Exploring the Differences Between Majoring in Theoretical Math and Applied Math

Mathematics, a vast and intricate field, can be divided into two primary branches: theoretical and applied mathematics. Like any other discipline, these sub-disciplines have their unique characteristics and objectives, approaching mathematical phenomena from different angles. This article aims to elucidate the differences between majoring in theoretical math and applied math, providing a deeper understanding of each field.

The Artist-Craftsman Analogy

To start, let's draw an analogy between the roles of an artist and a craftsman within the context of math. Just as an artist pursues innovation and expression through innovative aesthetic insights, a mathematician in the realm of pure mathematics focuses on the development and exploration of general theorems and their proofs. On the other hand, an applied mathematician strives for practical solutions and perfection in specific problem domains, tapping into the dynamic and modern aspects of mathematical applications.

The traditional view of classical perfection often ascribed to theoretical mathematics contrasts sharply with the contemporary pragmatic approach of applied mathematics. In the 21st century, the concept of 'beauty' in mathematics is more complex, encompassing both intricate and 'ugly' facets of modernity. Thus, it is more accurate to distinguish between artistic expression and practical perfection in this field. This distinction highlights the unique approaches and focuses of theoretical and applied mathematicians.

Core Differences

Since traditional labels may not fully capture the essence of these fields, it is helpful to define the core differences:

Theoretical Mathematics: Involves the study of abstract and general theorems and their proofs. The primary objective is to explore mathematical concepts and structures, often driven by a thirst for knowledge and understanding rather than immediate practical applications.Applied Mathematics: Focused on solving real-world problems using mathematical techniques and theories. Applied mathematicians work in diverse fields such as physics, engineering, finance, and more, developing models and algorithms to address practical challenges.

Examining these two fields side by side reveals the unique methodologies and objectives they pursue. While theoretical math emphasizes the exploration of mathematical structures and theorems, applied math focuses on practical solutions and problem-solving. Despite these differences, there is often an overlap in their approaches and applications.

Overlap and Blurring Boundaries

The line between theoretical and applied mathematics is often blurry, with many mathematicians working in both areas. A true artist in mathematics may create impromptu and fun pieces to showcase their broad repertoire, while a highly skilled craftsman might turn to artistic pursuits almost by accident.

Moreover, there is no deep-seated Platonic or metaphysical difference between the two branches. All mathematics, whether theoretical or applied, is fundamentally impure or pure, making no distinction in the final analysis. The heart of mathematical practice lies in its mutable and evolving nature.

Conclusion

In summary, while theoretical and applied mathematics differ in their primary focus and methodologies, the essence of mathematical practice remains intertwined. Whether driven by a quest for abstract knowledge or practical application, both branches contribute to the broader field of mathematics and advance human understanding.

Understanding the differences between these two branches can help students and professionals choose the path that best aligns with their interests and career goals. For those with a passion for innovation and exploration, theoretical mathematics may be the perfect choice. For those driven by practical problem-solving and real-world applications, applied mathematics provides a fulfilling and impactful career.