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In a letter to Robert Hooke in 1676, Newton wrote:
If I have seen further it is by standing on the shoulders of giants.
Do we know which giants Newton was referring to? And was he referring to a particular piece of work or in general to all his accomplishments thus far?
We must locate this passage into a double context :
the general historical context
the specific context of the "rivalry" between Hooke and Newton.
See Robert Purrington, The First Professional Scientist : Robert Hooke and the Royal Society of London (2009), Ch.8 : And All Was Light : Hooke and Newton on Light and Color, page 135-on.
For the general context, we have to take into account the diffusion of Descartes' Physics and philosophy around the middle of the 17th Century.
Newton made extensive study of Descartes' theories (regarding : motion of bodies, celestial physics and light) : see Isaac Newton, Philosophical Writings (editor Andew Janiak, 2004).
All Newtonian's theory was in contrast with Descartes' ones.
Abou the rivalry with Hooke, [see Purrington, passim and pages 141-42], we have to consider the
delivering [by Newton of] a long manuscript on light and color to the [Royal] Society. The paper, consisting of an “Hypothesis” and a “Discourse,” was read by Oldenburg in five parts between 9 December and 10 February 1675/6 [footnote : Newton to Oldenburg, 7 December 1675; Corresp. I, 362–386].
Newton began by saying that he would not make any hypothesis about the aether and its role in the propagation of light, not thinking it necessary «to concern my selfe whether the properties of Light, discoverred by me, be explained by this or Mr Hook’s or any other Hypothesis capable of explaining them . . . » [footnote : «An Hypothesis explaining the Properties of Light discoursed of in my severall Papers.» Corresp. I, 362–386.] Further on he discussed Hooke’s discovery of diffraction, noting others who had observed it as well, but certainly giving Hooke credit.
Hooke was, however, unimpressed, and after hearing the first part of the “Discourse” on 9 and 16 December, noted «that the main of it was contained in his Micrographia, which Mr. Newton had only carried farther in some particulars.» [footnote : Birch, 3, 269. Hooke made very much the same comment on Newton’s theory of planetary motion. Everything we know of Hooke suggests that he really believed these assertions.]
[...]
The result of this new exchange, indirect though it may have been, with Oldenburg as intermediary, was to rekindle the old animosity of four years before.
The rift between Hooke and Oldenburg was growing at this time, and Hooke felt that the Secretary was trying to exacerbate the ill will between himself and Newton. Ironically, this alienation prompted Hooke to write a very conciliatory letter to Newton [footnote : Hooke to Newton, 20 January 1675/6. Corresp. I, pp. 412–3], hoping to heal the rupture that he felt the Secretary had fomented. He wrote Newton on the day the latter’s heated reply was read to the Society, 20 January, and the Diary suggests that he wrote him immediately after the meeting, hoping to heal the rupture.
In Newton’s more than cordial reply to this letter [footnote : Corresp., I, 416–7], he mentioned having called at Hooke’s lodgings only to find him out. And it was in this letter that Newton penned the famous line:
«If I have seen further it is by standing on ye shoulders of Giants,»
making it clear that Hooke was one of those giants. This almost friendly exchange of letters between brought a sort of peace and established a basis for Hooke’s correspondence with Newton after Oldenburg’s death in 1677.
In conclusion, I think that we have to read it in a "multiple way" : Newton's theories and discoveries was made possible also by a careful study of the works of previous "Giants", like Descartes and Hooke, all of them surpassed by the ability of Newton to "see further".
Added
From the on-line transcription of David Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, vol. 1 (Edinburgh: 1855), in The Newton Project we can recover a longer quotation from the letter :
you defer too much to my ability in searching into this subject. What Descartes did was a good step. You have added much several ways, and especially in considering the colours of thin plates [emphasis added].
If I have seen farther, it is by standing on the shoulders of giants.
But I make no question you have divers very considerable experiments beside those you have published, and some, it's very probable, the same with some of those in my late papers. Two at least there are, which I know you have often observed, — the dilatation of the coloured rings by the obliquation of the eye, and the apparition of a black spot at the contact of two convex glasses, and at the top of a water-bubble; and it's probable there may be more, besides others which I have not made, so that I have reason to defer as much or more in this respect to you, as you would to me.
How much of this is flattery? How much is gratitude? Who knows...
Newton implicitly refers to the medieval physicists who had such a profound affect on the intellectual atmosphere of Galileo et al. that they took their discoveries as common knowledge. Some of the most famous of these physicists were:
St. Thomas Aquinas, the first to distinguish weight, mass, and the resisting medium
The French bishop, physicist, and economist Nicole Oresme, who determined the mean speed theorem of uniformly accelerated bodies: $v_\mathrm{avg} = v_f / 2$.
Bishop Oresme posed the famous Gedankenexperiment:
I posit that the Earth is pierced clear through and that we can see through a great hole farther and farther right up to the other end where the antipodes [poles] would be if the whole of this Earth were inhabited; I say, first of all, that if we dropped a stone through this hole, it would fall and pass beyond the center of the earth, going straight on toward the other side for a certain limited distance, and that then it would turn back going beyond the center on this side of the Earth; afterward, it would fall back again, going beyond the center but not so far as before; it would go and come this way several times with a reduction of its reflex motions until finally it would come to rest as the center of the Earth....
