“A work on tidal theory… led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work.”

the "ideas of analysis" to which he returned, are those quoted above.
Ausdehnungslehre (1844)

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Hermann Grassmann10

German polymath, linguist and mathematician 1809–1877

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“The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, not only the often very complex and unsymmetric formulae which are fundamental in tidal theory, but also the technique of development parallels the concept.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Ausdehnungslehre (1844)

“The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.”

W. W. Rouse Ball (1850–1925) English mathematician

W. W. Rouse Ball, History of Mathematics, (London, 1901), p. 463;

“The concept of centroid as sum led me to examine Möbius' Barycentrische Calcul, a work of which until then I knew only the title; and I was not little pleased to find here the same concept of the summation of points to which I had been led in the course of the development. This was the first, and… the only point of contact which my new system of analysis had with the one that was already known.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Ausdehnungslehre (1844)

“…nor have I found occasion to depart from the plan… the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange… had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

The Differential and Integral Calculus (1836)

“There is, then, in this analysis of variance no indication of any other than innate and heritable factors at work. (Coining of the phrase ‘analysis of variance’.)”

Ronald Fisher (1890–1962) English statistician, evolutionary biologist, geneticist, and eugenicist

The causes of human variability. Eugenics Review 10, 213-220, 1918.
1910s–1920s

“As I was reading the extract from your paper in the geometric sum and difference… I was struck by the marvelous similarity between your results and those discoveries which I made even as early as 1832…
I conceived the first idea of the geometric sum and difference of two or more lines and also of the geometric product of two or three lines in that year (1832). This idea is in all ways identical to that presented in your paper. But since I was for a long time occupied with entirely different pursuits, I could not develop this idea. It was only in 1839 that I was led back to that idea and pursued this geometrical analysis up to the point where it ought to be applicable to all mechanics. It was possible for me to apply this method of analysis to the theory of tides, and in this I was astounded by the simplicity of the calculations resulting from this method.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Letter to Saint-Venant (1845) as quoted by Michael J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1967)

“Analysis of a system reveals how it works; it provides know-how, knowledge, not understanding; that is, explanations of why it works the way it does.”

Russell L. Ackoff (1919–2009) Scientist

This [understanding of why systems work] requires synthetic thinking... Analysis is the way scientists conduct research. Synthetic thinking is exemplified by design.
Ackoff & Greenberg (2008) Turning Learning Right Side Up. p. 61 as cited in: Stephen M Millett (2011) Managing the Future: A Guide to Forecasting and Strategic Planning. p. 52.
2000s

“Everything was twice repeated,
Sometimes more than twice repeated,
As they worked through the agenda
(It seemed elastic, that agenda,
Becoming longer, never shorter),
Their utterances grew long, not shorter,
It was just like spreading butter.”

Gavin Ewart (1916–1995) English poet

"The Meeting", line 11, from The New Ewart (1982)

“The problem which Mondrian undertook to solve in nr. 116 [a new painting of Mondrian, exhibited in a group-exhibition in the Stedelijk Museum in 1915 in Amsterdam] was handled very successfully. This work spiritually dominates all others. It gives the impression of Repose; the repose of the soul. Its predetermined structure embodies 'becoming' rather than 'being'. This represents a true element in art, for art is not 'being', but 'becoming'. The idea of 'becoming' has been expressed in black and white…. Through years of hard work my own experiences have led me, before I came to know the theories of Uexkuell or Picasso, to prefer the use of the white-black-grey palette in works of a purely spiritual content…”

Theo van Doesburg (1883–1931) Dutch architect, painter, draughtsman and writer

Quote from Dutch art-magazine: 'Eenheid' (in Dutch: Unity) no. 283, 6 November 1915; as quoted in Theo van Doesburg, Joost Baljeu, Studio Vista, London 1974, p. 105
1912 – 1919

“This work… was designed in the first instance to be a second edition of a Treatise on Algebra, published in 1830, and which has been long out of print; but I have found it necessary, in carrying out the principles developed in that work, to present the subject in so novel a form, that I could not with propriety consider it in any other light than as an entirely new treatise.”

George Peacock (1791–1858) Scottish mathematician

Vol. I: Arithmetical Algebra Preface, p. iii
A Treatise on Algebra (1842)

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