study honeycomb structures, architectural floor designs, and Islamic mosaic art, which will help you build visualization and geometric reasoning skills.
Algebra & Number Theory
This field explores patterns in numbers, equations, and logical relationships. You’ll often work on proofs, sequences, and abstract problems, which will help you build strong reasoning skills used in pure math and cryptography.
17. Investigating Patterns in Prime Numbers
Research Question: Are there observable patterns in the distribution of prime numbers?
Difficulty Level: Beginner
You’ll explore sequences of prime numbers and analyze their distribution using mathematical reasoning and coding tools (NumPy or p5.js). You can use Python to generate large datasets and test hypotheses. This project helps you build logical thinking and pattern recognition skills, connecting to pure mathematics and number theory.
18. Solving Diophantine Equations
Research Question: How can you find and generalize integer solutions to polynomial equations?
Difficulty Level: Intermediate
In this project, you’ll explore equations that require integer solutions and test different solving techniques. You’ll develop proofs and identify patterns. This project will help you build algebraic reasoning and connect to number theory and pure mathematics.
19. Cryptography Using Modular Arithmetic
Research Question: How is modular arithmetic used in modern encryption systems?
Difficulty Level: Intermediate
Here, you can study encryption methods such as RSA (Rivest-Shamir-Adleman) and simulate them using modular arithmetic in tools like Python or Wolfram Mathematica. You can use coding tools to implement simple encryption models. You’ll develop problem-solving and computational skills as well as explore cybersecurity, computer science, and number theory.
20. Fibonacci Sequences in Natural Systems
Research Question: How do Fibonacci sequences show up in nature?
Difficulty Level: Beginner
Here, you can study examples in plants, shells, or growth patterns and model them mathematically. You can use image analysis or simple coding tools (GeoGebra, Scratch, or Wolfram Alpha). This project helps you build modeling skills and explore how it connects to biology and mathematics.
21. Exploring the Collatz Conjecture
Research Question: What patterns appear in sequences generated by the Collatz function?
Difficulty Level: Beginner
In this project, you can generate sequences manually or using code and analyze their behavior across large inputs. You can use Python or spreadsheets to track patterns. This project helps you build computational thinking and learn about number theory.
22. Properties of Perfect Numbers
Research Question: What defines perfect numbers, and how are they distributed?
Difficulty Level: Beginner
In this project, you’ll dig into what makes a number “perfect” by analyzing divisors and testing numbers using Python or Wolfram Mathematica to spot how rare and spread out they really are. You can uncover some patterns along the way, like how all known perfect numbers are even and connected to Mersenne primes. This will help you build your number theory knowledge and logical reasoning skills.
23. Applications of Pascal’s Triangle
Research Question: How is Pascal’s Triangle related to combinatorics and probability?
Difficulty Level: Beginner
In this project, you’ll explore patterns and derive relationships between rows and combinations in Pascal’s Triangle. You can use tools like GeoGebra or Python to visualize these relationships and see how the triangle connects to probability calculations, like predicting outcomes in coin flips or binomial distributions.
24. Testing Goldbach’s Conjecture
Research Question: Can every even number be expressed as the sum of two primes?
Difficulty Level: Beginner
Here, you can test large sets of numbers using coding tools like Replit or spreadsheets like Google Sheets and analyze results. This project helps you build computational and analytical skills and learn about number theory.
25. Finding Patterns in Polygonal Numbers
Research Question: How can polygonal number sequences be generalized mathematically?
Difficulty Level: Beginner
In this project, you explore how numbers like 1, 3, 6, 10 (triangular) or 1, 4, 9, 16 (square) form dot patterns that build geometric shapes. You can then derive algebraic formulas to generalize them for any polygon. You can use spreadsheets like Excel or Google Sheets to test and visualize these patterns, spotting connections between algebra and geometry that show up in areas like architecture and computer graphics.
Discrete Math & Computer Science
This area focuses on logic, algorithms, and structures used in computing. You’ll often work with graphs, coding, and combinatorics.
26. Sudoku as a Mathematical Problem
Research Question: How can Sudoku puzzles be solved using mathematical algorithms?
Difficulty Level: Intermediate
In this project, you can model Sudoku as a constraint satisfaction problem, where each row, column, and box acts as a mathematical rule. You can build a solver in Python using algorithms like backtracking or dancing links to crack even the hardest grids automatically. This project helps you understand how algorithms solve real challenges.
27. Error Detection in Coding Theory
Research Question: How can errors in data transmission be detected and corrected?
Difficulty Level: Intermediate
Here, you study error-detecting codes like parity checks and simulate them. You can use coding tools like crcmod or Jupyter Notebook to test reliability. This project helps you build analytical skills and learn about information theory.
28. Boolean Algebra in Logic Circuits
Research Question: How do logic gates use Boolean algebra to process information?
Difficulty Level: Beginner
In this project, you’ll explore how simple TRUE/FALSE logic powers every digital device. You can model circuits using Boolean expressions like AND, OR, and NOT gates to see how your laptop or phone processes information at its most basic level. You can simulate and test your own logic circuits using tools like Logisim or Python to build anything from a basic light switch circuit to a working binary adder.
