Cum studium et disciplina simul manent, pueri celerius discunt.

Here cum is a conjunction, not a preposition. It introduces a subordinate clause: cum studium et disciplina simul manent.

In this sentence, cum means when.

A learner may know cum as with, but that is only when it is used as a preposition followed by the ablative case, as in cum amico = with a friend. That is not what is happening here.

So here:

• cum = when
• it introduces a clause with a verb: manent

Because studium et disciplina is a compound subject: zeal/application and discipline.

Even though each noun is singular by itself, together they make a plural subject, so the verb must also be plural:

• studium manet = zeal remains
• disciplina manet = discipline remains
• studium et disciplina manent = zeal and discipline remain

That is why Latin uses manent, not manet.

Because this is a straightforward temporal use of cum: when.

Latin often uses:

• cum + indicative for a simple time idea, especially when
• cum + subjunctive for other meanings such as since, although, or certain more descriptive/background clauses

Here the clause simply states the circumstance in time:

• Cum studium et disciplina simul manent = When zeal and discipline remain together...

So the indicative manent is exactly what you would expect.

Simul means together or at the same time.

It modifies the idea of manent, so the sense is that studium and disciplina are present or remain together.

So:

• studium et disciplina simul manent = zeal and discipline remain together

Latin adverbs like simul are fairly flexible in placement, but here it sits naturally near the verb it modifies.

Because pueri is the subject of discunt.

• puer = boy
• pueri can mean either boys (nominative plural) or of the boy (genitive singular), depending on context

Here it must be nominative plural, because it is the noun doing the action of discunt:

• pueri discunt = the boys learn

Celerius is the comparative adverb meaning more quickly or, in smoother English, faster.

From the adjective celer, celeris, celere = quick, Latin forms:

• positive adverb: celeriter = quickly
• comparative adverb: celerius = more quickly / faster

So:

• pueri celeriter discunt = the boys learn quickly
• pueri celerius discunt = the boys learn faster / more quickly

The sentence is using the comparative form.

Latin comparatives do not always need an explicit second term.

So celerius can mean:

• more quickly
• faster

without saying exactly than what.

In context, it means something like:

• the boys learn more quickly
• the boys learn faster [than they otherwise would]

This is common in both Latin and English.

Both are present indicative active.

• manent = they remain
• discunt = they learn

This gives the sentence a general or regular meaning, not just a one-time event. It sounds like a general truth:

• When zeal and discipline remain together, boys learn faster.

They come from these dictionary forms:

• manent ← maneo, manere, mansi, mansum = remain
• discunt ← disco, discere, didici = learn

A beginner may also notice that they belong to different conjugations:

• maneo is 2nd conjugation
• disco is 3rd conjugation

That helps explain their different endings in other forms, though here both happen to be 3rd person plural present active.

Because they are the subjects of manent.

Latin marks grammatical function through case endings. Here:

• studium = nominative singular
• disciplina = nominative singular

Together they form the compound subject:

• studium et disciplina = zeal and discipline

That is why they are nominative.

Not as much as it would be in English.

Latin word order is relatively flexible because the endings show the grammatical roles. This sentence puts the cum clause first and the main clause second:

• Cum studium et disciplina simul manent, pueri celerius discunt.

That is a very natural arrangement. But Latin could rearrange parts for emphasis without changing the basic meaning.

For example, pueri could appear earlier or simul could move, and the sentence could still be understood because the forms still show who is doing what.

In other sentences, yes. Cum can mean things like:

• when
• since
• although

But in this sentence, when is the best interpretation.

Why?

1. The clause clearly gives the circumstance under which the main action happens.
2. The verb is in the indicative, which fits a simple temporal cum well.
3. Nothing in the sentence suggests a contrast like although.

So here a learner should understand cum as when.

It is a sentence with:

• a subordinate clause introduced by cum
• a main clause

Structure:

• Cum studium et disciplina simul manent = subordinate clause
• pueri celerius discunt = main clause

So the sentence means that the action in the main clause happens under the condition or time given by the subordinate clause. Grammatically, it is a simple example of a temporal cum-clause with a present-tense main clause.