AI in Math Research for High School Students: The Complete Guide (2026)

TL;DR: AI in math research means using computer models to spot patterns, test guesses, and check proofs on questions nobody has answered yet. High school students can do this work with a laptop, Python, and open math databases like the OEIS. You start with an area of math you enjoy, build a few core skills, and test one small question. If you love math but haven't written code yet, and you want to finish with a project that's truly yours, Veritas AI's Combination program takes you the whole way. You learn Python and AI in small mentor-led groups first. Then you design your own project one-on-one with a mentor, with publication support at the end.

In May 2026, OpenAI shared that one of its AI models had disproved a conjecture Paul Erdős first posed in 1946. The question behind it sounds simple. If you place a bunch of points on a flat page, how many pairs can sit exactly one unit apart? For nearly 80 years, most mathematicians believed a square grid was close to the best possible answer. The AI found a better arrangement, and a group of outside mathematicians checked the proof and confirmed it.

If you are a high schooler who loves math, news like this might make research feel far away. The good news is that the tools behind it, like Python and open databases of numbers and shapes, run on an ordinary laptop. What you bring is curiosity, a pattern you want to understand, and the patience to test your idea carefully. You can start with whichever corner of math you already enjoy.

What is AI in math research?

AI in math research means using computer models to help find new patterns, test guesses, and check proofs. Math research itself means answering a question nobody has answered yet, then proving your answer is always true. Homework works the other way around, since your teacher already knows the answer. A research question might ask whether a pattern in prime numbers keeps going forever, or which arrangement of shapes packs together best.

Much of this work uses machine learning, where a computer gets better at a task by studying lots of examples. You might feed a model thousands of knots, each with a few numbers measured about it. The model can spot a link between those numbers that no one noticed by hand. Newer AI models can even write out a full proof, like the Erdős result above. Either way, a person still checks every step, since a pattern only becomes math once someone proves it.

How is AI used in different areas of math?

AI now helps in almost every branch of math, and each branch puts it to work on a different kind of job. Here's how that breaks down across six areas.

Area of math	What AI helps with	A real-world example
Number theory	Finding hidden patterns in huge tables of numbers	Machine learning on elliptic curves from the LMFDB database revealed a wave-like pattern now called murmurations, and an undergraduate on the team worked out why
Geometry	Solving olympiad-style geometry proofs	AlphaGeometry 2 solves 84% of IMO geometry problems from 2000 to 2024, according to its official paper
Combinatorics and graph theory	Hunting for counterexamples	A neural network built by mathematician Adam Zsolt Wagner disproved several open graph theory conjectures
Knot theory	Linking two different ways of measuring a knot	DeepMind and Oxford mathematicians used AI to spot a link that led to a brand-new theorem
Algebra	Finding faster ways to calculate	AlphaEvolve found a way to multiply two 4×4 complex-valued matrices with 48 multiplications, beating a method from 1969
Logic and proofs	Writing proofs a computer can check	AlphaProof writes proofs in Lean, a language computers can verify, and with AlphaGeometry 2 it solved 4 of 6 problems at IMO 2024

Every row runs on the same loop. Examples go in, the AI suggests a pattern or an answer, and a person or a proof checker confirms it. That same loop works on much smaller questions, which is where your own research can begin.

Can high school students do math research?

Yes, high school students can do math research, with AI and public math databases doing a lot of the heavy lifting. Your lab can be a laptop with Python on it. The OEIS, an online library of number sequences, and the LMFDB, a database of curves and other number theory objects, hold the same data professional mathematicians use. Big results don't always need big machines, either. Wagner's counterexample search ran on his five-year-old laptop, taking between two and 48 hours per problem.

At a high school level, math research usually means one narrow question, lots of small cases, and a careful test. Say you notice that a sequence in the OEIS seems to follow a rule. You can compute its first 10,000 terms, train a simple model to predict the next ones, and see exactly where the rule breaks. Even if you never prove a full theorem, a sharp conjecture tested carefully on solid data counts as real research. If you do find a proof, even better, since that's the part that makes it last.

