If you enjoy applying math to solve real-world problems, mathematical modeling offers opportunities to tackle complex issues in biology, economics, engineering, and more.

Lastly, cryptography is the science of secure communication, protecting data using advanced mathematics like number theory. Key topics include elliptic curve and quantum cryptography.

Selecting a PhD topic in Mathematics can be challenging but exciting. Explore various areas, like pure or applied mathematics, and choose one that ignites your passion to stay motivated throughout.