{Quoted by K. V. Magruder from Le Livre du Ciel et due Monde (Madison: University of Wisconsin Press, 1968), translated by D. Menut, pg. 573.}
Bishop Oresme wrote (before Galilean relativity): “If air were enclosed in a moving ship, it would seem to the person situated in this air that it was not moved.” Book of the Heavens, Book II chapter 25, from Grant, A Source Book of Medieval Science, pg. 505, Harvard, 1974
Jean Buridan (d. ca. 1359) invented/discovered the concept of momentum and the equation $p=mv$.
Thomas of Bradwardine (c. 1295-1349) distinguished mean and instantaneous velocity.
Bradwardine determined in 1300 that for uniformly accelerated objects, $d = \frac{1}{2} a t^2$, which De Soto, O.P., (b. ca. 1494) applied to free-falling objects; Bradwardine thus wrote the first physics equation.
Jordanus de Nemore and Torricelli influenced Galileo's treatment of inclined planes.
Robert Grosseteste (c. 1168-1253) did experiments (not yet of course with modern rigor) and was keen on using mathematics; he is known for his work on understanding the rainbow. Thomas of Bradwardine (c. 1295-1349) at Merton College Oxford introduced the distinction between mean velocity (x/t) and instantaneous velocity (dx/dt) [and he was the first to write a physics equation]. Bradwardine had an enthusiasm for empiriometric physics that started a whole school called the Merton school (his successors include: William Heytesbury, Richard Swineshead, and John Dumbleton) that was extremely influential throughout Europe. Among other things, they were known for the Merton mean speed theorem, by which they proved the correct formula for free fall distance was given by $s=\frac{1}{2}at^2$. Interestingly, both Bradwardine and Grosseteste at some point in their lives were Archbishops of Canterbury. Nicole Oresme (<1348-1382) and Giovanni di Casali (c. 1350) independently developed use of 2-D graphs [long before Descartes (1596-1650)]. Oresme described all change using these graphs in particular local motion, including calculating area (integrating) under velocity curves to get distance. Oresme's arguments for the sun-centered and moving earth were widely known: he said, for example, that "...not only is the earth so moved diurnally, but with it the water and the air, as was said, in such a way that the water and the lower air are moved differently than they are by winds and other causes. It is like this situation If air were enclosed in a moving ship, it would seem to the person situated in this air that it was not moved." (p. 133, Dales.)
—A. Rizzi's Science Before Science pgs. 199-200
Also, I'm very surprised some here think Newton was referring to Descartes. Newton's physics was radically different than Descartes' (cf. this).
Even further back, Philoponus (late 5th, 2nd ½ of 6th century A.D.) is impressive:
He argued that the sun is fire and of terrestrial-like, corruptible matter. He devised a precursor to the notion of impetus which Buridan later developed, that which keeps moving bodies in motion even after the mover ceases being in contact with them; air does not keep projectiles in motion. He discovered that light rays travel the same both backwards and forwards. He invented functions of variables and their "courses" (what we'd call "first derivatives" in modern calculus). He discovered the law of inertia, that bodies in motion remain in motion unless something impedes their movement, literally a thousand years before Galileo, Newton, et al.!
He's certainly one of the "grands génies de l'Antiquité" ("great geniuses of Antiquity") and "principaux précurseurs de la Science moderne" ("principle precursers to modern Science"), as Pierre Duhem wrote in his magisterial, 10 volume work in the history of medieval physics:
Partially translated in:
cf. also:
Prior to Isaac Newton's tribute (above) to Rene Descartes and Robert Hooke in his above cited letter to the latter, it was reportedly the 12th century theologian and author John of Salisbury who was recorded as having used an even earlier version of this humbling admission---in a treatise on logic called Metalogicon, written in Latin in 1159, the gist of which is translatable as:
"Bernard of Chartres used to say that we are like dwarfs on the shoulders of giants, so that we can see more than they, and things at a greater distance, not by virtue of any sharpness of sight on our part, or any physical distinction, but because we are carried high and raised up by their giant size. (Dicebat Bernardus Carnotensis nos esse quasi nanos, gigantium humeris insidentes, ut possimus plura eis et remotiora videre, non utique proprii visus acumine, aut eminentia corporis, sed quia in altum subvenimur et extollimur magnitudine gigantea.)"Beyond the simplistic interpretation of the remark:
$\bullet$ 'standing on the shoulders of Giants'as merely describing:
$\bullet$ "building on previous discoveries",it seems to me that what Newton perhaps intended was to echo Bernard of Chartres' dictum that it doesn't necessarily take an exceptional intelligence to see farther; only someone both humble and willing to:
$\bullet$ first, clamber onto the shoulders of an acknowledged 'giant' and have the self-belief to see things at first-hand as they appear from a higher perspective (achieved more by the nature of height---and the curvature of our immediate space as implicit in such an analogy---than by the nature of genius); and, $\bullet$ second, avoid trying to see things first through the eyes of the 'giant' upon whose shoulders one stands (for the 'giant' might indeed be a vision-blinding genius)!Newton was certainly referring at least to Viete, who introduced the prototype of the symbolic notation which enabled the rapid development of tools leading to analysis. Also surely Newton was standing on the shoulders of Simon Stevin, Pierre Fermat, Isaac Barrow, and John Wallis.
