5000 math problems marathon

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The Goal

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

The project consists of 5000 problems structured across four 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.
  • Latest revision (July 2026): Expanded the project into a 5,000 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 theoretical math and domain applications.

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 committed to it seriously on January 1st, 2025. It is designed to develop the rigorous foundation required for advanced mathematics.

Progress

Updated Weekly

1622
/ 5000
Problems Solved
🧮
407
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 : Mathematics Fundamentals

Advanced Single Variable Calculus

Advanced Multivariable Calculus

Linear Algebra

Advanced Ordinary Differential Equations

Discrete Mathematics

Probability

Phase 2 : Domain Application

Phase 3 : Culmination Project