Creative Projects
08 Creative Projects: Building a Mathematics Portfolio That Shows Original Thought
Rashid, for applicants pursuing mathematics at places like Princeton, MIT, and Caltech, the most convincing signal is not simply high grades or test scores—it is evidence that you actively create mathematics. Admissions readers in these departments are accustomed to strong quantitative students; what differentiates applicants is a portfolio showing independent thinking, proof-writing ability, and a visible mathematical voice.
The committee flagged several opportunities where you can convert existing work and interests into concrete artifacts that admissions officers (and potentially mathematicians) can actually read. The goal over the next 6–9 months is to build a small but serious mathematical portfolio consisting of a preprint, expository writing, curated problem-solving work, and a community-facing resource. Each project should produce something publishable online—preferably with version control and documentation.
If you have programming languages, research tools, or mathematical software you already use, you have not provided that information yet. The technical suggestions below assume commonly used tools in undergraduate mathematics communities; you can adjust based on your current toolkit.
1. Convert Your Yale Research Project into a Number Theory Preprint
You indicated that you have conducted research connected with Yale. A powerful next step is turning that work into a formal preprint suitable for public dissemination.
The objective is not necessarily a breakthrough result; admissions readers care more about whether you can formulate definitions, prove claims clearly, and situate your work within existing literature.
Deliverable- A 8–15 page mathematical preprint written in LaTeX
- Posted to arXiv (if possible through a mentor endorsement) or submitted to an undergraduate mathematics journal
- Public GitHub repository containing the LaTeX source and revision history
- Abstract – concise statement of the problem and results
- Background – short literature overview explaining the problem context
- Main Theorem(s) – clearly stated with precise notation
- Proofs – step-by-step logical arguments
- Discussion – implications, extensions, or open questions
- LaTeX (Overleaf or local TeX environment)
- GitHub for version control
- Optional: SageMath or Python notebooks if computational exploration supports the work
Admissions officers at mathematically intense institutions often recognize arXiv formatting immediately. A clean preprint—even if modest in scope—signals authentic engagement with the mathematical research process.
2. Write an Original Expository Paper in Analytic Number Theory or Olympiad Mathematics
Pure research can be difficult to evaluate quickly in an admissions file. Expository writing solves that problem: it shows whether you can explain difficult mathematics clearly, which is a trait professors value enormously.
Consider choosing a concept from analytic number theory or Olympiad-style mathematics and presenting it in a uniquely accessible way.
Possible Expository Topics to Explore- The intuition behind Dirichlet’s theorem on primes in arithmetic progressions
- Generating functions as a problem-solving tool in Olympiad combinatorics
- The role of modular arithmetic in classical number theory problems
- Connections between continued fractions and Diophantine approximation
- Clear diagrams or conceptual illustrations
- Worked examples that build intuition step by step
- A short section describing how the idea appears in Olympiad problems
- 10–12 page LaTeX article
- Hosted on a personal GitHub repository
- Optional: short companion video or interactive notebook explaining key ideas
This kind of writing shows that you can function not only as a problem solver but also as a mathematical communicator.
3. Publish a Personal Olympiad Problem Collection
Another strong creative artifact is a curated set of challenging problems solved in your own voice. Instead of simply presenting answers, the focus should be on reasoning and strategy.
Many strong applicants solve difficult problems, but few document how they think. That is the differentiator.
Project Concept- “Twenty Problems That Changed How I Think About Mathematics”
- 20–30 Olympiad-style problems (number theory, combinatorics, geometry)
- Your full solutions written formally
- A commentary section explaining:
- How you first approached the problem
- What failed approaches taught you
- The key insight that unlocked the proof
- LaTeX problem book (30–40 pages)
- Public GitHub repository with tagged versions
- Optional interactive version using Jupyter or a simple website
Readers in admissions—especially faculty reviewers—often enjoy seeing a student’s genuine mathematical voice emerge through problem commentary.
4. Build Bilingual Math Resources for Arabic-Speaking Learners
Your background creates an unusual opportunity: connecting advanced mathematical thinking with the Arabic tutoring community. Few high school applicants present bilingual mathematical teaching materials, which makes this project both intellectually meaningful and distinctive.
The goal is not simply translation but conceptual teaching across languages.
Project Idea- A bilingual series titled something like “Mathematical Thinking / التفكير الرياضي”
- Short lessons explaining mathematical ideas in both English and Arabic
- Focus on reasoning rather than memorization
- Topics such as proof techniques, number theory patterns, or clever problem-solving strategies
- PDF mini-lessons written in LaTeX
- GitHub repository with all materials
- Optional short explanatory videos
- How mathematicians think about divisibility
- Proof by contradiction explained visually
- Strategies for attacking unfamiliar math problems
This project demonstrates intellectual generosity and communication ability—qualities that math departments value alongside raw problem-solving ability.
Portfolio Architecture
All projects should ultimately live in a single organized portfolio.
| Component | Deliverable | Where It Lives |
|---|---|---|
| Research Preprint | Formal number theory paper | arXiv / undergraduate math journal + GitHub |
| Expository Article | Concept explanation paper | GitHub + personal portfolio site |
| Problem Collection | Annotated Olympiad solutions | GitHub repository |
| Bilingual Resources | Arabic–English math lessons | GitHub + shareable PDFs |
If you do not yet have a GitHub presence, consider creating one. Admissions readers sometimes explore linked repositories when students include them in activity descriptions or supplemental materials.
GitHub Strategy
- Create a single organization or profile repository titled something like rashid-math-portfolio
- Use clear folders for each project
- Include readable README files explaining the mathematical goals
- Maintain commit history showing development over time
The goal is to show authentic intellectual work rather than a polished but opaque final product.
Suggested Timeline (Junior Year → Summer)
| Month | Key Actions |
|---|---|
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By the start of senior fall, this approach would give you something rare in undergraduate admissions: a coherent body of mathematical work. Instead of isolated achievements, admissions readers will see a student actively contributing to mathematical discussion, communicating ideas clearly, and building resources for others.
That combination—research, exposition, problem solving, and teaching—creates the kind of intellectual profile that math departments at Princeton, MIT, and Caltech tend to remember.