Some people seem to appreciate some of my explanations about math and so this post will have links to some of them. This is not comprehensive, and there are some that I've done and liked but can't find. I may redo them on my profile page and update the list. They're roughly organized.

Answers to Simple/Fun Questions

• If my speed continuously reduced as I neared my destination, how long would it take for me to get there?
• Rational Solutions to A^B = B^A
• Finding the Digits of Graham's Number
• Constructing solids from triangles
• Running in the Rain
• Using the ABC-Conjecture to solve a problem
• Numbers that are Sums of Squares in two different ways

Classical problems and Common Explanations

• Xeno's Paradox Variation
• Why are there 360 degrees in a circle? and Again
• What's behind "1 1=2"?
• Why does x^-1=1/x? and How to understand non-whole number exponents and What about x⁰?
• Imperial Units vs Metric Units
• Discovering Fraction Arithmetic
• Understanding Trigonometric Functions and Related
• Graphs and Functions
• Arithmetic and Addition
• Why Triangles are the "strongest" shape
• Explaining Incompleteness
• Banach-Tarski and Unmeasureable Sets
• On the nature of Imaginary Numbers and Inventing "i" and Again and Again
• Disproving Conjectures
• What are logarithms and In the context of Complex Analysis and More
• Negative times a Negative is Positive
• The Basis of Time
• Computing Trigonometric Functions
• Multiplication and Scaling
• What "is" Real Multiplication and Real Exponentiation
• Why is multiplication commutative?
• What is a Square?
• Real Division Algebras
• (NEW) The Monty Hall Problem

On Numbers and Base Representations

• Physics, quantity, and bases
• Why is the difference between a number and a number with reordered digits always divisible by 9?
• On Roman Numerals
• The (An) ontological nature of numbers
• Why does the "Divisible by 3 Trick" work?
• Cyclic Numbers
• Base 12 and Highly Composite Numbers
• How the final digits of numbers behave under multiplication
• Evenness and Oddness "in other bases"
• 0.999... = 1 (1)
• What base representations "are"
• What is a number system? and Again
• Numbers are not their Decimal Representations and Again and Again and Again
• (New) The Kempner Series

Prime Numbers

• Proof of the Infinitude of Primes and Again and Again
• Mersenne Primes
• On primes inert in the Gaussian Integers relate From factoring Primes to Number Fields related Lattices to Number Fields
• The importance of the Riemann Hypothesis and the Riemann Zeta Function and Again
• An explanation of the Riemann Hypothesis and Again and Again and Again and Related
• The "primeness" of 0 and 1
• Truncatable Primes
• The k-tuples Conjecture
• "Inventing" numbers
• Recentish results on Prime Numbers
• 1st Hardy-Littlewood Conjecture vs 2nd Hardy-Littlewood Conjecture
• On the definition of prime numbers and Again
• On our knowledge of Prime Numbers
• On the importance of Prime Numbers
• Primes and Addition and Again

Infinity, Division by Zero, and the Projective Line

• Various extensions of the real line to include division by zero and Again
• Creating Division by Zero through arithmetic and related
• On the Geometry of the Projective Plane
• On the Topology of the Projective Real Line and Again
• Perspectives on Infinity
• Divisibility by Zero Structures
• Obtaining Infinity through the equation x=x 1
• Sizes of Infinity
• What about 0/0?

Euler's Formula: I don't really like explanations of Euler's formula whose existences are predicated on Euler's formula existing a priori. Rather, I like ones where Euler's formula is the answer to a question one might naturally ask, showing how one might discover it rather than have it handed down by the math gods and justified through contrived explanations or magical/unintuitive Taylor series.

