My previous post ended with a quote by Augustus De Morgan and it was such a good one that I make no apologies for quoting him again, this time from an 1846 biography of Newton, which you can find transcribed online here. In attempting to assess Newton’s contribution to science, and the importance of his Principia, De Morgan writes:
it is difficult to put before the ordinary reader, even if he be a mathematician, a distinct view of the merit of any step in the formation of a system. Unless he be acquainted with the history of preceding efforts, he comes to the consideration of that merit from the wrong direction; for he reads the history from the end. He goes to the mail-coach, back from the railroad instead of forward from the old strings of pack-horses: from a macadamized road lighted with gas to the rough stones and the oil-lamps, instead of beginning with the mud and the link-boys.
As well as giving a wonderful sense of 1840s modernity, this reads to me very like a condemation of presentist history of science and, while it may still be a little linear and ‘whiggish’ (but, hey, ADM was a Whig!), it is a nice call for making sure old ideas are read in their right context. As he elsewhere wrote, in a letter to William Rowan Hamilton, “In reading an old mathematicain you will not read his riddle unless you plough with his heifer; you must see with his light if you want to know how much he saw”.
It is these little hints of a ‘better’ kind of history – one which pays attention to context, to the small guys surrounding the great ones, to the changing meaning of words and ideas – that mean I’m a big fan of De Morgan. I found I was pleased to see his criticism of William Whewell‘s philosophical and schematic History of the Inductive Sciences in a review, noting that it was necessary to “apply ourselves with antiquarian industry” to examine a history that would show that “the present accumulation of science, however massive, has grown particle by particle, and has never really experienced any sudden increase”. Right on Augustus! There was no such thing as the (or a) Scientific Revolution! Great too that he adds, “pointing out how science has advanced, involves in some degree a history of the human mind in every stage of its culture”, and therefore “the collateral influence exerted by other branches of knowledge on the philosophy of material nature…”. Hooray! Is this a cultural history of scientific knowledge I glimpse?!
Well, of course, not quite. Just as scientists have their heroes and notion of progress, historians may have them too. In admiring De Morgan, I am apt to select the quotes I like, and hint that they point the way to the kind of history I think is ‘good’ today. This would suggest that I am doing bad history, as well as assuming that there has been positive progress in historical understanding, and I should check myself and ask myself what I’m up to. But that said, just as I can both deny that a story of necessary progress in science is at all helpful for our understanding its history and I can admit that there has been a clear accumulation of data, technological devices and better medical treatments, so I can acknowledge that 21st-century history is as much a product of its time and biases as any other period of history and believe that we have more historical data available then ever before, a greater range of ways to understand it and that these facts can have a positive impact on how we understand and interact with the world around us.
So yes. De Morgan was an (over-?)principled mathematics professor, nonconformist, sometime table-turner and Victorian Londoner with a great interest in the history of mathematical ideas and the people who had them – a history which he told from the point of view of a principled, nonconformist mathematical Victorian Londoner. I will maintain that he had some good instincts for getting to grips with the field.