Learn Hardcore Esperanto: Ŝi volas, ke li lernu mem solvi la problemon. - She wants him to learn to solve the problem by himself.

If you said “Ŝi volas, ke li lernas”, it would sound like a mismatch: volas (want) expresses a wish, but lernas (simple present) states a fact. It would be more like “She wants that he is learning…”, which is not how Esperanto normally works.

So: volas, ke … lernu is the standard pattern for “wants him to learn / wants that he learn”.

What exactly does the -u ending on “lernu” mean?

The -u ending is called the volitive (often also grouped with the “imperative” forms). It expresses:

a command:
- Lernu! = Learn!
a wish/desire in a subordinate clause:
- Ŝi volas, ke li lernu. = She wants him to learn.
something hypothetical or not yet real, often depending on another verb or condition.

It does not have a tense by itself (no present/past/future built into it); the time is understood from context or from the main verb. In our sentence, volas is in the present, so lernu describes something she wants to happen from now on or in the future.

Why do we need the word “ke” here? Could we say “Ŝi volas li lernu…”?

You need ke. It introduces a content clause (a “that”-clause):

Ŝi volas, ke li lernu…
literally: She wants that he learn…

In Esperanto, a clause like “that he learn to solve the problem” is normally introduced by ke. Just saying “Ŝi volas li lernu…” is incorrect standard Esperanto.

Compare:

Mi scias, ke li venos. = I know that he will come.
Ŝi esperas, ke vi sukcesos. = She hopes that you will succeed.

So the pattern is:
[verb of knowing/wanting/saying/etc.] + ke + [finite clause].

Why is there a comma before “ke” in “Ŝi volas, ke li lernu…”?

Esperanto punctuation usually puts a comma before “ke” when “ke” begins a full subordinate clause that depends on the previous verb:

Ŝi diris, ke li venos.
Mi pensas, ke tio estas vera.

It marks the boundary between the main clause (Ŝi volas) and the subordinate clause (ke li lernu mem solvi la problemon).

This comma is standard and recommended, though you will sometimes see it omitted in very short sentences. In careful writing, it’s good practice to keep it.

Why is it “lernu … solvi” and not “lernu … solvas”?

Because after lerni (to learn), the next verb is normally in the infinitive (-i form):

lerni legi = to learn to read
lerni naĝi = to learn to swim
lerni solvi la problemon = to learn to solve the problem

In our sentence, the structure is:

ke li lernu (that he learn)
solvi la problemon (to solve the problem)

So solvi is an infinitive governed by lerni. Two finite verbs like “lernu solvas” in a simple row do not work in Esperanto; only one of them should be finite in that clause, the other (if it’s just “what he’s learning to do”) will be infinitive.

Could we say “ke li lerni mem solvi la problemon” (with lerni instead of lernu)?

No. After ke, you need a finite verb (with a personal ending: -as, -is, -os, -us, -u). The infinitive lerni cannot be used as the main verb of that clause.

Correct: ke li lernu mem solvi la problemon
Incorrect: ke li lerni mem solvi la problemon

Think of ke li lernu as a normal clause: li lernu has a subject (li) and a finite verb (lernu). An infinitive (lerni) doesn’t fill that role.

What exactly does “mem” mean here? Is it like “himself” or “by himself”?

Mem is an emphasizing word roughly meaning “himself / herself / itself / oneself / on one’s own”, depending on the context. It doesn’t replace a pronoun; it adds emphasis to it or to the action.

In this sentence, mem expresses the idea of doing it on his own / independently. The basic meaning:

Ŝi volas, ke li lernu solvi la problemon.
She wants him to learn to solve the problem.
Ŝi volas, ke li lernu mem solvi la problemon.
She wants him to learn to solve the problem *by himself / on his own.*

Without mem, there’s no particular emphasis on independence. With mem, it suggests she doesn’t want others to solve it for him or to rely too much on help; she wants him to manage it himself.

Can “mem” move to other positions like “ke li mem lernu solvi la problemon” or “ke li lernu solvi la problemon mem”? Does the meaning change?

Yes, mem is somewhat flexible, and its position slightly changes the nuance.

