Harvard Mathematics Department: Notable Faculty and Teaching Legends

The Harvard Mathematics Department is renowned for its distinguished faculty and researchers who have made significant contributions to the field. Among the best professors are Andrew Wiles, Shing-Tung Yau, Michael Hopkins, Noam Elkies, Daniel Harlow, and Bjorn Poonen. They are celebrated for their expertise in various areas such as number theory, algebraic topology, and mathematical physics.

Distinguished Faculty in the Harvard Mathematics Department

Andrew Wiles, a leading figure in number theory, is famous for his groundbreaking proof of Fermat's Last Theorem. His work in this field has continued to shape modern mathematics. Shing-Tung Yau, a key contributor to differential geometry and mathematical physics, has made significant advancements in understanding Calabi-Yau manifolds. Michael Hopkins, an influential mathematician in algebraic topology, has made important strides in stable homotopy theory. Noam Elkies, an expert in number theory and algebra, is recognized for his work on elliptic curves and lattice-based cryptography. Daniel Harlow is engaged in research at the intersection of mathematics and theoretical physics, particularly in quantum gravity. Bjorn Poonen specializes in arithmetic geometry, contributing to the study of algebraic varieties.

However, the Harvard Mathematics Department is more than just these well-known names. The department often features a range of other prominent faculty members, each leading in various areas of mathematics.

Teaching Excellence and Impact

Renowned professors in the Harvard Mathematics Department do not merely engage in cutting-edge research but are also dedicated to teaching and mentoring students. Their approach to education varies, reflecting their unique research experiences and philosophies.

Harry Lewis: A Legend in His Own Right

Harry Lewis is often remembered with mixed feelings, particularly for his teaching style in the "Theory of Computation" class. Students find him to be a challenging teacher who can break down complex ideas and remake one's understanding. Despite his intense and sometimes difficult teaching methods, Lewis has a profound impact on his students.

Lewis's class is characterized by his rigorous and symbolic approach to teaching formal mathematics. He emphasizes the importance of formality and the use of symbolism to prove concepts. Exams in his class are designed to test the ability to manipulate and understand these concepts, often in a terse and challenging manner. While other modern computer science classes may focus on current trends, Lewis's classes remain relevant and valuable, teaching timeless principles on the limits of what can be computed.

Despite his intense teaching style, Lewis's influence is undeniable, and many students credit him with transforming their understanding of computational theory. His legacy is marked by his unwavering commitment to rigorous formal mathematics, a subject that has remained at the core of computing and mathematics.

The Legacy of Harry Lewis

Harry Lewis is known for his hectoring and formal approach to teaching, reminiscent of the works of Bertrand Russell and Alfred North Whitehead. His impact on his students is profound, as they are often pushed to their limits to understand and prove complex theoretical concepts. This approach has made his classes not just a challenge but also a transformative experience for many.

Modern Ambassadors of Formal Theory in CS

While Harry Lewis's teaching style was intense, modern textbooks like Introduction to the Theory of Computation by Michael Sipser have taken the subject in a more accessible direction. These resources provide a structured and comprehensive approach to the subject, making it easier for students to grasp the fundamental concepts of theoretical computer science.

Conclusion

The Harvard Mathematics Department is a hub of intellectual rigor and innovation, with a diverse and distinguished faculty. From number theory to algebraic topology, these professors contribute significantly to the field while also imparting their knowledge with passion and dedication.

While some professors, like Harry Lewis, may teach in a challenging and sometimes off-putting manner, their impact on their students' understanding and education is significant. They remind us that sometimes, the best education comes from pushing the boundaries of one's knowledge and limits.