Unraveling Einstein’s Thought Process — “Logic will get you from A to B, imagination takes you everywhere” — Albert Einstein Let’s imagine you and your friend are traveling in a container in a certain direction with a speed of 30 kilometers per hour. Now you decide to play a catch game with your friend and…

A Look into Alan Turing’s Revolutionary Test for AI — Alan Turing (1912–1954) is one of the most influential and groundbreaking figures in the history of computing and artificial intelligence. He, being a mathematician, logician, computer scientist, and cryptanalyst, is known for his notable achievements across various disciplines within his relatively brief lifespan. …

A Window into the Rich World of Number Theory — “Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.” — Leonhard Euler Prime numbers are a fascinating and mysterious class of numbers…

How a Simple Alpha Factor Holds the Key to Understanding the Universe — “When I die. My first query to the devil will be, what is the meaning of the fine structure constant?” — Wolf gang Pauli The universe is full of constants, but none of them have captured the imaginations of scientists quite like the fine structure constant which appears all over…

Breaking Symmetry, Building Mass — In accordance with basic Newtonian mechanics, the weight of our body can be determined by measuring the amount of force exerted by its mass upon the ground. The acceleration resulting from gravity causes a force which is measured as weight. The concept of weight is relatively straightforward, but comprehending mass…

So We Need Polar Coordinates Instead — In this story, we will look into why the cartesian coordinate system (x,y,z) — the three directions in space, is not always a good choice. Next, I will introduce a few other coordinate systems which can solve certain types of problems more efficiently. First of all, What are coordinates? coordinates…

A Path from Challenge to Discovery — The Brachistochrone problem is a classic problem in physics that involves finding the path that a particle must take between two points in order to minimize its travel time, subject to certain constraints. The curve’s name comes from the Greek words “brachistos,” meaning shortest or quickest, and “chronos,” meaning time…

“Young men should prove theorems, old men should write books.” — G. H. Hardy (1877–1947) was a brilliant mathematician who made significant contributions to number theory and mathematical analysis. Born in 1877 in England, he was renowned for his eccentric personality and his predilection for pure mathematics, which he believed should be pursued for its own sake rather than for any…

From Falling Apples to Orbiting Planets — Thought experiments are a valuable tool in science, philosophy, and other fields. …