Science has benefitted from God's revelation in a great many ways. But before I explain how, understand that this multilayered complex reality we inhabit and are, in fact, a part of is symbiotic (though not pantheistic) with both a material and spiritual composition. This is why the biblical and scientific accounts of phenomena are complementary rather than contradictory, when properly understood.
Historically; the historic, scientific and theological literature all owe much to one another. Since you haven't yet had the opportunity to learn what they are, I should explain some of them starting with the influence of science on theology as you should find that fairly straight forward. Let's start with...
As Dr. Donald Mackay (Professor of Communication and Neuroscience at the University until his retirement in 1982 when he became Emeritus Professor), Dr. Michael Polyani (chemistry professor at Kaiser Wilhelm Institute, chemistry and social sciences professor at University of Manchester, professor to three Nobel Prize winners, and elected to the Royal Society and the American Academy of Arts and Sciences), and Dr. Thomas Torrance (winner of the Templeton Foundation Prize for Progress in Religion for singular contributions to the dialogue between science and theology) explained in the New Dictionary of Theology:
"One of the earliest was natural theology. From Robert Boyle (1627–91) to Paley, English literature is replete with attempts to make discoveries of science the basis of a Christian apologetic; it has been argued, somewhat doubtfully, that underlying such efforts lay a quest for social stability which might be bolstered by a strong Anglican church. Its unchanging formularies were to be confirmed by the unchanging laws of science. Be that as it may, the ‘argument from design’ survived, albeit in a weakened form, even the onslaughts of Darwinism. With today’s greater knowledge of the intricacies of the natural world, attempts have been made to revive it, though not with conspicuous success.
It was in fact the awesome regularity of the mechanical universe as emphasized by Isaac Newton that raised urgent questions of divine intervention. Did God intervene in the running of the machine he had created, or did he not? The dilemma was crystallized in the (probably apocryphal) remark by Laplace (1749–1827) that he had ‘no need of that hypothesis (God)’ in his cosmology. Thus arose a powerful stimulus to the growth of deism and its derivatives such as unitarianism. A recognition that all natural events (not merely those explicable by known scientific laws) must be seen as God’s activity was not absent in the late 18th century. But a God-in-the-gaps theology proved surprisingly resilient and represents another popular misunderstanding of the science/religion relationship.
A third response of theology to science has come in the area of biblical interpretation. It goes at least as far back as Galileo’s famous quip of 1615 that, in Scripture, ‘the intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes’—a response engendered at least in part by his own telescopic discoveries in vindication of Copernicus.
Since that time the discoveries and theories of science have not infrequently led to a revision of traditional interpretations of Scriptures. These include ancient views on the age of the earth, the structure of the universe, the extent of Noah’s flood and the origins of biological species (including human beings). Few commentators disagree when this happens over cosmology, but application of an identical methodology to questions of human origins is still controversial.
It is important not to imply a unique role for science in the reinterpretation of Scripture, but it cannot be neglected. Where a theological response to science has been claimed with much less justification is in the ‘demythologization’ (see Myth) programme prescribed by Bultmann and others. The assertion that ‘miracle’ is incredible in a scientific age is as unphilosophical as it is unhistorical. It ignores the fact that science is, by definition, concerned only with regularities and can therefore make no pronouncement on their breach; and it neglects to note that, at the very time when demythologization came into vogue, old-fashioned, positivistic scientific dogmatism was in decline. For this a variety of causes may be cited, notably the demise of the deterministic world of Newtonian mechanics in the face of successive challenges by thermodynamics, relativity and quantum theory.
Finally it may be briefly noted that the process theology of Whitehead, Hartshorne and others sprang, at least ostensibly, from a concern to understand God’s relationship to the world of nature as studied by science."
With respect to theologies influence on science, they went on to state:
"The origins and growth of science may be fruitfully considered in terms of a response to biblical insights liberated at, and since, the Reformation (Hooykaas, Russell). This response may be seen in the writings of many men of science and in the morphological similarity between scientific and religious theories. Five such insights may be identified:
1. The elimination of myth from nature: an animate, even ‘divine’, nature is not susceptible to scientific enquiry, nor compatible with biblical injunctions to treat nature instead as a dependent creation of God (Pss. 29, 89, 104, 137, etc.) who alone is to be worshipped (Dt. 26:11; Is. 44:24; Je. 7:18; etc.). The replacement of an organismic by a mechanistic universe (nature’s own ‘demythologization’) coincided with a renewed awareness of such teaching.
2. The laws of nature: the emergence of ‘laws of nature’ in the 17th century has been shown by Zilsel (Physical Review 51, 1942, pp. 245–279) as a derivative of biblical doctrines, citing inter alia Jb. 28:26 and Pr. 8:29. Later writers (Whitehead, Oakley, etc.) have strengthened this thesis.
3. The experimental method: both in English Puritanism and continental Calvinism the questioning manipulation of nature was strongly encouraged as an alternative to the abstract reasoning of ancient pagan cultures. It was seen as fully compatible with biblical injunctions to ‘test’ all things (1 Thes. 5:21; Rom. 12:2; Ps. 34:8; etc.).
4. Controlling the earth: Bacon and his followers saw in Scripture (Gn. 1:26; Ps. 8:6–8, etc.) a clear mandate for altering the natural world for human benefit.
5. To the glory of God: that scientific research could add lustre to the divine name was believed even by patristic writers, but it most strongly emerged in the 17th century. Thus John Kepler (1571–1630), in studying those heavens which declared the glory of God (Pss. 8, 19, 50), exclaimed he was ‘thinking God’s thoughts after him’. This of itself was a powerful motive for the scientific exploration of nature.
If science may, without exaggeration, be seen as historically dependent for its emergence on Christian theology, then, in an age when this has been largely forgotten, biblical theology has an even more important contribution to make. This is in the area of ethical direction. Crucial to such an impact is a renewal of the biblical concept of stewardship which may be seen as the only key to current dilemmas over areas of concern ranging from the pollution of the biosphere to a possible nuclear holocaust. All of these arise from a technology now made possible by science. Moreover, many aspects of modern science have been seen as eroding human dignity and worth, whether in the extrapolations of biological science to the so-called ‘sociobiology’, or in the naive reductionism that, in the manner of the Greek atomists, sees all phenomena in purely material terms. To an allegedly ‘scientific’ world-view so devoid of comfort and hope theology surely has much to say."
Reductive materialism is a false view of reality, the Christian worldview stands apart from all others in which science was materially "stillborn" as Distinguished Professor of Physics at Seton Hall Stanley Jaki wrote, science greatly benefited from the Christian revelation of God, historically science has itself been replete with "individuals and circumstances" consumed by their "petty boundaries and preconceptions" (read the Structure of Scientific Revolution by Thomas S. Kuhn as a suggested starting point for more information on that topic), the rise of modern science correlates with and springs from the Christian worldview embedded in Western Civilization not the "Islamic Golden Age" as you call it which I need to educate you with respect to, etc...
Note to mods: Though not necessary, this is why a section would be desirable. Your call. I leave it in your capable hands. Peace.
How exactly has science benefited from the "knowledge" of an unfalsifiable deity? The history of science is absolutely replete with individuals and circumstances that transcend petty religious boundaries and preconceptions. The Islamic Golden Age, for instance, is universally considered to be a high point in the developmental road that led to the modern scientific method. At its heart, science fundamentally doesn't require a deity to advance and flourish, and evidence abounds to support that.
Science and religion are two entirely separate entities.