Learn Hardcore Icelandic: Stundum læt ég símann hringja án þess að svara. - Sometimes I let the phone ring without answering.

Læt is the 1st person singular present tense of the verb láta, which among other meanings works as a causative verb: “to let, to allow, to cause (something to happen)”.
In læt ég símann hringja, it literally means “I let the phone ring”.
The structure is láta + object (accusative) + infinitive, similar to English “let someone/something do something”.

Why is símann in the accusative case here?

With láta in this causative construction, the thing that is being “made to do something” is put in the accusative.
So sími (nominative) becomes símann (accusative singular masculine):
(ég) læt + símann + hringja → I let the phone ring.
The phone is the direct object of láta.

Why is hringja in the infinitive and not conjugated, like hringir?

After this causative pattern láta + object + verb, the second verb stays in the infinitive.
So you say læt ég símann hringja (I let the phone ring), not læt ég símann hringir.
This is parallel to English “let the phone ring”, where ring is also in a base form, not rings.

What does the phrase án þess að svara mean structurally?

Literally, án þess að svara is something like “without that to answer”, but idiomatically it just means “without answering”.
It is a common pattern: án þess að + infinitive = without doing (something).
So án þess að svara = without answering, án þess að borða = without eating, etc.

Why do we need þess in án þess að svara? Why not just án að svara?

The preposition án (“without”) normally takes a genitive object.
Here, þess is a neuter genitive pronoun that fills that slot, and together with að + infinitive it forms a fixed construction: án þess að + infinitive.
You generally cannot drop þess; án að svara is ungrammatical in standard Icelandic.

Why is svara alone here? Shouldn’t it be svara símanum or something like that?

The verb svara (“to answer, respond”) normally takes a dative object (for example, svara honum = “answer him”).
In this sentence, the object is understood from context (answer the call / the phone), so it is left out: just án þess að svara.
That is very natural in Icelandic when the object is obvious and not needed for clarity.

What is the difference between síminn and símann?

Both forms come from the noun sími (“phone”).

síminn is nominative singular definite (“the phone” as the subject).
símann is accusative singular definite (“the phone” as a direct object).
Because of læt (from láta), the noun must be in the accusative, so we get símann.

Why is stundum placed at the beginning of the sentence? Could it go elsewhere?

Stundum means “sometimes” and is an adverb of frequency.
Putting it first (Stundum læt ég …) emphasizes the time/frequency and is very natural.
You can also say Ég læt stundum símann hringja án þess að svara, which is also correct; the nuance of emphasis changes slightly, but both word orders are fine.

Why is ég included? In some languages the subject pronoun can be dropped.

In modern Icelandic, subject pronouns like ég (“I”) are normally expressed, even though the verb ending already shows the person and number.
So læt ég is the standard way; læt símann hringja… without ég would sound incomplete or odd in normal speech, except in special contexts like imperatives or fragments.

Why is the verb læt in the present tense even though in English I might say “Sometimes I let the phone ring” or “Sometimes I’ll let the phone ring”?

Icelandic uses the present tense very often for general, habitual actions, just like English does with “I sometimes let…”.
So Stundum læt ég símann hringja… means “Sometimes I let the phone ring…” in a general, habitual sense.
There is no need for a future form here in Icelandic.

Is án þess að + infinitive the normal way to say “without doing X” in Icelandic?

Yes.
The standard pattern for “without doing X” is án þess að + infinitive:

án þess að borða – without eating
án þess að segja neitt – without saying anything
án þess að svara – without answering
There are other, more complex alternatives, but this is the basic and most common pattern.

Is there another common way to express the same idea as this sentence?

A very common alternative would be Stundum svara ég ekki í símann, literally “Sometimes I don’t answer the phone”.
Your original sentence Stundum læt ég símann hringja án þess að svara is a bit more vivid: it emphasizes the ringing going on and the deliberate choice to let it ring without answering.