How does math solve real world problems

In principle, all problems of nature can be solved with the language of mathematics

"The book of nature is written in the language of mathematics." Galileo Galilei put it this poetically almost 400 years ago. By this he meant that you can transfer many aspects of reality into mathematics, that is, translate them into another language, as it were. As an example, let's imagine that you want to embellish the living room of your new apartment with carpeting. Then you can easily determine the probable costs with a little elementary geometry: In principle, you only have to calculate the area of ​​a rectangle in square meters and then multiply it by the price per square meter of the carpeting.

With this consideration, certain aspects of the real living room were translated into mathematics. The applications of this method in engineering and natural sciences are usually much more complicated, but the idea is the same: The aspects of the question that are currently of interest are transferred to the world of mathematics, translated into its language and solved there. The back translation then - hopefully - solves the initial problem. Almost all sub-areas are used: geometry and algebra, numerics and stochastics. The specific problems to be solved can be arbitrarily complex.

Incidentally, this is not much different than when someone translates a problem ("Where is the nearest gas station?") Into English while on vacation in the USA and hopes for the help of locals. Here, too, the solution is determined in a different language.

No one today seriously doubts that Galileo was right. However, it is controversial why this is so. Is it a mystery that we cannot understand? Is God a mathematician? So is the world constructed according to mathematical principles that we can grasp better and better? Or is it all just a matter of convention? So is the applicability of mathematics just an illusion?

For many centuries philosophers and mathematicians tried in vain to find a generally accepted answer. There is now little hope that this will ever succeed.