Mathematics is full of formulas and theories that were developed without a specific application in mind, but later found to be incredibly useful in various fields. Here's a list of some notable examples from ChatGPT :

1. Complex Numbers and Euler's Formula: Initially seen as abstract and theoretical, they're now fundamental in electrical engineering and quantum physics.

2. Fourier Transform: Originally developed for heat transfer problems, it's now crucial in signal processing, image analysis, and quantum physics.

3. Non-Euclidean Geometry: Once considered purely theoretical, it's essential in the theory of relativity and global positioning systems (GPS).

4. Group Theory: Developed as a part of abstract algebra, it's now instrumental in physics, chemistry (especially crystallography), and cryptography.

5. Graph Theory: Originating from a recreational math problem, it's now key in computer science, network analysis, and biology.

6. Number Theory: Initially pursued for its intellectual challenge, it's fundamental in modern cryptography, like RSA encryption.

7. Calculus of Variations: Beginning as a mathematical curiosity, it's now used in physics, economics, and engineering to solve optimization problems.

8. Riemannian Geometry: Originally abstract in nature, it's crucial in general relativity and the description of spacetime.

9. Boolean Algebra: Developed from logic studies, it's the backbone of digital circuit design and computer science.

10. Set Theory and Cantor's Diagonal Argument: Seemingly abstract concepts, they're now foundational in computer science and logic.