In science, difficulties on theory refers to the apparent issues, fallacies, and or insurmountable barriers, depending, with a given argument or line of reasoning, point of view, or position on an issue.

“Long before arriving at this part of my work, a crowd of difficulties will have occurred to the reader. Some of them are so grave that to this day I can never reflect on them without being staggered; but, to the best of my judgment, the greater number are only apparent, and those that are real are not, I think fatal to my theory.”
Charles Darwin (1859), Origin of Species (§6: Difficulties on Theory) [1]

A theory, in short, is an unproven assertion; advanced for some or another reason, generally for the sake of explanation. The majority of theories or theorems will tend to fail; those that do not become law.

Etymology
The term and concept of “difficulties on theory” was made popular by English naturalist Charles Darwin who employed the term as the title of chapter six of his Origin of Species, which he again addressed in his closing chapter “Recapitulation and Conclusion”.

Hmolpedia
In all Hmolpedia articles, wherein a theory is discussed or summarized, a standing practice, aim, and or rule of thumb, modeled on the Darwin protocol, is to append a so-called difficulties on theory section to the end of each article, wherein the apparent issues with the said theory are addressed openly, with citation when available, so as to not have to re-tread old ground—to get all the cards out on the table, so to say.

Hmolpedia "difficulties on theory" sections tend to act as time savers. Generally, it takes a certain amount of time and mental energy to dissect and pick apart a given theory, the subtle issues of each held in purview, in clear view, only in that point in time when the bulk of the said theorist's work has recently been consumed; hence, it is advisable to state the facts or difficulties as they are apparent, when they are apparent, so as to not have to re-work the issue over again upon each return. If a given theory is a dead end cul-de-sac, it should be stated so frankly, allowing the reader to move on to more fruitful work.

Quotes
The following are related quotes:

“That many and grave objections may be advanced against the theory of descent with modification though natural selection, I do not deny. I have endeavored to give them their full force.”
Charles Darwin (1859), Origin of Species (§14: Recapitulation and Conclusion) [1]

References
1. Darwin, Charles. (1859). Origin of Species (§6: Difficulties on Theory (ΡΊ), pgs. 143-71; grave objections, pg. 375). Publisher.

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