The discussion revolves around whether studying the Philosophy of Mathematics and all proofs is necessary for proficiency in mathematics and physics. It explores the relevance of proofs in mathematical understanding and the role of philosophical inquiry in these fields.
Participants express differing opinions on the necessity of studying the Philosophy of Mathematics and proofs, indicating that no consensus exists on this topic.
Participants mention the importance of context when discussing proofs, suggesting that not all proofs are equally relevant at all stages of learning. There is also an acknowledgment that the interest in philosophical aspects may vary among individuals.
TheoEndre said:Do I need to study
No.TheoEndre said:The Philosophy of Mathematics
Yes, if "all the proofs" means all the proofs as presented in a specific course on a specific subject, such as analysis or algebra. However, even in a specific context not all proofs need to be studied on the first reading. Also, re-reading a proof (or trying to re-create it yourself) helps progressive understanding of that proof and its context.TheoEndre said:all the proofs
Yes, in my view, mathematics (pure, applied, it does not matter) is ultimately about proof. However, the motivation behind formulating and proving certain (sequences of) statements is often different for pure and applied mathematicians.TheoEndre said:in order to be good at maths
No, not in general, certainly not when starting. For physics, calculation and physical interpretation are probably more important. With that being said, there is of course a lot of cross fertilization between physics and mathematics.TheoEndre said:as well as physics?
Philosophy, no, but what do you mean by "all the proofs"? You won't have to study especially proof techniques, they come automatically as mathematics is based on proofs. The interest in historical and philosophical aspects should also come with time, as if you're really curious about your field of study, these aspects are also a matter of curiosity, normally. I doubt it will be tested, so it's a matter of the books you read in your spare time. Finally these topics make the difference between knowledge and education.TheoEndre said:Hello Everyone,
Do I need to study The Philosophy of Mathematics and all the proofs in order to be good at maths as well as physics?
Krylov said:My personal opinion follows.No.
Yes, if "all the proofs" means all the proofs as presented in a specific course on a specific subject, such as analysis or algebra. However, even in a specific context not all proofs need to be studied on the first reading. Also, re-reading a proof (or trying to re-create it yourself) helps progressive understanding of that proof and its context.
Yes, in my view, mathematics (pure, applied, it does not matter) is ultimately about proof. However, the motivation behind formulating and proving certain (sequences of) statements is often different for pure and applied mathematicians.
No, not in general, certainly not when starting. For physics, calculation and physical interpretation are probably more important. With that being said, there is of course a lot of cross fertilization between physics and mathematics.
fresh_42 said:Philosophy, no, but what do you mean by "all the proofs"? You won't have to study especially proof techniques, they come automatically as mathematics is based on proofs. The interest in historical and philosophical aspects should also come with time, as if you're really curious about your field of study, these aspects are also a matter of curiosity, normally. I doubt it will be tested, so it's a matter of the books you read in your spare time. Finally these topics make the difference between knowledge and education.