Mathematical equations can sometimes tell such a convincing tale, they can seemingly radiate reality so strongly, that they become entrenched in the vernacular of working physicists, even before there's data to confirm them. See Greene, Brian, Mind Over Matter, Smithsonian Associates. Smithsonian. Washington: Smithsonian Associates, July/August 2013, page 27.Even though this article deals with the discovery of the Higgs boson, the statement has relevance to genealogical research also. Unfortunately, there is no "mathematics" of genealogy. I have suggested in the past that we need to develop a standardized genealogical metadata that would serve approximately the same purpose, but have had little or no response to the idea.
If you think about it, much of what we posit as genealogical researchers falls in the category of theory. Although we may personally accept the evidence we have accumulated as "proof," there are no absolutes and, as I have posted recently, it is unlikely that any historical research, including genealogy, can achieve a significant measure of absolute truth on historical subjects. The statement above gives an insight into the workings of physical science that parallels the processes of historical inquiry. Just as in physics, stories and personal views of the past can become entrenched before there is adequate data to support them.
In the case of the mathematical equations that demonstrated the existence of the Higgs Field and ultimately resulted in the discovery of the Higgs boson, it took fifty years or so of research before the final confirmation. As is common in science, the initial theory was widely rejected and then slowly gained acceptance. As genealogists, we need to realize that some of our most cherished stories from the past may have no factual basis. In the case of the posited theory in physics, there is a peer review and publication mechanism for establishing valid theories. In genealogy, a similar process exists, but it is closed to all but a very small minority of genealogists. If I were to try and write an article, any article, for one of the established genealogical journals, it would likely be rejected out of hand. What is this?
Physics, unlike genealogy, is an established academic discipline. Publication is the way of advancing in the academic world. I am speaking from experience having participated in the process of publication in the field of Linguistics in the past. But genealogy has no established academic system. The accredited and certified genealogists have created their own closed system that is only very partially acknowledged and accepted generally among all genealogists. As a matter of fact, very few genealogists are even aware that such a system exists. The contrary is true in a physical science such as physics. All physicists are part of their own system. Because genealogy has no such centralized culture, the accredited genealogists act more like a social club than an academic culture.
Why would anything I wrote be rejected? Likely on purely formatting and stylistic grounds. So can genealogy achieve a breakthrough like those in physical science? No. Simply because there is no mechanism for this to happen. A widely related and repeated story, no matter how baseless, will never be corrected in genealogy.