Invalidates? Absolutely none. Good mathematics is eternal and the Elements has some beautiful mathematics.
What I meant to say is that in the fullness of time they have been expanded on and surpassed. You can still learn good and valid mathematics from Euclid, but you can learn it better form more modern sources.
As one example amoung many, good modern geometry books will let the reader know about the existence of non-Euclidean geometry and its differences, even if the focus is on traditional Euclidean geometry.
Also, modern books will use modern notation. Notation of course does not affect the ideas which are what is important, but someone trying to learn math today will need to learn the notation so that they can read other more advanced books that will assume the reader knows that stuff. Not to mention, notation can make things easier or harder (try doing multiplication in Roman Numerals).
Finally, many things that were proven tediously before have easier proofs developped over time, often with the ability to take recourse in Algebra. For the same reason, many open questions in Euclid's time now have answers.
However, notation actually does affect the ideas, and deeply. Euclid did not consider 1 a number, for perfectly sound reasons. Multiplication is a very different animal in Euclid's math, and his proportions are not just funny-looking fractions.
Overall, you are right. If someone is looking to get a broad survey of mathematics, Euclid is not a good source. But to start from scratch and learn rigorous math-by-proof, he has no equal.
What I meant to say is that in the fullness of time they have been expanded on and surpassed. You can still learn good and valid mathematics from Euclid, but you can learn it better form more modern sources.
As one example amoung many, good modern geometry books will let the reader know about the existence of non-Euclidean geometry and its differences, even if the focus is on traditional Euclidean geometry.
Also, modern books will use modern notation. Notation of course does not affect the ideas which are what is important, but someone trying to learn math today will need to learn the notation so that they can read other more advanced books that will assume the reader knows that stuff. Not to mention, notation can make things easier or harder (try doing multiplication in Roman Numerals).
Finally, many things that were proven tediously before have easier proofs developped over time, often with the ability to take recourse in Algebra. For the same reason, many open questions in Euclid's time now have answers.