Introduction
Stephen Hawking, the renowned theoretical physicist, has left an indelible mark on our understanding of the cosmos. However, his contributions to mathematics and mathematical physics are often overlooked in favor of his groundbreaking work in cosmology, general relativity, and quantum gravity. This article explores whether Stephen Hawking should be considered a great mathematician, examining his mathematical prowess and contributions, alongside his primary achievements in physics.
NSWTH: Hawking as a Professor of Mathematics
Although Stephen Hawking is celebrated as a theoretical physicist, he was officially designated as a Professor of Mathematics. His proficiency in advanced mathematical disciplines, particularly Riemannian geometry and the causal structure of spacetime, was acknowledged even by the esteemed authors of GRAVITATION. His expertise extended to path integral methods, singularity theorems, and differential geometry, placing him among the most sophisticated physicists in the world. Even Roger Penrose, renowned for his work in mathematical physics, was inspired by Hawking’s geometric insights.
Applying Mathematics to Physics
While Hawkins’ primary contributions were in physics, his ability to utilize advanced mathematics was unparalleled. His work on Hawking radiation exemplifies his mathematical prowess. This theory predicts that black holes emit radiation due to quantum effects, revolutionizing our understanding of black holes and the universe. However, his contributions to mathematics itself were not in the form of original discoveries, but in applying mathematical concepts to solve complex physical problems.
Prohibitive Factor: The Demand for Long Proofs
A great mathematician often contributes with long, rigorous proofs that require meticulous verification. While physics research also demands a robust mathematical foundation, the nature of mathematical discoveries necessitates a different level of rigor. This requirement is exemplified by the difficulty of solving problems within the context of general relativity, which requires deep knowledge of differential geometry.
Comparative Analysis: Hawking vs. Mathematicians
It is true that to be a great physicist, one must also be proficient in mathematics. The story of Hawking’s classwork and homework, recounted by his classmates and seen in early documentaries about him, highlights his exceptional mathematical abilities. During his undergraduate years at University of Oxford, Hawking partook in academic rivalries by starting homework late and studying only a few hours a day to prove his intelligence. However, he later regretted not dedicating more time to his studies.
During one particularly challenging class, the professor assigned 10 extremely difficult problems as homework. Hawking solved the first 8 in just one hour. While no one in his class managed to solve any of the problems, Hawking’s performance still stands out as a testament to his mathematical acumen. This anecdote underscores his potential as a professional mathematician had he chosen that path.
Conclusion
Stephen Hawking’s legacy as a mathematical physicist is evident in his innovative application of mathematics to physics. While he is not primarily recognized as a great mathematician due to a lack of original discoveries in pure mathematics, his work in black hole radiation, path integrals, and singularity theorems has had a profound impact on both physics and mathematics. Whether he is seen as a great mathematician or a great theoretical physicist, Stephen Hawking’s contributions to the fields of mathematics and science will continue to inspire future generations of researchers.