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The Height of Counterintuitive Mathematics — the Birthday Problem

The Height of Counterintuitive Mathematics — the Birthday Problem

Let me ask you this: say there’s a room filled with some number of people. There are no twins/triplets/quadruplets/… in this room. Each…
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Ansh Pincha
Optimization Made Trivial: the Lagrange Multiplier

Optimization Made Trivial: the Lagrange Multiplier

A primer on mathematical optimisation using the Lagrange multiplier.
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Ansh Pincha
The Pinnacle of Mathematical Beauty — Volume in Higher Dimensions

The Pinnacle of Mathematical Beauty — Volume in Higher Dimensions

We derive and analyze the volume of the unit n-ball in an endeavour to present the cold and austere beauty of mathematics.
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Ansh Pincha
DUTIS — Feynman’s Ingenious Integration Technique

DUTIS — Feynman’s Ingenious Integration Technique

Feynman’s Integral Trick and its applications. Truly some ingenious stuff.
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Ansh Pincha
Sophomore’s Dream —The Peak of Mathematical Elegance

Sophomore’s Dream —The Peak of Mathematical Elegance

In this article, we prove the Sophomore’s Dream and indulge oursleves in the pinnacle of elegant mathematics.
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Ansh Pincha
Fermat’s Little Theorem and its Generalization to Euler’s Theorem

Fermat’s Little Theorem and its Generalization to Euler’s Theorem

A primer on Fermat’s little theorem and its generalization to Euler’s theorem
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Ansh Pincha
A Measure Theoretic Approach to Probability (Part 3) — Expectation and Lebesgue Integrals

A Measure Theoretic Approach to Probability (Part 3) — Expectation ...

In this article, we explore a rigorous measure-theoretic definition of expected value and introduce Lebesgue integrals.
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Ansh Pincha
Introduction to Dynamics: Inertial Frames

Introduction to Dynamics: Inertial Frames

Newton’s laws and classical mechanics
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Yash
A Measure Theoretic Approach to Probability (Part 2)

A Measure Theoretic Approach to Probability (Part 2)

Using measure theory to define random variables as measurable functions.
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Ansh Pincha
A Measure Theoretic Approach to Probability (Part 1)

A Measure Theoretic Approach to Probability (Part 1)

Defining probability intuitively and elegantly— using the fundamentals of measure theory.
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Ansh Pincha
Divisibility of Primes (Part Two) — Clement’s Theorem and Twin Primes

Divisibility of Primes (Part Two) — Clement’s Theorem and Twin Primes

Twin primes and a necessary and sufficient condition for their characterization.
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Ansh Pincha
Divisibility of Primes (Part One)— Wilson’s Theorem and Counting Primes

Divisibility of Primes (Part One)— Wilson’s Theorem and Counting Pr...

An introduction to the divisibility of primes, Wilson’s theorem, and a closed-form for the prime counting function.
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Ansh Pincha
The World’s Sneakiest Substitution: Weierstrass’ Substitution

The World’s Sneakiest Substitution: Weierstrass’ Substitution

Trigonometric integrals made easy: an introduction to Weierstrass’ substitution.
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Ansh Pincha
The N-body Problem

The N-body Problem

A numerical simulation in MATLAB
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Yash
String Theory in Three Minutes

String Theory in Three Minutes

A Quick Introduction to String Theory
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Yash
Heisenberg’s (and the general) Uncertainty Principle

Heisenberg’s (and the general) Uncertainty Principle

An introduction of uncertainty principles and a heuristic derivation.
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Yash
Estimating π

Estimating π

Clickbaiting Monte Carlo methods
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Yash
Late to the Party: The LK-99 Kerfuffle

Late to the Party: The LK-99 Kerfuffle

A comprehensive discussion of replication failures in the LK-99 saga
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Yash
Bayes’ Theorem and the Monty Hall Problem

Bayes’ Theorem and the Monty Hall Problem

Introducing Bayes’ Theorem and solving the Monty Hall problem.
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Ansh Pincha
Manimating the Lorenz Attractor

Manimating the Lorenz Attractor

An introduction rendering the Lorenz Attractor in Manim
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Yash
The Butterfly Effect: Meet the Lorenz Attractor

The Butterfly Effect: Meet the Lorenz Attractor

Modeling the Lorenz Attractor in Python
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Yash
Distribution of Primes: The Prime Number Theorem (Part 1)

Distribution of Primes: The Prime Number Theorem (Part 1)

A qualitative exploration of the Prime Number Theorem.
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Ansh Pincha
Your Unfriendly Neighborhood Oligopoly

Your Unfriendly Neighborhood Oligopoly

On the Exploitive Nature of Modern Scientific Publishing
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Yash
The Infinitude of Primes — Euclid’s proof

The Infinitude of Primes — Euclid’s proof

An introduction to the infinitude of primes.
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Ansh Pincha
The Most Successful Cosmological Model

The Most Successful Cosmological Model

A Qualitative Introduction to the ΛCDM Model
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Yash
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