Very roughly:

ke li mem lernu solvi la problemon
Focus: he himself (and not someone else) should learn to solve the problem.
= She wants *him himself to learn to solve the problem.*
ke li lernu mem solvi la problemon (your original)
Focus: the process of learning to solve it by himself.
= She wants him to learn to solve the problem *by himself.*
ke li lernu solvi la problemon mem
Focus: he should solve the problem himself, without help.
The nuance is more on the solving than on the learning.

In practice, for many speakers these differences are subtle and can overlap, but:

“li mem …” usually emphasizes who does it.
“… mem” after the verb/phrase often emphasizes doing it without help / independently.

All of these word orders are grammatically possible, but “li mem lernu solvi la problemon” is a very natural way to say “he himself should learn to solve the problem”, and “… solvi la problemon mem” is very natural for “to solve the problem himself”.

Why do we say “la problemon” and not just “problemon” or “la problemo”?

There are two separate things here:

The article “la”
- la problemo = the problem (a specific one, known in the context)
  Here, the speaker is thinking of a particular problem.
The accusative -n: “problemon”
- problemon is the direct object of solvi (to solve).
  In Esperanto, direct objects of verbs normally take -n:
- Mi vidas la domon. = I see the house.
- Li solvas la problemon. = He solves the problem.

So we combine them:

la (the)
problem- (problem)
-o (noun ending)
-n (accusative object)

→ la problemon = the problem as a direct object.

You could in theory omit la in a very general statement (“lerni solvi problemojn” = learn to solve problems in general), but then the meaning becomes non‑specific and plural or generic. Here, la problemon is a particular, concrete problem.

Why is “problemon” in the accusative if it comes after the infinitive “solvi”, not directly after a normal finite verb?

Even though solvi is an infinitive, it is still a real verb that governs its own objects. Verbs in Esperanto take objects whether they are finite (-as, -is, -os, -us, -u) or infinitive (-i).

Compare:

Li volas solvi la problemon.
→ solvi takes la problemon as its object.
Li komencis legi la libron.
→ legi takes la libron as its object.

In your sentence:

lernu [solvi la problemon]

The object la problemon belongs to solvi, so it must be in the accusative. The fact that solvi is infinitive doesn’t change that.

Could we say “Ŝi volas, ke li mem solvu la problemon” instead? How would the meaning change compared to “lernu mem solvi la problemon”?

Yes, that’s a different but related sentence.

Ŝi volas, ke li lernu mem solvi la problemon.
Focus: she wants him to learn (acquire the skill) to solve the problem by himself.
Ŝi volas, ke li mem solvu la problemon.
Focus: she wants him to actually solve the problem himself (do it now / in this situation).

So:

lernu solvi → talks about the learning process.
solvu alone → talks about the act of solving.

Both use the -u form (volitive), but with different verbs: lernu (learn) vs solvu (solve).

Can this be translated literally as “She wants that he learn to solve the problem by himself”? Is that how “volas, ke … lernu” usually works?

Yes, a fairly literal translation is:

Ŝi volas, ke li lernu mem solvi la problemon.
≈ She wants that he learn to solve the problem by himself.

In English, we normally say “She wants him to learn…” rather than “She wants that he learn…”, but Esperanto keeps the “that + clause” structure:

Mi volas, ke vi komprenu. = I want you to understand.
Ni volas, ke ili venu frue. = We want them to come early.

So the basic pattern “volas, ke [subject] [verb in -u] …” corresponds to English “want [someone] to [do something]” or “want that [someone] [do something]”. The English structure changes; the Esperanto one is quite regular.

If “lernu” has no tense, how do we know when he is supposed to learn to solve the problem?

The -u form (like lernu) itself does not mark tense. Its time reference comes from:

The main verb:
- Ŝi volas, ke li lernu… → the wanting is now; the learning is something she wants to happen now or in the (near) future.
- Ŝi volis, ke li lernu… → she wanted it (in the past); the learning is something she wished for at that time.
The context of the conversation.

So lernu just says “should learn / is to learn”, and the actual time is understood from volas / volis / volos or from the situation being described.