This article is a summary of a YouTube video "How to lie using visual proofs" by 3Blue1Brown

3 Surprising Fake Proofs in Math

TLDRDiscover three false proofs that lead to incorrect mathematical results, including a fake proof for the surface area of a sphere and a simple argument that tries to prove pi equals 4. These examples highlight the importance of careful reasoning and the limitations of visual intuition in mathematics.

Key insights

🔍False proofs often rely on clever visualizations and intuitive reasoning, leading to incorrect results in mathematics.

⚠️Misleading arguments can sometimes seem convincing and can fool even experienced mathematicians.

🌐The curvature of surfaces and the limitations of visual intuition play a crucial role in understanding geometric concepts.

📏Limiting arguments in calculus require careful consideration to ensure accuracy and avoid incorrect conclusions.

🔢Visualizations and approximations can be powerful tools in mathematics, but they must be used with caution and rigor.


Are these fake proofs commonly known among mathematicians?

While some mathematicians may be familiar with these false proofs, they serve as cautionary examples and are not well-known.

Can visual proofs be trusted as valid arguments in mathematics?

Visual proofs can provide valuable insights, but they require rigorous reasoning and proof to ensure their validity.

Why do false proofs often seem convincing?

False proofs often exploit visual intuition and clever reasoning, leading to deceptive results that appear convincing at first glance.

Can these false proofs be extended to other mathematical concepts?

The underlying principles demonstrated by these false proofs can serve as cautionary lessons in various branches of mathematics.

How can mathematicians avoid falling for false proofs?

By maintaining a critical mindset, rigorously analyzing arguments, and seeking validation from established mathematical principles, mathematicians can avoid being deceived by false proofs.

Timestamped Summary

00:00Introduction to three fake proofs in mathematics

00:11Proof 1: False formula for the surface area of a sphere

01:37Proof 2: Incorrect argument for pi equals 4

06:10Proof 3: Euclid-style proof that all triangles are isosceles

09:49Reflection on the lessons and subtleties of these false proofs