We must first examine the nature of scientific discovery, and how these breakthroughs come about. The most commonly accepted model for the advancement of scientific thinking is through a process of observation and application of knowledge. Simply put, if a scientist observes a change in one variable and can relate this to another variable or factor, then conclusions can be reached which serve to further the understanding of the scientific community as a whole. In this fashion, knowledge is accumulated and improved upon, as more natural phenomena become rationalised and explained. For this to be true the scientist must have some cognitive skill with regards to any observations made, and either the knowledge or the understanding necessary to compose this into an external impact. This ability will be affected by a number of factors, and will be influenced by the scientist’s intellect, as well as any external factors such as time and location.
Louis Pasteur is credited with the quote: “In the fields of observation, chance favours only the prepared mind” . What he meant by this, is that observations will only yield meaningful conclusions, and lead to a discovery, if the mind of the observer has been properly prepared beforehand. However, it is uncertain what he meant by: “prepared mind”. This can be interpreted as the raw intellectual ability of the scientist, or the standard of knowledge possessed by the scientist (which is majorly influenced by the time period in which a discovery takes place). Regardless, it is the ability to make connections such as these which account for most, if not all, of scientific discoveries since the most fundamental observations made by the Greek mathematicians of 3rd century BC.
Although this model for scientific discovery is rational (it follows that an observation made by a competent mind will break new ground if given the right application), how can we account for the fact that ancient mathematicians had very few preformed conceptions upon which to base their discoveries, and yet made fundamental contributions in the fields of science and mathematics? The fact that these earliest physicists had no laws on which to base their work makes their formidable intellect and imagination all the more impressive. Indeed, this only serves to enforce the argument that such discoveries are the product of observational genius, as time and place obviously had very little influence on such discoveries.
Take the example of Archimedes, who is often acclaimed to be the first physicist and applied mathematician. Original and imaginative, whole branches of scientific thought began with him, which is staggering given the lack of works on which he could base an understanding of the natural world from. There were, of course, great technologies pre-existing Archimedes by thousands of years, and there may have been other contemporary physicists working on ideas similar to his. Despite this, Archimedes is widely regarded as one of the leading scientists of classical antiquity, with vast contributions to physics and mathematics- including an explanation of the principle of the lever. As he was able to make these discoveries irrespective of his place in time, it can only be concluded that intellectual ability was by far the more important factor in his contributions, as there was no scientific knowledge-base on which to build.
On the contrary, in Melvyn Bragg’s book titled On Giants’ Shoulders, Professor Lewis Wolpert makes the point that the geographical location of Ancient Greece was fundamental to the development of scientific thought, mainly due to the Greeks’ access to Euclidean geometry. Wolpert contends that this understanding of geometry was fundamental to the instigation of scientific thought, and this could only have happened in the crucible of Ancient Greece. As such, the global position of Archimedes at the time of his discoveries is significant, despite his exceptional ability.
Moreover, whilst time (and by extension, accumulated knowledge) may have had little influence on Archimedes’ discoveries, it undeniably had a great impact on later advancements. For instance, any later scientists that lack Archimedes’ insight and innovation would require this ‘knowledge-base’ on which to build theories, apply observations, and reach a higher ground of scientific understanding. Newton alludes to this concept in his famous quote: “If I have seen further it is by standing on the shoulders of giants” . Indeed, most advances in modern science require basic laws and concepts around which conclusions can be formed, and even exceptional academics such as Sir Isaac Newton have relied on the works of previous scientists. Researchers cannot be expected to make discoveries independent of any work that precedes them, and this is only accentuated by the fact that certain discoveries require technologies such as transmission electron microscopy, that are the direct product of time and place.
We also cannot ignore the impact that circumstance has over a person’s intellectual capability. Exceptional genius can often be quelled or at least subdued if a person’s position in society or geographical location has a negative impact on their ability to exercise such traits. For instance, up until recently the position of ‘scientist’ was not a particularly prestigious or well-paid job, a fact which Antoine Lavoisier resigned himself to when he became a tax-collector, studying science only part-time. This raises the concerning notion that even if a person possesses exceptional academic ability, they may never have the chance to utilise this capability and contribute to the scientific community. This, again, gives weight to the argument that scientific discoveries are the product of place and time.
It is note-worthy however, that there are examples of people throughout history who have become great scientists from very humble beginnings. The most prominent example of this is Michael Faraday, a bookbinder’s apprentice who made ground-breaking contributions to the fields of electromagnetism and electrochemistry, despite leaving school at the age of thirteen. As such there are clearly scientists whose exceptional intellect can manifest itself despite any limiting factors concerning background and education.
Of course, circumstance can have the exact opposite effect on such affairs. When considering the conditions that are particularly conducive to scientific advancement, one example immediately springs to mind: Wartime is widely regarded as a catalyst for great scientific invention, as many of history’s greatest discoveries have occurred, often directly, due to the pressures that only a nation at war can create.
