the first trial <stemming/to stem> from... vs. the first person to climb
Solution 1:
To summarize the question:
We can say the first trial stemming from as well as the first trial to stem from. So why can't we say the first person climbing Mount Everest as well as the first person to climb Mount Everest?
In Swan's examples each verb (win, climb, arrive) is what Quirk et al. in A Comprehensive Grammar Of The English Language p201 (henceforth just Quirk) would classify, according to a complex verb tree, as: Dynmamic > Durative > Conclusive > Agentive > Accomplishment.
One of the verbs that Quirk lists as falling into the above category is write. An example of write as a conclusive/accomplishment (using one of Swan's the oldest/first/only, etc constructions) is:
- Matt was the only child to write a 'thank you' letter (i.e. conclude or accomplish the action of writing it).
Swan's sentence Who was the first person to climb Everest without oxygen? will most likely be similarly interpreted as the accomplishment of getting to the top of the mountain.
These two sentences can be expanded to use the past simple in a relative clause:
- Matt was the only child who wrote a 'thank you' letter.
- Who was the first person who climbed Everest without oxygen?
But Quirk also lists write in another category, namely: Dynamic > Durative > Nonconclusive > Agentive > Activities.
An example of write in this category is:
- Matt was the only child writing at the end of the test (i.e. the focus is on the nonconclusive nature of an action in progress).
Similarly, it is possible to imagine a context using Swan's the first person + climb example where the focus is on the activity rather than the accomplishment. For example, describing an obstacle race:
- Mae was the first person climbing the wall, but Ximena was first over it.
These two sentences can be expanded as:
- Matt was the only child who was writing at the end of the test.
- Mae was the first person who was climbing the wall, but Ximena was first over it.
Another verb that falls into both the conclusive/accomplishment and the nonconclusive activity categories is read:
- Emiko was the first student to read Great Expectations (i.e. accomplish the task, reading it to the end).
- Emiko was the first student reading at the beginning of class (i.e. to get out her book and start reading).
So, in summary, the answer to the question why is it that you can't use '-ing' instead of 'to infinitive' in the following sentences? is:
You can, for climb and other verbs which fall into both the two categories listed by Quirk, where the focus is respectively on the conclusive/accomplishment nature of the verb in context or on its nonconclusive/activity nature.
Further thoughts
The OP states of the two trial texts that use the -ing form and to-infinitive form of stem respectively: 'both versions seem to be well-formed'. This seems to be the case for me too. However, it raises an interesting issue.
If we expand the -ing form in This is the first trial stemming from the investigation of Robert S. Mueller in a similar way as above, we get:
*This is the first trial that is stemming from the investigation of Robert S. Mueller.
But stem in this sense of the word is a non-progressive verb, so the expansion results in an ungrammaticality. In other words, This is the first trial stemming from the investigation cannot be regarded as a reduction in the same way as the first person climbing is a reduction from the person person who is/was climbing.
There is a discussion of this phenomenon in the chapter on Relative Clauses in The Grammar Book: An ESL / EFL Teacher's Course (p597):
Participles that do not derive from relative clauses
Our discussion of this topic is incomplete unless we point out that there are also adjectival -ing participles that could not possibly be accounted for via the pronoun + be deletion rule. Recall that verbs which are stative rather than dynamic rarely take the progressive aspect, yet stative verbs can and do occur as adjectival participles:
- Max built an additional room, measuring 12 by 12 feet.
This -ing particple cannot be derived from a reduced relative clause:
- *Max built an additional room, which is measuring 12 by 12 feet.
How to account for the structure of such adjectival participles remains an unsolved problem in need of further research.
Note: that The Cambridge Grammar Of The English Language (CGEL, p446) does not use the term reduced relative clause for -ing constructions such as above. They are classified under Post head modifiers > non-finite gerund-participial clauses. Example: People living near the site will be seriously disadvantaged.
And one last point, the CGEL (p118) has a simplified version of the Quirk's verb classification tree mentioned above, but includes the terms telic and atelic as follows: _ Accomplishments [telic] and Activities [atelic]. There is a discussion of these terms on ThoughtCo: telicity (verbs).
Solution 2:
Your last examples happen to use an expression that almost always is followed by an infinitive form.
The phrase "first person" in this syntax suggests that the following clause will describe a completed action. While a present participle could conceivably be used and understood, sticking to the infinitive both fits common usage and avoids complications from suggesting a continuous or progressive sense. For example, "the first person climbing Everest" might make sense in some contexts, like if that person were climbing Everest at the moment the statement was made, or if reference were being made to that moment of climbing in the past. Otherwise the participle form is context-locked in a way the to-infinitive isn't. More generally, "the first person (+infinitive)" is a common expression, and almost always takes a to-infinitive. Searches confirm how common it is. The Corpus of Contemporary American English gives 822 results for "first person to" and 8 results for "first person (-ing form of verb)." The British National Corpus gives 109 results for "first person to" and no results for "first person (-ing form of verb)."
He was the first person to climb Everest without oxygen.
This is not the same as a situation where the infinitive form and the present participle are both valid. In these situations, either form of climb is acceptable; the verb minimizes the distinction between the infinitive and the participle form such that either an atemporal sense or a continuous sense describe what's being tried or liked (see previous Stack Exchange questions 1 and 2):
He tried to climb Everest.
He tried climbing Everest.
He likes to climb Everest.
He likes climbing Everest.
So why does stemming and to stem work in the examples above? First, it's not attached to the same expression as "the first person" or some other personal form, so it need not conform to the same pattern in usage.
Second, all of your latter examples have personal subjects, and the infinitive verb describes the action that the person takes. There's nothing in the description that precludes a participle instead of an infinitive, but the infinitive may better capture the idea that the action is completed. In contrast, with "first trial," the verb form is describing something about this trial. The verb "stem," like "belong," "involve," and "pertain," primarily describes the trial's relationship to something else. These relationship verbs can appear in either infinitive or participle form. COCA confirms this, giving 8 results each for both "first trial to" and "first trial (-ing form of verb)."