-What is Mathematics?
-Formal system of knowledge?
-Mathematics as a language?
Maths is defined as the study of quantity, science of order and measure, the "Queen of sciences" etc. It is a area of knowledge that uses a formal system, which acts as a base for reason.
Here are the things that make up the formal system:
1. Axioms
2. Rules of Inference/ Deductive reasoning/ Proof
3. Theorems
It is the axioms that state the most basic rules in mathematics, like if a=b, and b=c, then a=c. These are often perceived as obvious, but its importance increases as the maths becomes more sophisticated.
Consequently, from the axioms we draw inferences, reason, and find proofs. This relies upon the logic that if the premises are true, then the conclusions must be true. We call these conclusions "theorems".
Our general understanding of math comes from these simple axioms and theorems. One example is one of Euclid's axioms, that two points can be joined to create 1 unique line. Simple premises such as this is what enables our mathematics to work.
If we define language as a means of communication, then math can be described as a language. There are limits to expressing a mathematical process (eg. The square root of two hundred and fifty divided by three plus seven), but in a mathematical form, ((250)^120)/10, we can rid of any ambiguities.
The strength of maths can be that it is a universal language. It lacks subjectivity and is mostly if not purely objective, thus it is interpreted in the same way as anyone in the world. It is a tool used in most other AOKs: areas of math such as statistics can help us with predictions in Economics and in the other humanities, likewise calculus was an area of math invented for Physics to expand.
The weakness of math seems to be that it is elitist. A sense of inferiority can be created when one cannot understand math. I personally don't find this a issue specific to math, although it may be most clearly seen in math. Many areas in art are very competitive, and because the truth can be hidden using subjectivity as an excuse, it's just not as clear, but it exists. People can feel more superior/inferior than others because of any type of talent they have, not just math exclusively. I think this seems to be the case in a school environment, because math is a subject which is compulsory and the gap is widened between 'classes'.
As a basis of discussion, we looked at how useful or meaningful is proving Fermat's Last Theorem.(to be cont.)
