Mathematics is a very philosophical subject, often mathematicians are trying to explain things we maybe cannot see, what we cannot observe in the real world, sometimes defying concepts which means it often takes a ‘leap of faith’ to obtain an answer to a problem.
But perhaps the greatest philosophical question regarding Mathematics is probably “What is Mathematics?”
The answer to this question is hard to find and varies from person to person, henceforth it is quite difficult to give an answer to, although most mathematicians would probably agree, mathematics is the search for truth, which again leads to another question, what truth?
Some mathematicians would say that Mathematics is about understanding the world, modeling the world in ideal situations to produce solutions that are close to the real world answers. That only by reducing the world into a series of idealized situations can we fully understand the principles behind what occurs in the real world.
Another group of mathematicians would say that Mathematics is about being exact and showing how the real world actually works, what happens when all the small influences that occur in our world (which are quite often ‘ignored’ by the above type of mathematicians) are taken into account. The mathematicians would argue that only by seeing how the world really works can you truly appreciate the beauty and the complexity of the world.
However this leads to both groups of Mathematicians saying to the other group “But do you really understand the world?”
The first group would argue that they can see how the world works at a fundamental level and from that they can use those, with modification, to show how the real world works. But the second group would argue back, saying that they do not understand the real world, that they only understand an approximation of the world.
The second group would say that by taking snapshots and seeing how everything interacts with everything else at any given time they can truly understand what is happening in the real world. Again the first group would argue back saying that they only observe how the world works and henceforth cannot possibly understand the way the world works.
The final group of mathematicians I’m going to write about often do Math for “Math’s sake”, Math that has no purpose in the real world, but they do this Math in the hope that some day in the future it will have a purpose and it will be useful.
However, we also have to realize that all of these groups rely on each other to a certain extent, and henceforth my thoughts are that Math is a subtle mixture of these concepts, I personally believe that the third group provides methods that the first group of Mathematicians can then use to provide the building blocks for which the second group expand on and try to further our understanding of the world.