Blog
Occasional Random thoughts from us.
The Banach–Tarski Paradox: How Can One Ball Become Two?
Cut a solid ball into five pieces, move them around without stretching, and reassemble two balls the same size as the original. It's a theorem. Here is what makes it possible, and why you can't do it with gold.
Sampling Techniques Unveiled: How Data Analysis Drives Real-World Decisions
In today's data-driven world, understanding statistics and data analysis is no longer a niche skill but a fundamental requirement for informed…
How Many Digits Does a Number Have? The Mathematics of Magnitude
How many digits does 2^100 have? Or 100 factorial? One logarithm answers both without calculating the number. Here is the formula, why it works, and what it says about the first digit too.
Decoding the Pythagorean Theorem: Real-World Applications of Triangle Geometry
The Pythagorean Theorem, a cornerstone of triangle geometry, isn't just an abstract mathematical concept confined to textbooks. It's a powerful tool with…
How Much Is a Trillion? Understanding Really Big Numbers
A million seconds is 11.6 days. A billion seconds is almost 32 years. A trillion seconds is longer than human civilization. Here is how to actually feel big numbers.
What Is the Largest Number You Can Name?
Two philosophers once held a public duel at MIT to name the biggest number. From googol to Graham's number to the Busy Beaver function, here is how mathematicians climb to unimaginable sizes, and where naming breaks down.
How Do You Count Something That Never Ends?
Primes are infinite, yet "0% of numbers" are prime. Evens and all numbers are the same size, yet evens are "half." Mathematicians use four different ways to measure infinite collections. Here is when to use each.
The Power of Variables: Establishing Foundations in Algebra
Algebra is the language of mathematics that allows us to express numbers and relationships in a more flexible way. At its core, algebra revolves around…
The Infinite Hotel: Understanding Hilbert's Paradox
A hotel with infinitely many rooms is completely full, yet it can still fit one more guest, infinitely many more, or infinitely many busloads. Here is how, and where the trick finally runs out.
42 Facts about 42!
How much do you know about the number 42? Click here to see 42 facts about 42. If you’re a fan of numbers, just like I am, then you’re going to love this!
Can Infinity Be Bigger Than Infinity?
Not only is there a bigger infinity, there is no biggest one. Cantor's theorem builds an endless tower of infinities, and one question about it turned out to be unanswerable.
The Difference between A Theorem, A Lemma, And A Corollary
Looking for the difference between a theorem, a lemma, and a corollary? You’re at the right place then. Click here to find out!