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Greg Martin
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IMHO, everything depends on how the classical text (C) and modern text (M) are written. I will not talk about "archaic terminology", "outdated notation", etc. One skill that one has to acquire as early as his or her student years is to be able to translate any coherent exposition from one format to the other (visual to symbolic and back is usually the hardest one for most people to master; just different naming and outdated words should present no problem whatsoever), so just read C adapting it to the standards of the M language in your head (like most people read Shakespeare translated into relatively modern English and lose next to nothing). I will assume that you do not read just for the pleasure of reading, but have a single objective in mind to learn something new. Otherwise the question becomes "Do you like reading old books or not?" and the answer to that is "My personal preference is ..., period." I will also assume that by M, we mean a decent textbook covering the same subject as C, not a latest research article that starts with something like "it is well known (see [A],[B],...,[W]) that the gimbling of the slithy toves in the wabe is the primary cause of the Tumtum tree cross-contramulgation" to exclude the comparisons Ryan is talking about.

So really there are two (extreme; the real situation is often somewhere in between) possibilities:

  1. C is written in a hard to comprehend way (like in the Besicovich famous quote that "the pioneering works are always ugly, so the reputation of a mathematician is determined by the number of badly written articles he has[they have] published") or is not really rigorous enough and M runs on the same ideas but is just better structured, formalized, and streamlined in a few places. If so, read M and leave C to the historians to play with. All you can get from reading C in this case is a totally unjustified feeling of the superiority of modern ways and language over the predecessors' ones if you lack common sense and the appreciation of the efforts that went into the development of the modern style if you have one. The purely mathematical gain is zero either way.

  2. C is reasonably well written and has some ideas that were later superseded by alternative treatments presented in M (like, say, the modern treatment of the maximal function estimates is almost always via the covering theorems and the original Hardy-Littlewood one was rather via the rising Sun lemma and decreasing rearrangements). Then you may really want to read C along with M to learn the ideas that are no longer present in the mainstream and that is what you really want to extract from there and preserve in your memory.

Of course, it would be even better (for the purpose of the information absorption efficiency; the word "better" has no meaning without an objective modifier) if somebody else had done that extraction and presented it in the modern language. That is what I really expect from the books in "history of mathematics". The dates, priority questions, and the peculiarities of the personal lives of the main characters do not interest me, so, to my taste, one of the best history of mathematics articles is a short chapter in Littlewood's "Miscellany" about how the computation of the position of Neptune was done compared with how it could be done most efficiently. Alas, very few history books satisfy this criterion, so often one has to do this extraction work by him- or herself.

Just my 2 cents :-)

IMHO, everything depends on how the classical text (C) and modern text (M) are written. I will not talk about "archaic terminology", "outdated notation", etc. One skill that one has to acquire as early as his or her student years is to be able to translate any coherent exposition from one format to the other (visual to symbolic and back is usually the hardest one for most people to master; just different naming and outdated words should present no problem whatsoever), so just read C adapting it to the standards of the M language in your head (like most people read Shakespeare translated into relatively modern English and lose next to nothing). I will assume that you do not read just for the pleasure of reading, but have a single objective in mind to learn something new. Otherwise the question becomes "Do you like reading old books or not?" and the answer to that is "My personal preference is ..., period." I will also assume that by M, we mean a decent textbook covering the same subject as C, not a latest research article that starts with something like "it is well known (see [A],[B],...,[W]) that the gimbling of the slithy toves in the wabe is the primary cause of the Tumtum tree cross-contramulgation" to exclude the comparisons Ryan is talking about.

So really there are two (extreme; the real situation is often somewhere in between) possibilities:

  1. C is written in a hard to comprehend way (like in the Besicovich famous quote that "the pioneering works are always ugly, so the reputation of a mathematician is determined by the number of badly written articles he has published") or is not really rigorous enough and M runs on the same ideas but is just better structured, formalized, and streamlined in a few places. If so, read M and leave C to the historians to play with. All you can get from reading C in this case is a totally unjustified feeling of the superiority of modern ways and language over the predecessors' ones if you lack common sense and the appreciation of the efforts that went into the development of the modern style if you have one. The purely mathematical gain is zero either way.

  2. C is reasonably well written and has some ideas that were later superseded by alternative treatments presented in M (like, say, the modern treatment of the maximal function estimates is almost always via the covering theorems and the original Hardy-Littlewood one was rather via the rising Sun lemma and decreasing rearrangements). Then you may really want to read C along with M to learn the ideas that are no longer present in the mainstream and that is what you really want to extract from there and preserve in your memory.

Of course, it would be even better (for the purpose of the information absorption efficiency; the word "better" has no meaning without an objective modifier) if somebody else had done that extraction and presented it in the modern language. That is what I really expect from the books in "history of mathematics". The dates, priority questions, and the peculiarities of the personal lives of the main characters do not interest me, so, to my taste, one of the best history of mathematics articles is a short chapter in Littlewood's "Miscellany" about how the computation of the position of Neptune was done compared with how it could be done most efficiently. Alas, very few history books satisfy this criterion, so often one has to do this extraction work by him- or herself.

