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Category Archives: Math

Measure Theory and the Lebesgue Integral

Written by: Karthik Prasad   Calculus is one of the greatest inventions in Mathematics. Its two primary tools—the derivative and integral—allow us to calculate the rates of change and work done respectively,and are used throughout the world. However, it doesn’t always do things the way

Artificial Intelligence: A Mathematical Marvel

Written by: Aarav Shah Source:    Artificial intelligence (AI) is rapidly transforming the world around us. From facial recognition on our smartphones to the algorithms driving autonomous vehicles, AI’s capabilities appear magical. But beneath the seemingly mystical surface lies a powerful and logical engine:

The Isoperimetric Inequality

Written by Karthik Prasad   Introduction  Perimeter and area are two fundamental values associated with any 2D figure, but how are they related? It seems simple, but it turns out that this question is much more complicated than most have previously thought—it took mathematicians thousands

Explaining the Properties of the Real Numbers

Written by: Karthik Prasad   The real numbers are something every math student is familiar with—after all, they are the numbers that make up the real world itself. However, we often take the existence and structure of these numbers for granted. We will discuss the

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The Yang-Mills Problem

Written by: Karthik Prasad Seven Problems. 1 million dollars for each one solved. The Yang-Mills Mass Gap problem is one of the fabled Millenium Problems and is of great interest in mathematical physics. Its statement is…incomprehensible for most, filled with abstract terms: prove that for

Category Theory

By: Andrew D. Katson Definition Category theory, as invented in 1945, is a field of mathematics that works with objects and their relationships. A category is a set made up of multiple elements, called “objects”, and their “mappings” (5, 11). In figure 1, we see

Untangling Mathematics: A Look Into DeepMind’s New AI

Written by: Gloria Wang As an expanding field with a wide variety of applications, artificial intelligence (AI) has been a hot topic for decades. Machine learning has been applied to board games, language, and healthcare. But for the first time, researchers have applied AI to

Debunking Flatland: Space Filling Curves

Written by: Gautham Anne   In 1877, George Cantor discovered that the number of points in a 2-dimensional plane is the same as the number of points in a 1-dimensional line. This is tremendously counterintuitive since a plane can have an infinite number of lines

The Physics of Water Wakes

Written by: Gautham Anne While watching boats travel by or a duck on a pond, one might wonder how the astonishing wake patterns emerge, such as the ones depicted in figure 1. One might also note that the wake patterns, regardless of whether it is