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The following subsection of Hardy's Divergent Series (zbMath link, freely available on Archive.org) occupies pages 18-20, and gives his thoughts on the matter and some citations. In particular he gives the example of Transactions of the Cambridge Philosophical Society, Vol. 8 (Archive.org link) (see bolded text below). I've taken some text out for brevity, but the whole section (and every part of the book I have read) is a joy to read.

1.7. A note on the British analysts of the early nineteenth century. We end this chapter with a few remarks about British work on these subjects during the years 1840-50, which has been analysed very carefully by Burkhardt in the article from which we have quoted. It was a long time before the writings of the great continental analysts were understood in England, and these British writings show a singular and often entertaining mixture of occasional shrewdness and fundamental incompetence.

(1) The dominant school was that of the Cambridge 'symbolists', Woodhouse, Peacock, D. F. Gregory, and others. They represented what may be described as the ' $f(D)$ ' school of analysis. They started from 'algebra', and had something of the spirit, though nothing of the accuracy, of tho modern abstract algebraists. They dealt in 'general symbols', on which operations were to be performed in accordance with certain laws: 'the symbols are unlimited, both in value and in representation; the operations upon them, whatever they may be, are possible in all cases; ...' But the foundations of their symbolism were both inelastic and inaccurate. 'They insisted on a parallelism between 'arithmetical' and 'general' algebra so rigid that, if it could be maintained, it would effectively destroy the generality; and they never seem to have realized fully that a formula true with one interpretation of its symbols is quite likely to be false with another. They were also very much at the mercy of catchwords like 'what is true up to the limit...', and it is not surprising that their permanent contribution to analysis should have been negligible.

[...]

(2) There is one volume of the Transactions of the Cambridge Philosophical Society (vol. 8, published in 1849 and covering the period 1844-9) which contains a very singular mixture of analytical papers and gives a particularly good picture of the British analysis of the time. It contains Stokes's famous paper ' On the critical values of the sums of periodic series', in which 'uniform convergence' appears first in print; papers by S. Earnshaw and J. R. Young which are little more than nonsense; and a long and interesting paper by de Morgan on divergent series, a remarkable mixture of acuteness and confusion.

[...]

The following subsection of Hardy's Divergent Series (freely available on Archive.org) occupies pages 18-20, and gives his thoughts on the matter and some citations. In particular he gives the example of Transactions of the Cambridge Philosophical Society, Vol. 8 (Archive.org link) (see bolded text below). I've taken some text out for brevity, but the whole section (and every part of the book I have read) is a joy to read.

1.7. A note on the British analysts of the early nineteenth century. We end this chapter with a few remarks about British work on these subjects during the years 1840-50, which has been analysed very carefully by Burkhardt in the article from which we have quoted. It was a long time before the writings of the great continental analysts were understood in England, and these British writings show a singular and often entertaining mixture of occasional shrewdness and fundamental incompetence.

(1) The dominant school was that of the Cambridge 'symbolists', Woodhouse, Peacock, D. F. Gregory, and others. They represented what may be described as the ' $f(D)$ ' school of analysis. They started from 'algebra', and had something of the spirit, though nothing of the accuracy, of tho modern abstract algebraists. They dealt in 'general symbols', on which operations were to be performed in accordance with certain laws: 'the symbols are unlimited, both in value and in representation; the operations upon them, whatever they may be, are possible in all cases; ...' But the foundations of their symbolism were both inelastic and inaccurate. 'They insisted on a parallelism between 'arithmetical' and 'general' algebra so rigid that, if it could be maintained, it would effectively destroy the generality; and they never seem to have realized fully that a formula true with one interpretation of its symbols is quite likely to be false with another. They were also very much at the mercy of catchwords like 'what is true up to the limit...', and it is not surprising that their permanent contribution to analysis should have been negligible.

[...]

(2) There is one volume of the Transactions of the Cambridge Philosophical Society (vol. 8, published in 1849 and covering the period 1844-9) which contains a very singular mixture of analytical papers and gives a particularly good picture of the British analysis of the time. It contains Stokes's famous paper ' On the critical values of the sums of periodic series', in which 'uniform convergence' appears first in print; papers by S. Earnshaw and J. R. Young which are little more than nonsense; and a long and interesting paper by de Morgan on divergent series, a remarkable mixture of acuteness and confusion.

[...]

The following subsection of Hardy's Divergent Series (zbMath link, freely available on Archive.org) occupies pages 18-20, and gives his thoughts on the matter and some citations. In particular he gives the example of Transactions of the Cambridge Philosophical Society, Vol. 8 (Archive.org link) (see bolded text below). I've taken some text out for brevity, but the whole section (and every part of the book I have read) is a joy to read.

1.7. A note on the British analysts of the early nineteenth century. We end this chapter with a few remarks about British work on these subjects during the years 1840-50, which has been analysed very carefully by Burkhardt in the article from which we have quoted. It was a long time before the writings of the great continental analysts were understood in England, and these British writings show a singular and often entertaining mixture of occasional shrewdness and fundamental incompetence.

