what is mathematics? Is it meaningless? can it help in building career?
Answers
Mathematics teaches us humility by revealing the ideal consistency and empirical invisibility of logic. As A.D. Aleksandrov says so sagely in Mathematics: Its Content, Methods and Meaning
Mathematics is the art of making the discrete continuous and the continuous, discrete.
Truth, Aleksandrov says, is concrete - and mathematics is a process of abstracting concrete elements such that they may be manipulated and metamorphosed into complexes which have evolved new forms and functions with respect to their parts. Thus, number theory is to geometry as proteins are to DNA etc.
So, mathematics reveals mechanisms of logical consistency and the existence of a relationship between ideal and empirical forms. Thus, it is an art which is internally consistent but it cannot verify itself. In the same way, biology describes methods for naming elements and processes which constitute the phenomenon of Life but they cannot explain either bios or logos - we merely rearrange our words into semantic functions like we arrange mathematical identities into similar functions .
In summary, mathematics is about Making Sense - and a devotion to it will lead us to Gödel’s end. We can know it works - we can know that the Real and the “Imaginary” can share the same space such that explainations of complex transcendence may emerge in simple profundity. However, we cannot know why this is. The art of mathematics gives us tools to make images of the mysteries of reality - those tools cannot and will not render that reality in actuality.
In other words, as mathematics advances, we incorporate it into our thinking. As our thinking becomes more sophisticated, we generate new mathematical concepts and new mathematical structures: the subject matter of mathematics changes to reflect how we think.