Mathiation

19/08/2026

Unfamiliar contradiction practice

Can an equation look possible but have no integer solutions?

Using proof by contradiction, we assume that integers x and y satisfy:

x squared minus 4y equals 2.

Careful parity reasoning then forces an impossibility: an even integer would have to equal an odd integer. Therefore, no such integers can exist.

A concise unfamiliar-proof example for UK A-Level Mathematics students.

Think. Solve. Elevate.
Nailed it!

https://mathiation.com

゚viralシ

16/08/2026

Prove that √2 is irrational using proof by contradiction.

We begin by assuming the opposite: that √2 is rational and can be written as a fraction p/q in its lowest terms. The argument then shows that both p and q must be even—contradicting our assumption that the fraction was in its lowest terms.

A concise, exam-ready proof for UK A-Level Mathematics students.

Think. Solve. Elevate. Nailed it!

15/08/2026

A4 - Disproof by Counterexample

How can one example disprove an entire mathematical statement?

To disprove the claim “P(x) is true for every x in a domain,” find one valid value for which P(x) is false.

The method:

State the universal claim.
Choose an object from its domain.
Verify that it satisfies the conditions.
Show that the conclusion fails.
One valid counterexample is enough.

Check the domain. Verify. Break.

Nailed it!

゚viralシ

20/07/2026

🌌 Can mathematics really allow a wormhole?

Most people think wormholes belong only in science fiction. But according to Einstein’s theory of General Relativity, the equations tell a much more interesting story.

In this short animation, you’ll discover:
✅ How Einstein’s field equations describe spacetime
✅ The mathematics behind a traversable wormhole
✅ Why keeping a wormhole open requires something extraordinary
✅ The difference between a mathematical solution and physical reality

No science-fiction hype—just real mathematics explained visually.

🎥 Watch the video and let me know:
If we could create a wormhole one day, where would you travel first?

📚 Mathiation – Think • Solve • Elevate

12/07/2026

Every mathematical proof follows a logical structure. In this lesson, you’ll learn how assumptions, deductions, and conclusions work together to prove a statement with certainty. Build the foundation for A-Level Mathematics and beyond. 📐✨

🌐 Learn more: https://mathiation.com

11/07/2026

A simple double pendulum follows precise mathematical laws, yet tiny changes in its starting position create completely different motion.

Watch how the Euler–Lagrange equations explain one of the most fascinating examples of deterministic chaos.

Follow for beautiful mathematics.

25/06/2026

25/06/2026

Most patterns in mathematics eventually break—but this one fooled one of history’s greatest mathematicians.

Pierre de Fermat believed every number of the form (2^{2^n}+1) was prime. The first five examples agreed with him, making the conjecture look unbeatable.

Then Leonhard Euler discovered a single hidden factor—641.

That one counterexample shattered the pattern and became one of the most beautiful moments in the history of mathematics.

Can you spot why 641 works before the reveal?