3000 math problems marathon

Designed by Freepik

The Goal

Cultivate a rigorous foundation in mathematics and formal proof-writing, developing the analytical skills required for advanced mathematics.

The project consists of 3000 problems structured across three main phases:

Curriculum Evolution:

  • Initial Plan: 2700 Alcumus problems, 150 Stanford Online proofs, and 150 Real Analysis problems.
  • First Revision: Shifted to 2400 Alcumus problems, 150 Stanford proofs, 150 Elementary Math proofs, and 300 Real Analysis problems to explicitly increase rigorous proof-writing practice.
  • Second Revision (July 2026): Expanded the project into a 5000 Math Problems Marathon. I realized that rushing through materials to meet a deadline compromised deep learning, so I pivoted to a comprehensive multi-year roadmap that includes core university-level math and domain applications.
  • Latest Revision (August 2026): Scaled the marathon back down to 3000 problems. I moved the core university-level math into a future separate project so I can actually finish this one without burning out.

The Motivation

Back in secondary school, I became interested in critical thinking and logic, which led me to the axiomatic side of mathematics: starting from a few assumptions and building everything through reasoning. That completely changed how I saw math.

Before that, math had mostly been about memorizing formulas and applying them on exams. Discovering proof-based reasoning showed me a deeper and more meaningful side of the subject, and I wanted to pursue it seriously.

The problem was that my early training had gaps. I had learned enough to pass exams, but not enough to reason rigorously or write proofs. After several unstructured attempts to “relearn everything”, I found the Art of Problem Solving and its Alcumus platform, which emphasized challenging problems and careful thinking.

Through that approach, math became creative and demanding rather than mechanical.

I first considered this project when I started university, but I committed to it seriously on January 1, 2025. It is designed to develop the rigorous foundation required for advanced mathematics.

Progress

Updated Weekly

1906
/ 3000
Problems Solved
🧮
491
hours
Spent on the Project
⏳

Phase 0 : Problem Solving & Mathematical Reasoning

Alcumus (by the Art of Problem Solving)

Alcumus Progress

My Alcumus profile. You can look me up on AoPS; my username is anordinarylearner

Note: I only consider correctly solved problems.

Stanford Online’s Introduction to Mathematical Thinking

Introduction to Mathematical Thinking

Pk0001, CC0, via Wikimedia Commons

View the course assignments and my solutions:

Phase 1 : Mathematical Methods

MIT Math Boot Camp for Engineers

Note on Phase 1: Although I will do hundreds of practice problems to get fluent in the topics covered in the course (Single-variable calculus, Multivariable calculus, Ordinary differential equations, Linear algebra, Series, Probability and statistics), I will only write up 150 problems for the site. I will leave out computational problems and only publish formal proofs, key derivations, and really interesting problems that show the deeper ideas behind each topic.

Phase 2 : Domain Application

Phase 3 : Culmination Project