An example of such an innovation is radar, which was discovered and secretly developed by several nations before and during World War II. Radar uses a transmitter that emits radio waves, allowing objects of high electrical conductivity to be detected, with their relative movement ascertained though an appreciation of the Doppler effect. Developed pre-war, radar showed great potential as an object-detection system that could be used to anticipate enemy ships and aircraft. Due to this potential and the rising pressures in pre-war Europe, projects such as this were given status and funding by the government that may not have been awarded during peacetime.
As such, breakthroughs were made in the science behind radar technology as it was developed first at the Naval Research Laboratory, and then at the British Air Ministry. This work culminated with the design and installation of aircraft detection and tracking stations along the East and South coasts of England by the outbreak of WWII in 1939. The technology provided vital information in advance which helped the Royal Air Force win the Battle of Britain in late 1940. Whilst this scientific discovery was developed to be used as an air-defence system, it has various other applications such as radar ast
ronomy, and has enabled scientists to make observations that were previously obscure without the proper equipment.
As this discovery would have taken much longer to culminate had wartime not have been such a pressure on research, it is apparent that contemporaneous matters such as this have a great influence over scientific discovery. This is not only true in areas of military technology, but also in medicine and human biology, as wartime provides a huge influx of patients that require medical attention. This may not be significant in modern times, with a near comprehensive working knowledge of the human body, but in a less medically informed time period, a large patient base can have a huge impact on the understanding of human biology.
As always there are instances of ambivalence, when it is unclear which scientific discoveries are the product of time or place, and which are the product of exceptional genius. I would argue that the discoveries made in Renaissance Italy epitomise such a situation. This is because Italy, and essentially the city of Florence, was the early epicentre of the Renaissance period, and clearly a time and place of driven and committed innovation. Such an environment would have a huge influence over scientific advancement, as any breakthroughs would inspire and impel others to do the same. Interestingly, such an exciting time driving the pursuit of scientific knowledge was propagated partly by the raging military campaigns of the period. As alluded to earlier, wartime can be a huge pressure on the advance of scientific understanding, and this seems to be the case in Renaissance Italy. As Paul Strathern contends in his book The Artist, the Philosopher and the Warrior, “…as in ancient Greece, such achievements frequently occur when the civilisation that produced them is under threat”.  It is true that the Italian city states of the time were weak and divided, but far from undermining the academic stability of the region; this prevented Italy from lapsing back into a time of intellectual stagnation.
However, the political pressures were not the only thing driving the Renaissance, and once again we appreciate the importance of exceptional genius in scientific discoveries as it becomes clear that a number of exceptional characters, both political and intellectual, were responsible for a period of such intense discovery. Most would consider Leonardo da Vinci as the most prominent innovative force, as he was an unparalleled visionary and the most talented military engineer in Italy at the time. He is the perfect example of a genius who transcends his point in time, and whose advanced thinking did not depend on the current, and often unfounded, scientific method.
Throughout his life he produced more than 200 anatomical drawings of astonishing detail and accuracy, in the course of which he made many discoveries far ahead of his time, as well as correcting many conceptual errors that had persisted through the medieval era since classical times. According to Strathern, da Vinci was able to detect the circulation of the blood some 150 years before it was fully discovered and explained by the British physician William Harvey, and even came close to determining the difference between arterial and venal blood, remarking: “The blood which returns when the heart opens again is not the same as that which closes the valves of the heart”. 
Da Vinci was not restricted by contemporaneous matters in his inventions, and assuredly possessed an exceptional genius and imagination. This contention is strengthened by Strathern, who states that: “Instead of being taught what to do, what to think, he dreamed of what he wanted to do, and no formal schooling persuaded him otherwhise”.  The fact that da Vinci and many of his contemporaries were independent thinkers facilitated this time of scientific insight, and the intellectual prowess of such people was a huge enabling factor in Renaissance Italy’s intellectual domination.
As such, we can view the Renaissance as a mixture of the two influences. It was obviously a period of intense discovery and revolutionary thinking, but this was brought about by a collection of geniuses who drove their respective intellectual communities to succeed. In this we see that the influences of circumstance and genius are far from mutually exclusive, but rather more symbiotic, as the two can work together to produce a period of fervent curiosity and scientific innovation.
In the same way that time and place have an influence over scientific discoveries that are made, some are influenced directly by chance or coincidence. For example, it was a fortuitous accident that Alexander Fleming isolated the world’s first antibiotic, revolutionising modern medicine. In fact, it was completely by chance that Fleming stumbled upon the anti-bacterial effects of the fungus Penicillium notatum, when he left cultures of staphylococci to stand in his laboratory. Upon return he discovered that one of the cultures had been contaminated, causing the colonies of staphylococci immediately surrounding the growth to be destroyed. This simple observation marks the start of modern antibiotics, and happened almost completely by chance. It was the archetypal ‘right place, right time’ discovery that has proved to be instrumental in the development of modern antibiotics, saving many millions of lives since mass production began in 1945.