29. Combinatorics in Password Security
Research Question: How strong are password systems based on combinatorics?
Difficulty Level: Beginner
In this project, you can use combinatorics to calculate just how many possible passwords exist for different character sets and lengths. You can code your own password strength analyzer in Python to test different combinations and see firsthand how small changes like adding one extra character or symbol dramatically increase security.
30. Pattern Recognition in Machine Learning
Research Question: How do algorithms identify patterns in datasets?
Difficulty Level: Intermediate
For this project, you can experiment with simple machine learning models using tools like Python libraries. You’ll analyze how models learn from data, which will help you develop data science and AI-related skills.
31. Comparing Algorithm Efficiency
Research Question: Which algorithms perform more efficiently and why?
Difficulty Level: Intermediate
Here, you can implement and test different algorithms, measuring their runtime and complexity. You can use a programming language like Python. This project will help you build computational thinking skills and learn about computer science.
32. Graph Theory in Social Networks
Research Question: How are individuals connected within social networks?
Difficulty Level: Intermediate
In this project, you’ll model social connections using graph theory and analyze metrics like centrality or clustering. You can use tools like Gephi or NetworkX in Python to visualize and analyze these networks. This project helps you connect graph theory to real-world applications in sociology, recommendation algorithms, and even epidemic spread modeling.
33. Cellular Automata and Simulation
Research Question: How do simple rules generate complex patterns in systems?
Difficulty Level: Intermediate
In this project, you can simulate systems like Conway’s Game of Life, where just a few simple rules about cell survival and reproduction generate complex, lifelike patterns that evolve unpredictably over time. You can code your own cellular automaton in Python or use tools like Golly to run and tweak simulations. This project helps you explore how complexity science uses these models to study everything from population growth to traffic flow.
34. Network Optimization Problems
Research Question: How can networks be optimized for maximum efficiency?
Difficulty Level: Intermediate
Here, you’ll apply graph theory and optimization algorithms to improve network performance. You can code and visualize these solutions by using Python’s NetworkX library or tools like Gephi. This will show you how your math directly applies to how companies like Google Maps and Amazon optimize their networks every day.
Applied Math & Mathematical Modeling
This field uses math to solve real-world problems by building models and simulations. You will often combine math with coding or actual data.
35. Modeling Traffic Flow Using Mathematics
Research Question: What factors contribute to traffic congestion patterns?
Difficulty Level: Intermediate
In this project, you can simulate traffic flow using equations or simple coding models, analyzing variables like speed and density. You can collect observational data or use existing datasets. This will help you build modeling and problem-solving skills and explore civil engineering and applied mathematics.
36. Population Growth Models
Research Question: How do populations grow under different environmental conditions?
Difficulty Level: Beginner
Here, you’ll compare exponential and logistic growth models using real-world data. You can graph and analyze trends using Excel or Python. This project is a great way to build analytical and modeling skills and explore biology, ecology, and economics.
37. Queueing Theory in Real Life
Research Question: How can waiting times in queues be minimized?
Difficulty Level: Intermediate
Here, you can model real-life systems like banks or cafes using probability and queueing formulas like the M/M/1 model to balance customer arrival rates against service speeds. You can collect real data from a local shop or simulate different scenarios in Python or Excel. This will help you build analytical and modeling skills and learn about operations research and business.
38. Climate Change Data Modeling
Research Question: What patterns and trends can you find in climate data over time?
Difficulty Level: Beginner
For this project, you analyze datasets on temperature, CO₂ levels, or sea levels using regression and visualization tools. You can run your analysis in Python using Pandas and Matplotlib, or keep it simpler in Excel. You’ll develop data interpretation skills and learn how climate scientists track and communicate environmental change.
39. Resource Allocation Optimization
Research Question: How can limited resources be distributed most efficiently?
Difficulty Level: Intermediate
Here, you can model allocation problems using mathematical techniques like linear programming to find the most efficient solution mathematically. You can model and solve these problems by using Python’s SciPy library or Excel’s Solver tool. This project helps you build decision-making and analytical skills and connects to economics and operations research.
40. Solving the Traveling Salesman Problem
Research Question: What is the most efficient route connecting multiple locations?
Difficulty Level: Intermediate
In this project, you’ll find the shortest possible route that visits a set of cities exactly once and returns to the start. You can use optimization techniques like nearest-neighbor, dynamic programming, or genetic algorithms. Then, you can implement or visualize them in Python by using tools like NetworkX. This will allow you to apply math to real-world logistics challenges like delivery routing and circuit board design.
One more option – Horizon Academic Research Program
If you’re looking for a competitive mentored research program in subjects like investigative journalism, media studies, political reporting, data journalism, and the ethics of news and information, consider applying to Horizon’s Research Seminars and Labs! This is a selective virtual research program that lets you engage in advanced research and develop a research paper on a subject of your choosing. Horizon has worked with 1000+ high school students so far and offers 600+ research specializations for you to choose from. You can find the application link here!
Image source: Horizon Academic Research Program