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a minor typo
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Martin Sleziak
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The following is purely my opinion, but the specific question that you posed seems to invite such answers.

Strictly speaking, I'd say that the answer to your question is "Yes", a lack of textbooks in a new area is a barrier to entry. However, my experience over the past 30+ years is that areas don't stay "new" for long, and as things become more solidified, people write introductory (graduate level) textbooks. This may be to promote their vision, or it may simply be because they find the subject beautiful and want to share that beauty with others. To take an older example, Grothendieck's revolution in algebraic geometry created a large barrier for entry, but Hartshorne's book appeared when I was in graduate school, and it provided a way in. Was it perfect? No. Have other books, possibly better introductions, appeared since. Sure. But it was there, and I think it's fair to say that it helped train a generation (or more) of algebraic geoemtersgeometers and those in allied fields. (I'm in the latter group.)

So "yes", lack of graduate level texts in a area is a barrier to entry. But is it a long-term problem. I'd suggest that the answer is "No", because a new area of mathematics that's thriving tends to acquire such textbooks.

The following is purely my opinion, but the specific question that you posed seems to invite such answers.

Strictly speaking, I'd say that the answer to your question is "Yes", a lack of textbooks in a new area is a barrier to entry. However, my experience over the past 30+ years is that areas don't stay "new" for long, and as things become more solidified, people write introductory (graduate level) textbooks. This may be to promote their vision, or it may simply be because they find the subject beautiful and want to share that beauty with others. To take an older example, Grothendieck's revolution in algebraic geometry created a large barrier for entry, but Hartshorne's book appeared when I was in graduate school, and it provided a way in. Was it perfect? No. Have other books, possibly better introductions, appeared since. Sure. But it was there, and I think it's fair to say that it helped train a generation (or more) of algebraic geoemters and those in allied fields. (I'm in the latter group.)

So "yes", lack of graduate level texts in a area is a barrier to entry. But is it a long-term problem. I'd suggest that the answer is "No", because a new area of mathematics that's thriving tends to acquire such textbooks.

The following is purely my opinion, but the specific question that you posed seems to invite such answers.

Strictly speaking, I'd say that the answer to your question is "Yes", a lack of textbooks in a new area is a barrier to entry. However, my experience over the past 30+ years is that areas don't stay "new" for long, and as things become more solidified, people write introductory (graduate level) textbooks. This may be to promote their vision, or it may simply be because they find the subject beautiful and want to share that beauty with others. To take an older example, Grothendieck's revolution in algebraic geometry created a large barrier for entry, but Hartshorne's book appeared when I was in graduate school, and it provided a way in. Was it perfect? No. Have other books, possibly better introductions, appeared since. Sure. But it was there, and I think it's fair to say that it helped train a generation (or more) of algebraic geometers and those in allied fields. (I'm in the latter group.)

So "yes", lack of graduate level texts in a area is a barrier to entry. But is it a long-term problem. I'd suggest that the answer is "No", because a new area of mathematics that's thriving tends to acquire such textbooks.

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Joe Silverman
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The following is purely my opinion, but the specific question that you posed seems to invite such answers.

Strictly speaking, I'd say that the answer to your question is "Yes", a lack of textbooks in a new area is a barrier to entry. However, my experience over the past 30+ years is that areas don't stay "new" for long, and as things become more solidified, people write introductory (graduate level) textbooks. This may be to promote their vision, or it may simply be because they find the subject beautiful and want to share that beauty with others. To take an older example, Grothendieck's revolution in algebraic geometry created a large barrier for entry, but Hartshorne's book appeared when I was in graduate school, and it provided a way in. Was it perfect? No. Have other books, possibly better introductions, appeared since. Sure. But it was there, and I think it's fair to say that it helped train a generation (or more) of algebraic geoemters and those in allied fields. (I'm in the latter group.)

So "yes", lack of graduate level texts in a area is a barrier to entry. But is it a long-term problem. I'd suggest that the answer is "No", because a new area of mathematics that's thriving tends to acquire such textbooks.

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