Math Quotes
About
520 quotes collected during 7 years of intensive mathematical self-study (2011-2018), from the 77 Neurons Project Perelman — a collaborative mathematics study project.
Special Tags
A personal categorization system developed during the study:
| Tag | Meaning |
|---|---|
| Justif | Philosophical justifications — quotes that justify or motivate mathematical concepts |
| Curious | Curious and/or prolix — interesting tangents and verbose explanations |
| Origins | Historical origins — where concepts actually came from (often not taught) |
| PhilTake | Philosophical take — less formal, zoomed-out perspectives on formal ideas |
| AA | The Amazing Ancients — surprisingly modern insights from ancient mathematicians |
| IKIT | “I Knew It!” — quotes confirming intuitions you had but couldn’t articulate |
| Sep | Separate — reminders not to confuse mathematicians with their polished work |
| Clueless | Brilliant but unaware — great ideas whose importance wasn’t recognized at the time |
| Humor | Mathematical humor |
Topic Categories
- Foundations — Logic, Set Theory, Proof techniques
- Analysis — Calculus, Real Analysis, Measure Theory
- Algebra — Linear Algebra, Group Theory, Abstract Algebra
- Geometry — Differential Geometry, Topology, Euclidean
- Physics — Mechanics, Relativity, Quantum
- Philosophy — Nature of Math, History, Beauty
Formal Validation
After years of self-study, I enrolled in a Mathematics MSc at Emporia State University to externally validate the knowledge gained. The program was discontinued after COVID-19.
| Course | Score | Date |
|---|---|---|
| MA701 Mathematical Proofs | 99.18% | Apr 2018 |
| MA728 Vector Spaces | 97.61% | May 2019 |
| MA735 Advanced Calculus I | 98.47% | Dec 2019 |
The Journey
These three courses represent only a fraction of the actual study. The self-directed curriculum (“ThePlan”) followed a historical, insight-driven approach—understanding why mathematics developed the way it did, not just how to apply techniques.
Foundations: Proof theory, Linear Algebra (Hefferon), Real Analysis I-III (Zakon), Calculus on Manifolds (Spivak), Number Theory, Algebra, Topology (Stillwell)
Advanced: Abstract Algebra (Dummit), Differential Geometry 1-5 (Spivak), Dynamical Systems (Smale), Functional Analysis
Mathematical Physics: Whittaker’s trilogy, Arnold’s Mathematical Methods of Classical Mechanics, Lanczos’s Variational Principles of Mechanics
The goals: The three-body problem, chaos in dynamical systems, Lie group integrators, and the deep connections between variational calculus and classical mechanics.
The journey included eigenvalue theory, Lie groups, category theory, algebraic geometry, and the foundations of analysis through constructive mathematics.
“If I ever finish this, I will be a very pleased person for at least one day.” — ThePlan, 2012