(1) The dominant school was that of the Cambridge 'symbolists', Woodhouse, Peacock, D. F. Gregory, and others. They represented what may be described as the ' $f(D)$ ' school of analysis. They started from 'algebra', and had something of the spirit, though nothing of the accuracy, of tho modern abstract algebraists. They dealt in 'general symbols', on which operations were to be performed in accordance with certain laws: 'the symbols are unlimited, both in value and in representation; the operations upon them, whatever they may be, are possible in all cases; ...' But the foundations of their symbolism were both inelastic and inaccurate. 'They insisted on a parallelism between 'arithmetical' and 'general' algebra so rigid that, if it could be maintained, it would effectively destroy the generality; and they never seem to have realized fully that a formula true with one interpretation of its symbols is quite likely to be false with another. They were also very much at the mercy of catchwords like 'what is true up to the limit...', and it is not surprising that their permanent contribution to analysis should have been negligible.

[...]

(2) There is one volume of the Transactions of the Cambridge Philosophical Society (vol. 8, published in 1849 and covering the period 1844-9) which contains a very singular mixture of analytical papers and gives a particularly good picture of the British analysis of the time. It contains Stokes's famous paper ' On the critical values of the sums of periodic series', in which 'uniform convergence' appears first in print; papers by S. Earnshaw and J. R. Young which are little more than nonsense; and a long and interesting paper by de Morgan on divergent series, a remarkable mixture of acuteness and confusion.

[...]

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Calvin Khor
  • 313
  • 2
  • 12

The following subsection of Hardy's Divergent Series (freely available on Archive.orgfreely available on Archive.org) occupies pages 18-20, and gives his thoughts on the matter and some citations. In particular he gives the example of Transactions of the Cambridge Philosophical Society, Vol. 8 (Archive.org link) (see bolded text below). I've taken some text out for brevity, but the whole section (and every part of the book I have read) is a joy to read.

1.7. A note on the British analysts of the early nineteenth century. We end this chapter with a few remarks about British work on these subjects during the years 1840-50, which has been analysed very carefully by Burkhardt in the article from which we have quoted. It was a long time before the writings of the great continental analysts were understood in England, and these British writings show a singular and often entertaining mixture of occasional shrewdness and fundamental incompetence.

(1) The dominant school was that of the Cambridge 'symbolists', Woodhouse, Peacock, D. F. Gregory, and others. They represented what may be described as the ' $f(D)$ ' school of analysis. They started from 'algebra', and had something of the spirit, though nothing of the accuracy, of tho modern abstract algebraists. They dealt in 'general symbols', on which operations were to be performed in accordance with certain laws: 'the symbols are unlimited, both in value and in representation; the operations upon them, whatever they may be, are possible in all cases; ...' But the foundations of their symbolism were both inelastic and inaccurate. 'They insisted on a parallelism between 'arithmetical' and 'general' algebra so rigid that, if it could be maintained, it would effectively destroy the generality; and they never seem to have realized fully that a formula true with one interpretation of its symbols is quite likely to be false with another. They were also very much at the mercy of catchwords like 'what is true up to the limit...', and it is not surprising that their permanent contribution to analysis should have been negligible.

[...]

(2) There is one volume of the Transactions of the Cambridge Philosophical Society (vol. 8, published in 1849 and covering the period 1844-9) which contains a very singular mixture of analytical papers and gives a particularly good picture of the British analysis of the time. It contains Stokes's famous paper ' On the critical values of the sums of periodic series', in which 'uniform convergence' appears first in print; papers by S. Earnshaw and J. R. Young which are little more than nonsense; and a long and interesting paper by de Morgan on divergent series, a remarkable mixture of acuteness and confusion.

[...]

The following subsection of Hardy's Divergent Series (freely available on Archive.org) occupies pages 18-20, and gives his thoughts on the matter and some citations. In particular he gives the example of Transactions of the Cambridge Philosophical Society, Vol. 8 (Archive.org link) (see bolded text below). I've taken some text out for brevity, but the whole section (and every part of the book I have read) is a joy to read.

1.7. A note on the British analysts of the early nineteenth century. We end this chapter with a few remarks about British work on these subjects during the years 1840-50, which has been analysed very carefully by Burkhardt in the article from which we have quoted. It was a long time before the writings of the great continental analysts were understood in England, and these British writings show a singular and often entertaining mixture of occasional shrewdness and fundamental incompetence.

(1) The dominant school was that of the Cambridge 'symbolists', Woodhouse, Peacock, D. F. Gregory, and others. They represented what may be described as the ' $f(D)$ ' school of analysis. They started from 'algebra', and had something of the spirit, though nothing of the accuracy, of tho modern abstract algebraists. They dealt in 'general symbols', on which operations were to be performed in accordance with certain laws: 'the symbols are unlimited, both in value and in representation; the operations upon them, whatever they may be, are possible in all cases; ...' But the foundations of their symbolism were both inelastic and inaccurate. 'They insisted on a parallelism between 'arithmetical' and 'general' algebra so rigid that, if it could be maintained, it would effectively destroy the generality; and they never seem to have realized fully that a formula true with one interpretation of its symbols is quite likely to be false with another. They were also very much at the mercy of catchwords like 'what is true up to the limit...', and it is not surprising that their permanent contribution to analysis should have been negligible.

