Geometry
Ptolemy’s Incredible Theorem
Ptolemy was an ancient astronomer, geographer, and mathematician who lived from (c. AD 100 — c. 170). He is most famous for proposing the…
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Probability Theory
What is the Significance of the Kolmogorov Axioms for Mathematical Probability?
It is widely said that the Kolmogorov axioms provide the standard mathematical formalization of Probability.
Set Theory
Proving Cantor’s Theorem
“No one will drive us from the paradise which Cantor created for us” — David Hilbert
Analysis
Understanding Why 0.99999… = 1
…And the Foundations of Calculus
Number Theory
How to Prove That e is Irrational
Two Simple Proofs of the Irrationality of e
Applied Mathematics
The Johnson-Lindenstrauss Lemma
Why you don’t always need all of your coordinates
Probability Theory
Beauty in Simplicity: Markov’s Elegant Inequality
In this article, we introduce the simple but very useful Markov’s inequality for non-negative random variables.
Complex Analysis
A Gentle Introduction to Analytic Continuation
How to Extend the Domain of Analytic Functions
Grothendieck
The Anarchist Abstractionist — Who was Alexander Grothendieck?
Mathematician Alexander Grothendieck was born in 1928 to anarchist parents who left him to spend the majority of his formative years with foster parents.
Number Theory
A Formula For Fibonacci Sequence
Fibonacci numbers are one of the most captivating things in mathematics. They hold a special place in almost every mathematician’s heart…
Number Theory
The Invention Of Zero
Assigning Value To The Concept Of Nothing
Analysis
Mighty Ruler Conquers Quadratic Equations
The methods of finding roots of a quadratic equations are quite easy and are very well understood. There are all kinds of approaches…