History
You Can (Literally) Count On Me
The History of the Abacus
Latest
Relativity
Deriving Einstein’s Gravity Equations From Thermodynamics
Is Gravity Just an Average of the Behavior of Unknown “Atoms” of Spacetime?
Mathematical Modelling
Particle Swarm Optimization
This story will cover the fundamentals of Metaheuristics and will give you an introduction to the basic concept of the Particle Swarm Optimization (PSO) algorithm.
Numerical Analysis
The Simplest Cubic Root
A very simple Cubic polynomial root approximation using architectural symmetry and similar triangles
Chess
Chess and Mathematics
At first glance, these two disciplines may seem unrelated. However, mathematics and chess have a large amount of unexpected connections.
Probability Theory
The Probabilistic Method
Maybe the most interesting proof method
Infinity
There are Different Kinds of Infinities
From Brilliance to Madness
Philosophy
Beginner’s Guide to Mathematical Constructivism
The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set of all sets, together with the logical ones, like Russell’
Calculus
The Best Numerical Derivative Approximation Formulas
Approximating derivatives is a very important part of any numerical simulation. When it is no longer possible to analytically obtain a value for the derivative, for example when trying to simulate a complicated ODE. It is of much importance though, as getting it wrong can have detrimental effects on the
Complex Analysis
Beyond Infinity
Analytic Continuation and its Applications in Quantum Physics
Geometry
Understanding Perpendicular Lines and Orthogonal Trajectories
When two lines are perpendicular (or orthogonal) with each other, it means they form a 90° angle when they intersect. If you were taught about perpendicular lines in Algebra or for the SAT, you were probably forced to memorize something like “the slope of the perpendicular line is the negative
Probability Theory
Monty Hall Revisited
How a causal framework can help you avoid the Monty Hall trap (and going home with a goat)