Engineers vs Mathematicians: Where Does Math Skill Lie?

The age-old debate between engineers and mathematicians often centers around their skill in mathematics. While mathematicians may excel in proving the existence of solutions, engineers focus more on the practical application of these solutions to create usable results. This article explores the differences and similarities between the two fields, focusing on the math skills and practical applications of engineers and mathematicians.

The Role of Proving and Application

In terms of mathematical proofs, mathematicians are renowned for their ability to demonstrate the existence of solutions. A typical exchange might go like this:

Mathematician: I have proven that an answer exists.
Engineer: So, uhh, what is it?

While proving the existence of a solution is indeed crucial, it is only the first step in the engineering process. Engineers must also find a numerical answer that is relevant to the problem at hand. This highlights a key difference between the two professions: mathematicians often pursue theoretical advancements, while engineers apply these advancements to real-world issues.

Real-World Applications and Financial Management

My father, an engineer, and my mother, a nurse, both played a significant role in managing the household finances. Initially, my father handled the finances, but my mother took over and realized she could do it more effectively. She would sometimes hand me the checkbook when she couldn't balance it, and both times it was due to identical checks over several months. This highlights that while my mother had a keen eye for detail, the practical application of mathematics in everyday life can be equally important.

During one of my Quora certifications, I stated that mathematics is too vast for any single person to learn everything. Mathematicians often specialize in specific areas, such as pure or applied mathematics. Pure mathematicians may delve into very abstract areas with few real-life applications, whereas applied mathematicians, like myself, work with practical problems such as cryptanalysis and statistics.

Practical Knowledge in Engineering

Engineers, too, have their specialties. My father had degrees in mechanical engineering, electrical engineering, automotive engineering, and business management. My in-laws include several civil engineers. They work on complex calculations that involve electrical phase shifts, wear rates, and load stresses, all of which have real-world applications. For instance, they must apply sound engineering principles to ensure the safety and reliability of the structures they design.

Engineers must master difficult and highly reliable techniques, such as Laplace transforms, to ensure that their work is not only theoretical but also practically sound. They are often faced with the unforgiving nature of the real world, where mistakes can have serious consequences. This forces them to develop a well-honed skill set, whether it be balancing a checkbook or ensuring that a bridge can withstand the weight of traffic.

Conclusion

In summary, both engineers and mathematicians are highly skilled in mathematics, but their applications differ significantly. While mathematicians may excel in proving the existence of solutions, engineers focus on applying these solutions to real-world problems. Hence, in ordinary life, engineers often get to demonstrate their mathematical skills more frequently and in more practical ways.

Both professions play a critical role in advancing our understanding of the world, but their methods and approaches are distinct. Understanding these differences can help bridge the gap between theory and practice, benefiting both fields and society as a whole.