Were it possible to trace the succession of ideas in the mind of Sir Isaac Newton, during the time that he made his greatest discoveries, I make no doubt but our amazement at the extent of his genius would a little subside. But if, when a man publishes his discoveries, he either through a design, or through habit, omit the intermediary steps by which he himself arrived at them, it is no wonder that his speculations confound them, and that the generality of mankind stand amazed at his reach of thought. If a man ascend to the top of a building by the help of a common ladder, but cut away most of the steps after he has done with them, leaving only every ninth of tenth step, the view of the ladder, in the condition which he has pleased to exhibit it, gives us a prodigious, but unjust view of the man who could have made use of it. But if he had intended that any body should follow him, he should have left the ladder as he constructed it, or perhaps as he found it, for it might have been a mere accident that threw it in his way… I think that the interests of science have suffered by the excessive admiration and wonder with which several first rate philosophers are considered, and that an opinion of the greater equality of mankind, in point of genius, and power of understanding, would be of real service in the present age.” - Joseph Priestly, The History and present State of Electricity
The section where I’ve added an ellipsis is a section where he discusses Newton in more detail. That entire part of the text is worth reading. Priestly wrote the book before he did his work on the composition of air. The book is, as far as I am aware, the first attempt at actual history of science. (I’m meaning to read the whole thing at some point, but the occasionally archaic grammar makes for slow reading.)
Euler is one of the few mathematicians who provide an exception to this rule. To quote Polya (Mathematics and Plausible Reasoning):
Euler seems to me almost unique in one respect: he takes pains to present the relevant inductive evidence carefully, in detail, in good order. His presentation is “the candid exposition of the ideas that led him to those discoveries… Natural enough, he tries to impress his readers, but, as a really good author, he tries to impress his readers only by such things as have genuinely impressed himself.
(the quoted passed in the text is apparently from Condorcet, although I don’t know the initial source)
Polya is, of course, one of the few other mathematicians who break this mould. Explicitly writing books about the process of discovery.
It’s a coincidence that I was thinking along these lines recently. Most science is just the result of tiny footsteps put one after the other, but when you see the final result it is impressive. Most teaching books are in fault because they only portray the end result whereas the painstaking but simple steps that lead there often in a natural way are omitted.
It is an issue that has been discussed here before. Eliezer generally uses Einstein as the example rather than Newton. See for example Einstein’s Superpowers and My Childhood Role Model.
The section where I’ve added an ellipsis is a section where he discusses Newton in more detail. That entire part of the text is worth reading. Priestly wrote the book before he did his work on the composition of air. The book is, as far as I am aware, the first attempt at actual history of science. (I’m meaning to read the whole thing at some point, but the occasionally archaic grammar makes for slow reading.)
Euler is one of the few mathematicians who provide an exception to this rule. To quote Polya (Mathematics and Plausible Reasoning):
(the quoted passed in the text is apparently from Condorcet, although I don’t know the initial source)
Polya is, of course, one of the few other mathematicians who break this mould. Explicitly writing books about the process of discovery.
You quoted:
But I just read the original and it is written:
Now it makes more sense to me, the ‘a’ makes all the difference.
Mistranscription by me. Fixed now. Thanks.
It’s a coincidence that I was thinking along these lines recently. Most science is just the result of tiny footsteps put one after the other, but when you see the final result it is impressive. Most teaching books are in fault because they only portray the end result whereas the painstaking but simple steps that lead there often in a natural way are omitted.
It is an issue that has been discussed here before. Eliezer generally uses Einstein as the example rather than Newton. See for example Einstein’s Superpowers and My Childhood Role Model.
The book is available for free on google books, can you tell us the page nr. of the quotation please?
575 and 576 in the edition on Google Books.