It is essential to recognize that making sweeping generalizations about any group of professionals, such as mathematicians criticizing modern physicists, can be unfair and not representative of the entire community. In reality, the relationship between mathematicians and physicists is highly collaborative, and both fields often complement each other in advancing scientific knowledge.
However, it is true that some physicists may face challenges when it comes to mathematical rigor. Physics is a vast and diverse field, and while many physicists are highly proficient in mathematics, some may not have the same level of expertise as mathematicians, who often specialize solely in that field. Some potential mathematical deficiencies observed among certain physicists may include:
Lack of Formal Mathematical Training: Physics education generally involves learning mathematical tools and techniques relevant to solving physical problems. However, some physicists might not have extensive formal training in advanced mathematical concepts and proofs.
Over-Reliance on Numerical Methods: In some cases, physicists might resort to numerical simulations to tackle complex problems instead of seeking analytical solutions. While this can be effective for practical purposes, it may lead to a limited understanding of the underlying mathematical principles.
Simplification of Models: To make problems more tractable, physicists might make simplifying assumptions that do not hold in all situations. This approach can lead to less mathematically rigorous conclusions.
Non-Rigorous Use of Mathematics: Some physicists may apply mathematical techniques without fully understanding the underlying mathematical foundations or the potential limitations of their applications.
It is important to note that these deficiencies are not universal among physicists, and many researchers in theoretical physics, especially at the cutting edge, have deep mathematical expertise and rigorously apply mathematical principles in their work.
Criticism and healthy debates between mathematicians and physicists are not uncommon in academia, and such discussions can lead to fruitful collaborations and advancements in both fields. Collaboration and mutual understanding are crucial in building a more comprehensive and accurate understanding of the natural world.