There is some difference between core PHP and the frameworks. Core PHP is the basic programming language that allows developers to create dynamic web pages without any need of an extra library which may not be possible if you work with PHP framework. So it is somehow important that you learn about the Core PHP programming to understand the development of dynamic pages.
Core PHP knowledge is important for developers as it will refine your coding skills. Core PHP comes with many functionalities that will allow coders to reuse the codes but PHP frameworks have some fixed set of rules which allow one developer to pass on the code and so on. PHP frameworks save your time by providing code consistency.
Frameworks make use of MVC models that separates the logic from the views which ensure great practise and keep the code clean.
How Core PHP and framework related to mathematics
If you want to solve complex mathematical problems then how you will tackle the situation. You will either go for a step-by-step process or you will use the scientific calculator to do the steps for you. You can do the same using Core PHP and the framework. If you are going for step by step process then Core PHP will solve your purpose else you can use a framework for the scientific calculator work.
Well, people will prefer the process that takes less time and calculation work. This means that people preferring using the core PHP will struggle which makes it inconsistent as there is no assistance provided. Thus, the framework makes your work easier and efficient.
Using a scientific calculator provides you with accurate and error-free results which are reliable which not be the case with step by step processes.