[...]

(2) There is one volume of the Transactions of the Cambridge Philosophical Society (vol. 8, published in 1849 and covering the period 1844-9) which contains a very singular mixture of analytical papers and gives a particularly good picture of the British analysis of the time. It contains Stokes's famous paper ' On the critical values of the sums of periodic series', in which 'uniform convergence' appears first in print; papers by S. Earnshaw and J. R. Young which are little more than nonsense; and a long and interesting paper by de Morgan on divergent series, a remarkable mixture of acuteness and confusion.

[...]

The following subsection of Hardy's Divergent Series (freely available on Archive.org) occupies pages 18-20, and gives his thoughts on the matter and some citations. In particular he gives the example of Transactions of the Cambridge Philosophical Society, Vol. 8 (Archive.org link) (see bolded text below). I've taken some text out for brevity, but the whole section (and every part of the book I have read) is a joy to read.

1.7. A note on the British analysts of the early nineteenth century. We end this chapter with a few remarks about British work on these subjects during the years 1840-50, which has been analysed very carefully by Burkhardt in the article from which we have quoted. It was a long time before the writings of the great continental analysts were understood in England, and these British writings show a singular and often entertaining mixture of occasional shrewdness and fundamental incompetence.

(1) The dominant school was that of the Cambridge 'symbolists', Woodhouse, Peacock, D. F. Gregory, and others. They represented what may be described as the ' $f(D)$ ' school of analysis. They started from 'algebra', and had something of the spirit, though nothing of the accuracy, of tho modern abstract algebraists. They dealt in 'general symbols', on which operations were to be performed in accordance with certain laws: 'the symbols are unlimited, both in value and in representation; the operations upon them, whatever they may be, are possible in all cases; ...' But the foundations of their symbolism were both inelastic and inaccurate. 'They insisted on a parallelism between 'arithmetical' and 'general' algebra so rigid that, if it could be maintained, it would effectively destroy the generality; and they never seem to have realized fully that a formula true with one interpretation of its symbols is quite likely to be false with another. They were also very much at the mercy of catchwords like 'what is true up to the limit...', and it is not surprising that their permanent contribution to analysis should have been negligible.

[...]

(2) There is one volume of the Transactions of the Cambridge Philosophical Society (vol. 8, published in 1849 and covering the period 1844-9) which contains a very singular mixture of analytical papers and gives a particularly good picture of the British analysis of the time. It contains Stokes's famous paper ' On the critical values of the sums of periodic series', in which 'uniform convergence' appears first in print; papers by S. Earnshaw and J. R. Young which are little more than nonsense; and a long and interesting paper by de Morgan on divergent series, a remarkable mixture of acuteness and confusion.

[...]

Source Link
Calvin Khor
  • 313
  • 2
  • 12

The following subsection of Hardy's Divergent Series (freely available on Archive.org) occupies pages 18-20, and gives his thoughts on the matter and some citations. In particular he gives the example of Transactions of the Cambridge Philosophical Society, Vol. 8 (Archive.org link) (see bolded text below). I've taken some text out for brevity, but the whole section (and every part of the book I have read) is a joy to read.

1.7. A note on the British analysts of the early nineteenth century. We end this chapter with a few remarks about British work on these subjects during the years 1840-50, which has been analysed very carefully by Burkhardt in the article from which we have quoted. It was a long time before the writings of the great continental analysts were understood in England, and these British writings show a singular and often entertaining mixture of occasional shrewdness and fundamental incompetence.

(1) The dominant school was that of the Cambridge 'symbolists', Woodhouse, Peacock, D. F. Gregory, and others. They represented what may be described as the ' $f(D)$ ' school of analysis. They started from 'algebra', and had something of the spirit, though nothing of the accuracy, of tho modern abstract algebraists. They dealt in 'general symbols', on which operations were to be performed in accordance with certain laws: 'the symbols are unlimited, both in value and in representation; the operations upon them, whatever they may be, are possible in all cases; ...' But the foundations of their symbolism were both inelastic and inaccurate. 'They insisted on a parallelism between 'arithmetical' and 'general' algebra so rigid that, if it could be maintained, it would effectively destroy the generality; and they never seem to have realized fully that a formula true with one interpretation of its symbols is quite likely to be false with another. They were also very much at the mercy of catchwords like 'what is true up to the limit...', and it is not surprising that their permanent contribution to analysis should have been negligible.

[...]

(2) There is one volume of the Transactions of the Cambridge Philosophical Society (vol. 8, published in 1849 and covering the period 1844-9) which contains a very singular mixture of analytical papers and gives a particularly good picture of the British analysis of the time. It contains Stokes's famous paper ' On the critical values of the sums of periodic series', in which 'uniform convergence' appears first in print; papers by S. Earnshaw and J. R. Young which are little more than nonsense; and a long and interesting paper by de Morgan on divergent series, a remarkable mixture of acuteness and confusion.

[...]