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29 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 ...
ACR's user avatar
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17 votes
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What kind of mathematical education did Leibniz have?

Mauro Allegranza's comment pretty much says it all but to elaborate a bit one could mention that Leibniz came to mathematics rather late in his intellectual career and was essentially a self-educated ...
Mikhail Katz's user avatar
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14 votes
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Where did Leibniz explore the product rule of differential calculus?

It is discussed in multiple manuscripts, letters and publications from 1675 to 1701. According to Fracois Ziegler's post on MO Did Leibniz really get the Leibniz rule wrong?, Leibniz originally ...
Conifold's user avatar
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10 votes
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Why is differentiation under the integral sign named the Leibniz rule?

This rule is, indeed, due to Leibniz, although it was Johann Bernoulli who realized its broader implications, and there is an interesting story to its discovery. It is told in Chapter 3 of Families of ...
Conifold's user avatar
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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 ...
terry-s's user avatar
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10 votes

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 ...
José Hdz. Stgo.'s user avatar
10 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 (...
KCd's user avatar
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9 votes

What is the title of the 1676 Memoir in which Leibniz first used the Chain Rule?

I retracted my previous answer in the comments since it was actually for the product rule, not the chain rule. Sorry about that. After performing another search, I was able to find some links that ...
Andrew R.'s user avatar
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9 votes

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 ...
Mikhail Katz's user avatar
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8 votes

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 ...
ShinyDemon's user avatar
7 votes
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Source of claim that Leibniz discovered separation of variables for ODEs in 1691?

The reference is probably to a treatise sent to Huygens on 5 October 1691, where Leibniz says (and illustrates with several examples) that "Whenever the subtangent [$=y/y'$, but it would also work for ...
Viktor Blasjo's user avatar
7 votes
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Are there any direct comments by Isaac Newton on Leibniz's living force / vis-viva?

The controversy was not so much about the tension between vis viva and mechanics, as about what is the "true" quantity of motion, vis viva or momentum, and what is the "metaphysical&...
Conifold's user avatar
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6 votes
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How to understand Poincaré's interpretation of Newton's anagram "aaaaabbbeeeeii"

See more detail about this anagram (there were actually two of them) here: https://mathoverflow.net/questions/140327/arnold-on-newtons-anagram Whatever the literal translation of the anagrams is, ...
Alexandre Eremenko's user avatar
6 votes

Where did Leibniz explore the product rule of differential calculus?

Leibniz states the product rule in his first paper on the calculus (1684). It's in the middle of the fist page (page 467) as can be seen here: https://www.maa.org/press/periodicals/convergence/...
Viktor Blasjo's user avatar
5 votes
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What did physics mean in 17th century?

In his letter, I would assume he's referring to a problems in astronomy and mechanics. But the term physics was much more broad up until the 19th century. This is covered in good detail in e.g. J. L. ...
Sam Gallagher's user avatar
4 votes

Leibniz's stand on axioms and definitions

To elaborate on Leibniz's comment that "The axioms are not, as you say, indemonstrable" (see the answer https://hsm.stackexchange.com/a/369/604): Leibniz was rather successful in choosing ...
Mikhail Katz's user avatar
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4 votes

What is the difference between Calculus of Newton and that of Leibniz?

I'm not a historian, but I have to answer this because the previous answers have gotten it completely wrong. Leibniz's $\displaystyle \frac{df}{dx}$ is not equal to $f'(x)$. I think there are two main ...
benrg's user avatar
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4 votes

What is the difference between Calculus of Newton and that of Leibniz?

From Loemker's translation, "Leibniz's reasoning, though it strives for a broader application of the law of inverse squares than to gravity alone, is less general than Newton's (Principia, ...
Sholto Maud's user avatar
4 votes

What does it mean by "d-ism of Leibniz" and "dotage of Newton" in simple English?

I think the two other answers here when combined offer a complete explanation of Knuth's word game. He calls Leibniz notation "d-ism" to combine the English word "deism" with Leibniz's use of the ...
Ethan Bolker's user avatar
4 votes
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Where can I find the Royal Society report on the controversy over the invention of differential calculus?

At request of Leibniz himself, the Royal Society appointed a commission which had the task of dealing with a dispute that followed an article by John Keill published in 1710 in "Philosophical ...
BakerStreet's user avatar
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3 votes

Leibniz conjecture that geometry is a form of algebra

In his essay in Antognazza's volume ('18), Probst notes that Leibniz wanted to transform geometry into a pure doctrine of magnitudes without any direct relation to geometric objects. (p. 216). ...
Mikhail Katz's user avatar
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3 votes
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When did derivative mean not only "slope of tangent" but also "instantaneous rate of change"?

"Fermat was interested in minima and maxima, and realized these occur when the tangent has zero slope. When was it realized that this slope of tangent was the same thing as an instantaneous rate ...
Mikhail Katz's user avatar
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3 votes
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Did Leibniz sketch a design for a machine capable of solving a system of linear equations?

I've found an indirect reference into: Joseph Ehrenfried Hofmann, Leibniz in Paris 1672-1676 (1974, German ed.1949), page 30 and footnote 27: still in 1674 he [Leibniz] has plans for constructing an ...
Mauro ALLEGRANZA's user avatar
3 votes
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What was the mechanical principle of Leibniz's "integraph"?

Leibniz did indeed describe a mechanism for tracing the solution to any differential equation of the form dy/dx=f(x) using tractional motion. For a detailed explanation, see Viktor Blåsjö, The myth of ...
Viktor Blasjo's user avatar
2 votes

Did Leibniz use infinite numbers?

It appears that they are right in the "metaphysical" sense, here is a passage from Leibniz's letter to Bernoulli (1699):"I concede an infinite multitude, but this multitude forms neither a number nor ...
Conifold's user avatar
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2 votes

What navigation instrument did Leibniz develop?

Leibniz bragged as early as 1671 about solving the problem of longitude, among a long list of other major problems, with the help of his "combinatory art" At the time he was euphoric about the ...
Conifold's user avatar
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2 votes
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Why do we use Leibniz's “version” of calculus instead of Newton's?

There are many notations for derivatives as the concept has been expanded in many different ways. For example, there is also Heaviside's operational D. This is also used for the Frechet and Gateaux ...
Mozibur Ullah's user avatar
2 votes

Did any mathematicians of the time (the 17th Century) try out an intermediary between Bernoulli's and Nieuwentijdt’s infinitesimals?

These are assorted comments too long for a comment. Boyer is unreliable and should not be used as a source. Bernoulli's "proof" of the existence of infinitesimals was rejected by Leibniz, ...
Mikhail Katz's user avatar
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1 vote

Did Leibniz also design analog computers?

Yes, Leibniz did design a famous computing machine called the stepped-reckoner. It was a (digital) computer, but not an analog computer. Don't confuse digital with electronic. The difference is only ...
DaveIdito's user avatar
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