My Blog Posts

Differential Geometry
- 1. Origin of Non-Euclidean Geometry – A Historical Overview (Jan 28, 2025)
- 2. A Historical Overview of the Origin of Non-Euclidean Geometry – Continued (June 13, 2025)
- 3. Spherical Geometry – Another kind of Non-Euclidean Geometry (June 13, 2025)
- The Angular Excess of a Spherical Triangle (June 13, 2025)
General Topology
- 1. What is Topology? (May 31, 2025)
- 2. What is a Homeomorphism? (June 12, 2025)
- 3. Interior, Exterior, Boundary, Closure (July 11, 2025)
- 4. Basis & Sub-basis for a Topology (September 20, 2025)
Mathematical Physics
- 1. Classical Mechanics: A Mathematician’s Perspective (June 22, 2025)
- 2. Space-Time: The World of 4 Dimensions (June 23, 2025)
Analysis
- Symmetric Derivatives and Pseudo-derivatives: Reimagining Tangent Slopes (January 25, 2026)
Small Blog Posts
- 1. Mobius Strip: A One-Sided Wonder (Feb 3, 2025)
- 2. Pseudosphere: A Sphere Of Negative Constant Curvature (Feb 3, 2025)
- 3. Geodesic and Normal Curvatures (May 22, 2025)
- 4. Curves in space – The Osculating Plane and the Frenet-Serret Frame (May 22, 2025)
Matrix Groups
- 1. Matrix Lie Groups Explained: Rotations in Plane and Complex Numbers as Matrices (July 31, 2025)
Representation Theory
- 1. Representation Theory: An Invitation to See Symmetry (January 17, 2026)
Classical Geometry
- 1. Pedal Curves: Calculus in Motion (May 31, 2025)
- 2. Conic Sections – Part I (June 1, 2025)
Partial Differential Equations
- Partial Differential Equations: Classifying the Dynamics of the Continuum (June 27, 2025)
Algebra
- Perron and Cohn’s Irreducibility Criteria — Powerful yet Less Celebrated Alternatives to Eisenstein (Dec 14, 2025)
Miscellaneous
- The Birth of Elliptic Integrals & Elliptic Functions: A Brief Historical Overview (Jun 26, 2025)
- Bridging Geometry & Calculus – Unifying Homology with Cohomology (July 3, 2025)
- Differentiation Without Calculus: If Only Newton Knew Pascal’s Triangle (July 17, 2025)
- Infinitude of Primes: A Topological Proof (November 2, 2025)
- Groupoids in Topology: From Partial Algebra to Category-Theoretic Insights (December 9, 2025)
- A Geometric Interpretation of a Math Olympiad Identity (December 18, 2025)
- Unfolding a Logarithmic Integral: Feynman’s Approach to a Non-Elementary Integral (January 1, 2026)
- Fundamental Domains: Geometry, Group Actions, and Complex Analysis (January 19, 2026)
- Morse Theory: How Calculus Reveals the Shape of Space (February 23, 2026)
Artificial Intelligence & Machine Learning (AI/ML)
- The Manifolds Hypothesis: A Heuristic Idea (November 22, 2025)
- From Point Clouds to Curves: Unfolding the Manifold Hypothesis with Socio-Biological Data (January 13, 2025)