Just my 2 cents :-)

IMHO, everything depends on how the classical text (C) and modern text (M) are written. I will not talk about "archaic terminology", "outdated notation", etc. One skill that one has to acquire as early as his or her student years is to be able to translate any coherent exposition from one format to the other (visual to symbolic and back is usually the hardest one for most people to master; just different naming and outdated words should present no problem whatsoever), so just read C adapting it to the standards of the M language in your head (like most people read Shakespeare translated into relatively modern English and lose next to nothing). I will assume that you do not read just for the pleasure of reading, but have a single objective in mind to learn something new. Otherwise the question becomes "Do you like reading old books or not?" and the answer to that is "My personal preference is ..., period." I will also assume that by M, we mean a decent textbook covering the same subject as C, not a latest research article that starts with something like "it is well known (see [A],[B],...,[W]) that the gimbling of the slithy toves in the wabe is the primary cause of the Tumtum tree cross-contramulgation" to exclude the comparisons Ryan is talking about.

So really there are two (extreme; the real situation is often somewhere in between) possibilities:

  1. C is written in a hard to comprehend way (like in the Besicovich famous quote that "the pioneering works are always ugly, so the reputation of a mathematician is determined by the number of badly written articles [they have] published") or is not really rigorous enough and M runs on the same ideas but is just better structured, formalized, and streamlined in a few places. If so, read M and leave C to the historians to play with. All you can get from reading C in this case is a totally unjustified feeling of the superiority of modern ways and language over the predecessors' ones if you lack common sense and the appreciation of the efforts that went into the development of the modern style if you have one. The purely mathematical gain is zero either way.

  2. C is reasonably well written and has some ideas that were later superseded by alternative treatments presented in M (like, say, the modern treatment of the maximal function estimates is almost always via the covering theorems and the original Hardy-Littlewood one was rather via the rising Sun lemma and decreasing rearrangements). Then you may really want to read C along with M to learn the ideas that are no longer present in the mainstream and that is what you really want to extract from there and preserve in your memory.

Of course, it would be even better (for the purpose of the information absorption efficiency; the word "better" has no meaning without an objective modifier) if somebody else had done that extraction and presented it in the modern language. That is what I really expect from the books in "history of mathematics". The dates, priority questions, and the peculiarities of the personal lives of the main characters do not interest me, so, to my taste, one of the best history of mathematics articles is a short chapter in Littlewood's "Miscellany" about how the computation of the position of Neptune was done compared with how it could be done most efficiently. Alas, very few history books satisfy this criterion, so often one has to do this extraction work by him- or herself.

Just my 2 cents :-)

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fedja
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IMHO, everything depends on how the classical text (C) and modern text (M) are written. I will not talk about "archaic terminology", "outdated notation", etc. One skill that one has to acquire as early as his or her student years is to be able to translate any coherent exposition from one format to the other (visual to symbolic and back is usually the hardest one for most people to master; just different naming and outdated words should present no problem whatsoever), so just read C adapting it to the standards of the M language in your head (like most people read Shakespeare translated into relatively modern English and lose next to nothing). I will assume that you do not read just for the pleasure of reading, but have a single objective in mind to learn something new. Otherwise the question becomes "Do you like reading old books or not?" and the answer to that is "My personal preference is ..., period." I will also assume that by M, we mean a decent textbook covering the same subject as C, not a latest research article that starts with something like "it is well known (see [A],[B],...,[W]) that the gimbling of the slithy toves in the wabe is the primary cause of the Tumtum tree cross-contramulgation" to exclude the comparisons Ryan is talking about.

So really there are two (extreme; the real situation is often somewhere in between) possibilities:

  1. C is written in a hard to comprehend way (like in the Besicovich famous quote that "the pioneering works are always ugly, so the reputation of a mathematician is determined by the number of badly written articles he has published") or is not really rigorous enough and M runs on the same ideas but is just better structured, formalized, and streamlined in a few places. If so, read M and leave C to the historians to play with. All you can get from reading C in this case is a totally unjustified feeling of the superiority of modern ways and language over the predecessors' ones if you lack common sense and the appreciation of the efforts that went into the development of the modern style if you have one. The purely mathematical gain is zero either way.

  2. C is reasonably well written and has some ideas that were later superseded by alternative treatments presented in M (like, say, the modern treatment of the maximal function estimates is almost always via the covering theorems and the original Hardy-Littlewood one was rather via the rising Sun lemma and decreasing rearrangements). Then you may really want to read C along with M to learn the ideas that are no longer present in the mainstream and that is what you really want to extract from there and preserve in your memory.

Of course, it would be even better (for the purpose of the information absorption efficiency; the word "better" has no meaning without an objective modifier) if somebody else had done that extraction and presented it in the modern language. That is what I really expect from the books in "history of mathematics". The dates, priority questions, and the peculiarities of the personal lives of the main characters do not interest me, so, to my taste, one of the best history of mathematics articles is a short chapter in Littlewood's "Miscellany" about how the computation of the position of Neptune was done compared with how it could be done most efficiently. Alas, very few history books satisfy this criterion, so often one has to do this extraction work by him- or herself.

Just my 2 cents :-)