• Euler's Formula as a result of exploring exponentiation and Again
• Simplified explanation of the above for those with less mathematical experience
• Trigonometry, Complex Angles, and Euler's Formula
• What is something raised to the ith power?
• Euler's Formula from an Integral Identity

Pi

• Pi and Normal Numbers
• Pi and Irrational Numbers
• Pi, Spheres, and the Gamma Function and Related and Again
• Computing Pi and Again and Again
• On the Value of Pi
• Why we should expect Pi to be irrational
• Pi, bases, and infinite series
• Pi and the Gaussian Integral
• Number Theoretic Formula for Pi

Number Theory and Diophantine Equations

• On the solution to Fermat's Last Theorem and Again
• The role of induction in Fermat's Last Theorem
• Addition on Conic and Elliptic Curves
• Explanation of the Langlands Program
• Tunnell's Theorem on Congruent Numbers
• Pythagorean Triples in context
• From Quadratic to Galois
• The ABC Conjecture and Again
• Hurwitz Theorem (ignore the language of "most irrational")
• Contextualizing a 3b1b video as Hilbert's Theorem 90
• Perspectives on Galois Theory
• Heegner Numbers and Better
• Elliptic Curves
• Solving Polynomials
• Hasse Principle
• Perfectoid Spaces
• RSA Cryptography and Elliptic Curve Cryptography
• An explanation of p-adic numbers
• A bit of an overview of Number Theory
• An overview of Class Field Theory
• The Erdos Discrepancy Problem

Linear Algebra

• The usefulness of the Determinant
• The, usefulness and applications of Linear Algebra
• How Linear Algebra intuition allows us to intuit some things about higher dimensions
• On the context-dependent nature of Vectors and Tensors
• On the nature of "Tensors" and Again and Again and Again and Again
• On the nature of Vectors in the context of "Functions are Vectors" and Related
• Linearity and Differential Equations
• Hilbert Spaces vs Euclidean Spaces
• Affine Spaces vs Vector Spaces

Calculus

• An overview of Calculus emphasizing Limits
• The difference between 𝛥x and dx
• Difference Operators and Differential Operators
• On Differentials and the Chain Rule and Again and Again and Again
• Limits and the Order of Operations
• The Significance of "e" and The Origins of "e" and Again and Again and Again
• An explanation of the Fundamental Theorem of Calculus and Again
• On Antiderivatives and the Fundamental Theorem of Calculus and Again
• On Infinitesimals
• Understanding Limits
• On an improper integral
• Ease of Differentiation vs Integration and Related and Again
• Limits at Infinity
• Geometry and Straight Lines
• Divergence of the Harmonic Series
• Higher Order Derivatives and Approximations
• What are Fractional Derivatives?

Probability

• On the importance of knowing a distribution
• Uniform Metrics on the Real Line
• The Gaussian, Stable Distributions, and the Central Limit Theorem
• A problem highlighting the Inclusion-Exclusion Principle
• Directional Statistics
• Interpreting the Standard Deviation
• The Central Limit Theorem

Fourier Transforms

• Fourier Transforms and Functional Analysis
• An explanation of Laplace Transforms and Another

Hot-takes on -1/12. Don't @ me.

• Understanding -1/12 and Again
• Definitions of "infinite sums"

Perspectives on Math

• Contemporary Math that is not yet super-applicable
• A small (dated) slice of contemporary research
• More "contemporary" math
• Axioms and Theories
• Foundationalism in Math
• Some ideas and some mathematicians
• On gaining a conceptual understanding

Miscellaneous

• On the Boundary of the Mandelbrot Set
• An illustration of a Blow-Up! and Again
• Irrationality of many mathematical constants
• How to solve something like 2^x=x² "arithmetically" and Again
• Visualization as a crutch and Again and Again
• On Navier-Stokes Problem
• On the capabilities of big-name mathematicians
• Why PEMDAS? and Again
• Explaining a graph built from primes
• On the nature of functions
• On corners and Related
• A fun Algebraic interpretation of Borromean Rings
• On Abel Prize Winners
• Approximate versions of physical theories
• Fun and Math
• On the nature of inventing math
• The uses of Factorials
• On the Construction of a Heptagon
• Some answers relating to Quantum Computing
• Geometry vs Topology
• Some uses of the Riemann Zeta Function
• Pascal's Triangle and Powers of 11
• Continued Fractions and the Upperhalf Plane
• The Isoparametric Inequality
• On Roots and Logarithms
• Algebraic Surfaces
• The Golden Ratio in an Equation
• A discussion on Chain Complexes
• The Complex Hyperbola and Euler's Formula