There have been recent theoretical advancements in mathematical physics that have significantly deepened our understanding of quantum computing, string theory, and loop quantum gravity-three pivotal areas at the intersection of physics and mathematics. In terms of quantum computing, developments in error correction methods that are tolerant to faults and novel algorithms have expanded the frontiers of computational power by employing the mathematical framework of quantum mechanics. Within string theory there are more sophisticated mathematical formulations particularly regarding duality and compactification scenarios which provide new insight into the unification of forces and nature of space-time. On contrary, loop quantum gravity is still making progress through the development of spin foam models as well as improved techniques for quantizing space-time geometry whereby it presents a way to the background-independent approach to a quantum theory of gravity. Together these advances not only challenge existing paradigms but also open up prospects for a deeper, more comprehensive understanding of what universe fundamentally entails.