"Scientific method refers to bodies of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning. A scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses."
I often hear from scientists and wanna-be scientists (like me) that the scientific method is the only way possible forward in understanding the universe. Logical reasoning and the scientific method have their place in the scheme of things. But to say that they are primarily responsible for all progress is putting the cart before the horse. In the definition above, formulation of a hypothesis is taken as a part of the scientific method. However, this formulation is often mysterious, and no one can really explain how a "productive" hypothesis is arrived at. Most of the times logic and reasoning have nothing to do with it.
The anonymous Indian genius that conceived zero, Kepler, Newton, Kekulé, Marie Curie and Einstein all have one thing in common: they created a paradigm shift in our understanding of nature. The paradigm shift was not in the proof they offered but the hypothesis itself. While proof is important, it is secondary to the hypothesis. I doubt if anyone of these giants have explained how they came up with the hypotheses. Given a "productive" and viable hypothesis, someone can and will come up with a proof eventually just as Fermat's last theorem demonstrated.
The modern scientists spend their lifetimes perfecting the scientific method. But they probably do not spend enough time understanding how the hypotheses are made. It is assumed that a good scientist "knows" how to arrive at one. There is no process, no class (that I know of) and no "formal" guidelines to come up with a good hypothesis. No good hypothesis no significant progress. That's a limitation of the scientific method.
The ancient Indian sages approached the process in a different manner. Many of them were true yogis and attained samadhi by meditation. The claim is that when one attains samadhi, the knowledge about the true nature of the universe arises spontaneously. Perhaps this is the source of all hypotheses. They made seemingly amazing leaps in understanding the nature. Often they didn't explain how they arrived at that knowledge, but only stated it with authority. Frequently one hears the phrase "self evident" with such statements. It is left for the later commentators to comment on that statement and expound it. Some commentaries on Patanjali's Yoga Sutras say this: if all the books are burnt and all knowledge is lost save the Yoga Sutras, then rest of the knowledge can still be developed by accomplished yogis.
I know that there will be some scientist types on DC who will grill me on this one (where is Commonsense?), but I will make this claim: scientists will do much better in their disciplines if they include meditation in their curriculum. Have you noticed how often multiple scientists come up with the same new idea that miraculously solves a difficult problem that mankind has grappled with for ages? In my opinion this phenomenon is not magic or coincidence, but it can be explained by our spiritual nature. We are all connected by an underlying thread and that manifests itself in these mysterious ways. In fact someone even conducted a maze running experiment on rats that showed that once a particular maze is solved by one rat, other rats find it easy to solve.