Maths seeks to prove theorems explaining the world of mathematics through a process of deduction and induction.
To keep Maths as close to the ‘truth’ as we can we aim to prove every theorem and new discovery by tracing it back to the core axioms that we hold as certain (note not truth), if there is a clear process leading to the formulae/theorem that clearly follows the laws and axioms of mathematics then we can hold this as certain. The mathematical process of getting from our core axioms to this new formulae or theorem is a process of deduction (especially in the cases of finding a value etc.) and occasionally induction which is simply the process of using different ideas and facts to draw a conclusion which in a mathematical sense could be applying axioms etc.
Maths is a surprisingly social/ collaborative subject yet maintains the individual and solitary subject we stereotypically view it as.
As we saw in the video played to us in class many many mathematical discoveries could simply have never been reached without fellow mathematicians collaborating and publishing their work. In the video Wiles would have never been able to find a solution to Fermat’s last theorem without the research papers and work of mathematicians worldwide (e.g. the Japanese mathematicians) and his fellow colleagues at Cambridge, yet the fact that he isolated himself and worked in secret for 7 years shows the solitary, closed off nature we tend to associate with mathematics and mathematicians.
Although it is not typically seen as one Mathematics has the potential to be an emotional subject with revelations and highs and lows of its own.
People rarely view Mathematics as an emotional subject or one requiring creativity, however, as we saw last class for those who are dedicated and passionate about mathematics it can be a very emotional experience. It was quite a shock to see words such as revelation as this word has religious or at least philosophical connotations when many see mathematics as a subject that should be and mostly is devoid of emotion, much as the sciences are.
Thanks Saniya. Insightful and clearly articulated as usual.
I note your description of maths as a “subject that should be and mostly is devoid of emotion, much as the sciences are.” I guess we could distinguish between the *content* of maths and science, which as you say should be devoid of emotion, and the *process* of discovery. This latter process is, I guess, much like any other process involving humans – open to the range of feelings, emotions, intuitions, and all the other things that make us fallible and human. I suppose one might also argue that the content reflects human cognition in some way….in that aliens might not disagree with 1 + 1 = 2 , but they might have ‘invented’ some totally different branches of maths.
I thought you were very sharp in class today; well done and thank you for your participation.
N