What skills are needed for AI in math research?

AI math research draws on three kinds of skills: math, coding, and writing. Here's what helps most in each.

• Python: Most AI and math experiments run in Python. It helps to feel comfortable writing loops, saving results, and fixing errors when they show up. If Python is brand new to you, these online Python courses can help you build the basics.

• Math libraries: These are bundles of ready-made code. SymPy does exact algebra with symbols, NetworkX builds and measures graphs, and NumPy crunches long lists of numbers. scikit-learn gives you simple machine learning models to test patterns.

• SageMath: This is an open-source math system built on Python. Number theorists use it to work with primes, curves, and other objects stored in the LMFDB.

• Proof writing: A proof by induction or by contradiction is what turns a pattern into a result. You may have seen your first proofs in geometry class or at a math circle.

• Discrete math and number theory: Primes, divisibility, counting, and graphs are full of open questions that are easy to state. That makes them great starting points.

• Statistics: It helps you tell a real pattern from a lucky streak. A rule that works for the first 100 numbers can fall apart by the millionth.

• LaTeX: This is the language almost every math paper is typed in. It turns fractions, sums, and symbols into clean, readable equations.

Nobody starts with this whole list checked off. Pick the two skills your question needs first, and the rest will come as you work.

How to start an AI math research project in 5 steps

Most AI math projects move through the same five steps, whichever area of math you choose. Here's how to work through them.

1. Choose your path and the area of math you enjoy. You can work on your own and set your own pace. You can also ask a math teacher to check in on your progress, or bring the idea to your school's math club or a local math circle. If your math is strong but you've never trained a model, Veritas AI's AI Scholars program is built for that exact gap. You learn Python and core AI in live classes with one mentor for every five students, no coding background needed, and you build a full AI project with a small team of peers. Whichever path you take, pick one row from the table above to focus on.

2. Turn your interest into one small, open question. "Are there infinitely many twin primes?" has stumped mathematicians for generations. "How often does this OEIS sequence land on a prime in its first 100,000 terms?" is something you can test this month. Read the sequence's OEIS entry first, since its comments show what's already known.

3. Compute small cases, then look for a pattern. Write code that produces the first few thousand examples, and plot them. Patterns jump out of a graph much faster than out of a list. If you're using machine learning, train a model to predict one property from the others, and record how often it gets it right.

4. Hunt for counterexamples. A rule in math has to hold for every single case, so push your conjecture as hard as the computer allows. Try bigger numbers, stranger shapes, and edge cases, changing one thing at a time. If one example breaks your rule, finding it counts as a result too.

5. Try to prove what survives, then write it up. Explain your question, your data, your code, and what you found, including the cases that didn't work, plus a short note on which AI tools you used and what each one did. Share a draft with a teacher or your math circle so they can spot gaps early.

Never written a proof or a line of code? That's a completely normal place to start. Tonight, you can look up the Fibonacci numbers on the OEIS and read through the comments for questions people are still asking.

8 AI math research ideas for high school students

Each of these ideas comes with a real database or tool you can open today.

• Look for murmurations in elliptic curves (number theory). Elliptic curves are equations like y² = x³ + ax + b, and each one has a number for every prime. Download thousands from the LMFDB, average those numbers, and plot them to see if the wave pattern shows up in a new family.

• Predict a knot's properties from its other measurements (knot theory). KnotInfo lets you download invariants, numbers that describe a knot, as a spreadsheet. Train a model to predict one invariant from the others, a mini version of the DeepMind study.

• Search for a counterexample to a graph conjecture (graph theory). The House of Graphs collects graphs that have already broken conjectures. Test a conjecture on them with NetworkX, then let a learning search build new candidates.

• Build a bigger cap set with SET cards (combinatorics). FunSearch found a record cap set, a group of SET cards with no SET, of 512 in eight dimensions. Write your own search for smaller dimensions and compare it with the known answers.

• Predict Collatz stopping times (number theory). The Collatz rule halves even numbers and turns odd ones into 3n + 1. Count each number's steps to reach 1, then see if a model can predict them from its binary digits.

