fundamental-2
Explanation
The Joke
A woman is lecturing (apparently to an audience shown in silhouette) and explains: "If you give a function f to Mathematica and say 'What's the derivative of the integral?' Mathematica will return f." The caption below reads: "This is known as the Fundamental Theorem of Calculus for Engineers."
The Fundamental Theorem of Calculus states that differentiation and integration are inverse operations -- so the derivative of the integral of f is just f. This is a foundational result in mathematics, proved rigorously and elegantly. The joke is that for engineers, the "proof" of this theorem is simply that the software Mathematica (a computational math tool) gives you back f when you try it. Engineers are stereotypically more interested in practical results than formal proofs.
The Humor
The humor targets the long-running rivalry between mathematicians and engineers. Mathematicians care deeply about rigorous proofs; engineers care about whether the answer works. Reducing one of the most important theorems in calculus to "the computer says so" is a perfect encapsulation of the engineer's pragmatic worldview. It is also a gentle dig at the reliance on tools like Mathematica -- if the software confirms it, that is good enough.
References
The Fundamental Theorem of Calculus is one of the central results in mathematical analysis, linking the concept of the derivative with the integral. Mathematica (now Wolfram Mathematica) is a computational software system widely used in engineering, mathematics, and science.