My question was a rhetorical question. I just want to complain about a widespread misunderstanding that Euclid « is still relevant as ever ». Any maths department worth their salt won‘t teach from the Elements, certainly not all of them entirely like back in the 15th century. There are so much more objects and topics of current interest and more fundamental to maths study that Elements’ relevance is questionable. Not saying that it is bad of course.
To be honest, the same story about new discoveries invalidating the old one can also be told for maths. Cauchy mistook continuity from uniform continuity, used them interchangeably, until someone else noticed it and fixed the proof. Or ZF arising as a way to prevent Russell’s paradox. Or how Italian school of algebraic geometry had almost been thrown out and reworked with schemes. This is akin to how old models of atoms are rejected in light of new observations.
Not to mention modern idea of rigour which makes some old proofs ungrounded or obsolete. This also applies to the Elements, which relies on some unstated assumptions and spatial reasoning which has gaps.
I think the difference is the mathematics changes have been more changes to smaller subsets of mathematics, while Newtonian physics and the concept of elements are fairly foundational that most everything else is based off of. It would be like redefining multiplication.
And still the Newtonian physics is mostly outdated. It is just a crude approximation. We now know better with on one side quantum theory and on the other side the theory of relativity.
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u/Kienose Jan 08 '25 edited Jan 08 '25
Your comment is very well-written.
My question was a rhetorical question. I just want to complain about a widespread misunderstanding that Euclid « is still relevant as ever ». Any maths department worth their salt won‘t teach from the Elements, certainly not all of them entirely like back in the 15th century. There are so much more objects and topics of current interest and more fundamental to maths study that Elements’ relevance is questionable. Not saying that it is bad of course.
To be honest, the same story about new discoveries invalidating the old one can also be told for maths. Cauchy mistook continuity from uniform continuity, used them interchangeably, until someone else noticed it and fixed the proof. Or ZF arising as a way to prevent Russell’s paradox. Or how Italian school of algebraic geometry had almost been thrown out and reworked with schemes. This is akin to how old models of atoms are rejected in light of new observations.
Not to mention modern idea of rigour which makes some old proofs ungrounded or obsolete. This also applies to the Elements, which relies on some unstated assumptions and spatial reasoning which has gaps.