• Teach a model to guess the next term of a sequence (sequences). Train a model on a few thousand OEIS sequences to predict each next number, then find which kinds fool it.

• Test whether prime gaps can be predicted (number theory). Use SymPy to list the gaps between back-to-back primes and train a model to guess the next one. Barely beating random guessing is a real finding about how primes behave.

• Turn a small proof into Lean code (logic). Learn Lean through the puzzle levels of the Natural Number Game. Then write one fact from your project in Lean so a computer confirms every step.

The best idea is the one tied to a question you already wonder about. If none of these click yet, you can borrow a setup from these AI research ideas and swap in a math question of your own.

How to publish AI math research in high school

To publish AI math research in high school, you pick a journal or competition that accepts math projects, follow its rules, and submit your write-up. Not every student venue takes math, so choose one before you write. The Journal of Emerging Investigators, for example, lists mathematics among the topics it doesn't accept. These four venues all welcome math work and are common places to start.

Venue	Type	Who can enter	What to know for an AI math project
National High School Journal of Science	Online journal	High school students	Peer-reviewed, with its own math section
Regeneron ISEF	International science fair	Students who qualify through an affiliated fair	Has a Mathematics category with subcategories like number theory, combinatorics and graph theory, and geometry and topology, which includes knot theory
Junior Science and Humanities Symposium	Research symposium	Grades 9 to 12	Sponsored by the U.S. Department of Defense. Math projects fit its Mathematics and Computer Science category, and you present first at a regional symposium
Regeneron Science Talent Search	National competition	High school seniors	Individual projects only, so team research can't be entered. Society for Science calls it the nation's oldest science and math competition for seniors

If your project isn't finished yet, spend a study break reading a few student papers in the NHSJS math section. One, for example, walks through how linear algebra powers regression, a common machine learning method. Seeing how other students wrote up their math makes your own write-up much easier to start.

FAQs

1. What is the difference between math research and math competitions?

Math competitions give you hard problems with known answers, while math research asks questions nobody has answered yet. In AI math research, you might spend months on one question, with code and models as welcome tools. The pattern-spotting and tight arguments you practice in competitions carry straight over.

2. Will AI replace mathematicians?

AI is changing how mathematicians work, and people are still the ones deciding what's worth studying. Even OpenAI, whose model disproved the Erdős conjecture, writes that people choose the problems that matter and interpret the results. That makes asking sharp questions, and judging AI's answers, even more valuable for you.

3. Is ChatGPT good at math?

ChatGPT is a useful helper for math research, and it still makes mistakes you have to catch. It can explain a confusing paper or find the bug in your code. It can also write a smooth proof that hides one wrong step. Test each claim on small cases, and track down any paper it names before you cite it.

4. How do you write a math research paper?

A math research paper states its results as clearly as possible, then proves or tests each one. After the abstract and introduction come your definitions, main results, and proofs. An AI project adds a section on your data, code, and model. Most math papers are typed in LaTeX, and these tips on writing an AI research paper walk you through the rest.

5. How do you find a research mentor in high school?

You can find a math research mentor through a teacher, a nearby university, or a mentored research program. A math teacher who enjoys proofs often makes a great first mentor. You can also email a professor whose paper you've read and name the exact question you're exploring. If you'd like a mentor to guide an AI math project from idea to finished paper, Veritas AI's AI Fellowship with Publication & Showcase pairs you with one for 15 one-on-one sessions. Two more with a publication expert help you prepare it for a journal or showcase.

Where to learn more about AI in math research

These sites let you keep exploring the data, problems, and tools from this guide.

• OEIS: A searchable library of integer sequences, with comments on what's known and what's still open about each one.

• LMFDB: A large database of elliptic curves, number fields, and other number theory objects, used in the murmurations discovery.

• Erdős Problems: A site that tracks the problems Paul Erdős posed and which ones are solved, open, or recently settled.

• Natural Number Game: A puzzle-style introduction to writing proofs in Lean.

• Regeneron ISEF Mathematics category: The full list of math subcategories, useful for seeing where your project might fit.