30
votes
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What does it mean by "d-ism of Leibniz" and "dotage of Newton" in simple English?
It is a play of words by Charles Babbage. Deism was a religious belief or rather a movement promoting the idea that God exists but it does not interfere with whatever happens in this world. This old ...
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27
votes
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What is the difference between Calculus of Newton and that of Leibniz?
Newton's notation, Leibniz's notation and Lagrange's notation are all in use today to some extent they are respectively:
$$\dot{f} = \frac{df}{dt}=f'(t)$$
$$\ddot{f} = \frac{d^2f}{dt^2}=f''(t)$$
You ...
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19
votes
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What cipher(s) did Isaac Newton use?
Newton used anagrams which are not the usual ciphers. It is not designed for a secret communication, but only for proving at a later time that you knew something. So nobody is supposed to be able to ...
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11
votes
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Why is there little scholarship devoted to Book II of Newton's Principia?
It can certainly be agreed that Book 2 of the Principia has received less attention than Books 1 and 3. According to I B Cohen (1999):--
"Book 2 of the Principia differs from books 1 and 3 in a ...
- 2,809
10
votes
Was English mathematics behind Europe by many years because of Newton's notation?
Several factors come together to suggest that the idea that "English mathematics [was] ever significantly behind -- by say 50 years, 100 years, or even centuries" (i.e. in the post-Newtonian 18th or ...
- 2,809
9
votes
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Why is calculus missing from Newton's Principia?
There are too separate issues here. The method of fluxions and fluents, Newton's version of calculus, is amply represented in Newton's extant papers, starting with 1669 On Analysis by Equations with ...
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9
votes
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What mathematics did Isaac Newton learn at school?
Newton studied at school and at the university, but he mostly taught himself by reading. (At his secondary school he certainly learned Latin,
Greek, the Bible and some arithmetic. In the universities,...
- 42.6k
8
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What is the difference between Calculus of Newton and that of Leibniz?
You should definitely take a look at the second chapter of Arnold's Huygens & Barrow, Newton & Hooke. The late Prof. Arnold summarized therein the difference between Newton's approach to ...
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8
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What is the difference between Calculus of Newton and that of Leibniz?
Beyond the issue of notation, Newton experimented with a number of foundational approaches. One of the earliest ones involved infinitesimals, whereas later he shied away from them because of ...
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8
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Is Newton going to be the new Aristotle?
I suggest that the baseless suggestion offered in this question can best be answered by Einstein's own words about Newton, written in 1919.
The background was the now-well-known eclipse expedition ...
- 2,809
8
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What does it mean by "d-ism of Leibniz" and "dotage of Newton" in simple English?
The first answer is excellent but just for context on the actual math:
Newton notation for derivative of f(x):
$ \dot f(x) $
Leibniz notation for derivative of f(x):
$ \frac {df}{dx} $
Newton's ...
- 81
7
votes
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How did Newton and Kepler (actually) do it?
Goldstine, A History of Numerical Analysis from the 16th through the 19th Century (1977), describes Kepler's approach (p. 47), which may be found in Kepler's Epitome Astronomiae Copernicanae (1618), ...
- 1,311
7
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Was Newton's method of finding derivatives of his fluents based on applying the chain rule?
The answer is more of a yes, but with many buts. Newton did not have the modern concept of function, it was introduced by Dirichlet in the 19th century, or even its predecessor as assignment of values ...
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7
votes
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Is there anything written by Newton's roommate Wilkins about him?
Part of the problem may be that Newton's roommate's name is spelled as Wickins or Wickens, not to be confused with bishop John Wilkins, Newton's older contemporary. Since they did live in the same ...
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7
votes
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How close was Hooke to developing a comprehensive system of gravity?
Hooke was not close (as far as we can judge from his surviving work) to what Newton accomplished. Yes, he conjectured the inverse square law. He understood correctly some simple qualitative features ...
- 42.6k
7
votes
What problem led to the discovery of Calculus?
You remember incorrectly. Calculus was found by Archimedes, Gregory of Saint-Vincent, Galileo, Kepler, Descartes, Pascal, Cavalieri, Fermat, Barrow,
Wallis, Brounker, Huygens, Leibniz, J. Gregory, N. ...
- 42.6k
6
votes
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Allegations of Newton's untruthfulness
A comprehensive scientific biography of Newton is "Never at rest" by Westfall.
He tells the story, and expresses no doubt about it. The article in Wikipedia is an example of sloppy writing.
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6
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Allegations of Newton's untruthfulness
The article cited by the questioner incorrectly represents the limited amount of historical evidence that we have about the incident described. When the article is compared with the evidence, it can ...
- 2,809
6
votes
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How did Newton prove his third law of motion?
It was not "the experiment". First, Newton considered "his" laws to be "common knowledge" already "abundantly" confirmed and accepted by experts (he names ...
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6
votes
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When did the word "Real number" begin to be used as an official terminology to refer to both rational and irrational numbers?
It is hard to say what "official" means exactly, it is not like there was a bureau of terminological standards. But "real numbers", "real values" and "real ...
- 65.8k
6
votes
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Ideas about the speed of light between Galileo and Romer?
I do not think it is a virtue to make unsupported assertions just because we happen to believe them now. Following available evidence does not makes one not smart or disappointing, that is how science ...
- 65.8k
5
votes
Why is calculus missing from Newton's Principia?
Although this question and the answers now have some age to them, I suggest that it's important not to overlook the mythical character of the assumption that underlies this question. The question ...
- 2,809
5
votes
How did Newton and Kepler (actually) do it?
Kepler's Proofs will get you started on your quest.
This article mentions 987 folio pages of arithmetic; you should also look at the tables and methods of Copernicus.
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Best books/papers on Newton and his mathematical physics
The standard book about Newton's life is Never at Rest by Richard Westfall.
On my opinion it is a very good book, it covers his life in great detail, and gives a general overview of his activities (...
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5
votes
Difficulty in Understanding Newton's Principia
It would probably not have been easy for a contemporary mathematician to formulate a direct critique that Newton was difficult to understand without also 'reflecting' unwanted discredit on the skill ...
- 2,809
5
votes
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Was Newton's successful calculation of precession of equinoxes a fluke?
Numerical agreement was (at best) a fluke; quoth e.g. A. Berry, A short history of astronomy (1898, p. 235):
The amount of the precession as
calculated by Newton did as a matter of fact agree ...
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5
votes
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What was Isaac Newton's contribution to optics?
Contribution of Newton to optics is enormous. He is considered a founding father of physical optics.
I can only give some examples. His main discovery was that the sunlight can be dissolved into ...
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5
votes
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Is there a record of how Newton built his telescope?
We know relatively little about Newton's original model from 1668, modern versions draw lineage from the improved 1671 version. There is a record with its detailed description, with some comments on ...
- 65.8k
5
votes
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Mr. Newton at the Royal Mint
This is not mathematics, but Newton invented the ridges on coins to prevent theft. I am not sure if he invented it while he was director of the Royal Mint, but I suspect so.
In good ol times, coins ...
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5
votes
How did the idea of a formal derivation emerge?
The motivation for applying derivatives to polynomials over general fields is their use in detecting multiple roots: if $K$ is a general field, a polynomial $f(x)$ in $K[x]$ has no repeated roots if ...
- 4,014
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