This is not to say that a certain level of scientific nous was not required for the discovery of penicillin: Fleming had already developed a reputation as an excellent researcher by the time of penicillin’s discovery, and was well-known amongst other scientists for his earlier work. He had spent years searching for natural anti-bacterial agents following World War I, after observing the inefficacy of wartime antiseptics in the treatment of sepsis. Without such research being conducted, the culture within which the Penicillium notatum developed would not have been able to instigate such a monumental chain of events. More importantly, had Fleming not been a distinguished researcher and pharmacologist, the discovery of penicillin may well have simply passed him by. Indeed, the application of knowledge and experience is crucial in the face of such an observation as, to the untrained eye, a “halo of inhibition around a blue-green mould”  is not immediately recognisable as one of the greatest scientific discoveries of the early 20th century.
Regardless, it may still be argued that chance has a large part to play in any scientific discovery, and that even a scientist of exceptional calibre would require a certain moment of inspiration to realise the implications of any observations made. This can be applied to Fleming’s discovery in that even a veritable genius would not have been able to isolate such an elusive anti-bacterial treatment through intellect and deduction alone. Whilst it may be too far to call humanities greatest discoveries ‘serendipitous’, there is a strong case for the influence of time and place in many, if not most, of history’s scientific triumphs.
On the contrary, there are examples throughout history of intellectual brilliance that transcends time. It certainly wasn’t serendipitous when Einstein developed his quantum theory of light. Equally, time and place had no part to play in the publication of his general theory of relativity; it was purely the product of the man whose name became synonymous with the word ‘genius’. However, it may be noted that true genius such as his is rare, and few enough individuals possess the intellect capable of making such discoveries independent of their place in time. Regardless, the simple fact of the matter is that for a discovery to be made, any knowledge gained requires an application. These ideas often form in a single mind, and an individual can typify as well as exemplify a sudden breakthrough in thought. Although circumstance undoubtedly has an influence
over such individuals, it is the intellect of the mind making the connections that ultimately makes a discovery. As Einstein himself famously said: “Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand”. 
This forward thinking is absolutely crucial in the formation of new ideas, as the transition between scientific models can only take place if previous concepts are challenged. In his book The Structure of Scientific Revolutions, Thomas S. Kuhn argues that the evolution of scientific theory does not emerge from the accumulation of facts, but rather through ‘paradigm shifts’ that radically change scientific thought and interpretation in a particular field. This concept was highly controversial upon its release in 1962, as many believed that it introduced an element of the irrational into a scientific method that should be totally logical. He challenged the prevailing view that scientific progress is a “development-by-accumulation” of facts and theories, by asserting an episodic model in which periods of conceptual continuity are interrupted by periods of revolutionary science.
Paradigm shifts are more than just standard discoveries within pre-determined scientific theory; they change the theory itself, uprooting all previous work and causing scientists to look again at any observations they have made. A prime example of such a paradigm shift is the Copernican revolution. At its centre was Nicolaus Copernicus, a Renaissance mathematician and astronomer who was largely responsible for a major shift in scientific theory when he formulated the heliocentric model of the universe. This model placed the Sun, rather than the Earth, at the centre of the solar system and was hugely controversial at the time. To be able to look at data objectively is difficult, especially when given presumptions about the natural world, and yet Copernicus was able to overcome the misconceptions concerning the structure of the solar system when formulating his model. It is often necessary to stand on the “shoulders of giants”, but this can be false support when the presupposed paradigm is fundamentally wrong. To see past this requires a great amount of insight, which Copernicus demonstrated when he disputed the Ptolemaic model of the solar system, and thinking beyond the accepted paradigms of the time in a display of exceptional intellectual and imaginative ability.
Knowledge requires application. State of understanding alone cannot produce innovation of thought. That is the nature of innovation: it cannot be stimulated by preconceived and possibly out-of-date thinking; it must be brought into being by intellectual genius that can introduce new paradigms and change scientific thinking. Apart from some rare exceptions, great scientific discoveries require both genius and the right state of knowledge. However, as state of knowledge alone cannot succeed in discovery, genius must be regarded as the more important factor.
1) Wikiquote (January 2014), Loius Pasteur, available at: http://en.wikiquote.org/wiki/Louis_Pasteur
2) Bragg, Melvyn (1998), On Giants’ Shoulders, Hodder and Stoughton
3) Alan Dower Blumlein webpage (May 2012), The Story of Radar, available at: http://www.doramusic.com/Radar.htm
4) Strathern, Paul (2010), The Artist, the Philosopher and the Warrior, Vintage
5) Wikipedia (February 2014), History of Penicillin, available at: HHHHHjh http://en.wikipedia.org/wiki/History_of_penicillin
6) Antibiotic resistance (September 2001), History of Antibiotics, available at: http://web.archive.org/web/20020514111940/http://www.molbio.princeton.edu/courses/mb427/2001/projects/02/antibiotics.htm
7) Kuhn, Thomas (1996), The Structure of Scientific Revolutions, University of Chicago Press