Be Impressive with Mathematics

A satirical note showing how (1+1=2) can be obscured using complex identities to appear more impressive for academic reviewers.
Mathematics
recreational-math
Author

Abdullah Al Mahmud

Published

April 23, 2026

Suppose we want to publish something that is as simple as

\[ 1 + 1 = 2 \tag{1} \]

This is not very impressive. If we want our article to be accepted by IEEE reviewers, we have to be more abstract. So, we could complicate the left hand side of the expression by using

\[ \ln(e) = 1 \quad \text{and} \quad \sin^2 x + \cos^2 x = 1 \]

and the right hand side can be stated as

\[ 2 = \sum_{n=0}^\infty \frac{1}{2^n}. \]

Therefore, Equation (1) can be expressed more scientifically as:

\[ \ln(e) + (\sin^2 x + \cos^2 x) = \sum_{n=0}^\infty \frac{1}{2^n} \tag{2} \]

which is far more impressive. However, we should not stop here. The expression can be further complicated by using

\[ e = \lim_{z \to \infty} \left( 1 + \frac{1}{z} \right)^z \quad \text{and} \quad 1 = \cosh(y) \sqrt{1 - \tanh^2 y}. \]

Equation (2) may therefore be written as

\[ \ln \left[ \lim_{z \to \infty} \left( 1 + \frac{1}{z} \right)^z \right] + (\sin^2 x + \cos^2 x) = \sum_{n=0}^\infty \frac{\cosh(y) \sqrt{1 - \tanh^2 y}}{2^n} \tag{3} \]

Note: Other methods of a similar nature could also be used to enhance our prestige, once we grasp the underlying principles.

Source: Ahsan Jaame