Sunt qui putent forum esse scholam viventem, in qua pueri et puellae non minus quam in libris discant.

This is a very common Latin pattern: sunt qui ... literally means there are people who ... or there are those who ....

So Sunt qui putent ... means something like:

• There are people who think ...
• or more literally, There are those who would think ...

Latin often uses sum + a relative clause this way instead of a simple noun like nonnulli.

Because this is a relative clause of characteristic.

In English, we often just say there are people who think. In Latin, when the antecedent is indefinite like there are people who..., the relative clause often uses the subjunctive.

So:

• sunt qui putant = there are people who think
• sunt qui putent = there are the sort of people who think / there are people who would think

The difference is subtle, but the subjunctive is very idiomatic here.

Qui is a relative pronoun, nominative plural masculine.

It refers back to an understood idea like people or those after sunt:

• sunt qui = there are those who...

Even if the group is mixed, Latin often uses the masculine plural as the default form.

This is an indirect statement after putent.

After verbs of thinking, saying, knowing, and similar verbs, Latin often uses:

• accusative + infinitive

So here:

• forum = accusative subject of the indirect statement
• esse = infinitive
• scholam viventem = predicate accusative

In other words:

• putent forum esse scholam viventem
• they think that the forum is a living school

Because they are both inside the accusative-and-infinitive construction.

In an indirect statement:

• the subject becomes accusative
• the predicate noun/adjective also goes into the accusative

So:

• direct statement: forum est schola vivens
• indirect statement: putent forum esse scholam viventem

That is why both parts are accusative.

Viventem is the present participle of vivere: living.

It agrees with scholam:

• feminine
• singular
• accusative

So:

• scholam viventem = a living school

It is not vivam because that would be the adjective vivus, -a, -um (alive, living) rather than the participle. Latin can use either in some contexts, but viventem emphasizes the idea of actively living or full of life.

Also note that viventem belongs to the 3rd declension participial pattern, so the accusative singular feminine is -em, not -am.

Qua refers to scholam, not to forum.

Why?

• scholam is feminine singular
• qua is feminine singular
• forum is neuter, so it would require quo

So:

• in qua = in which
• and it refers to the school

The sense is: a living school, in which boys and girls learn...

The simplest explanation is that this clause also describes the kind of school being talked about:

• scholam viventem, in qua ... discant
• a living school, one in which ... boys and girls learn

So again, Latin often uses the subjunctive in a relative clause of characteristic.

You can also say that the whole clause is dependent on reported thought after putent, which makes the subjunctive feel even more natural. But for a learner, the key idea is:

• in qua ... discant = in which ... would learn / learn

Non minus quam means no less than.

So:

• non minus quam in libris discant
• they learn no less than in books

It is a comparison:

• non minus = not less
• quam = than

So the children learn in the forum just as truly, or just as much, as they do in books.

Literally, in libris means in books.

In English we might more naturally say:

• from books
• through books
• in books

Latin often uses in with the ablative to express the setting or medium in which something is found or learned. So in libris discere can mean learning from what is contained in books.

Because predicate nouns do not have to match in gender; they match in case, not necessarily in gender.

Here:

• forum is neuter because that is just the gender of the noun forum
• schola is feminine because that is just the gender of the noun schola

Latin is perfectly happy to say that one thing is another even if the two nouns have different genders. The important thing is that, in this construction, both are accusative:

• forum ... scholam viventem

Yes, Latin sometimes can use ubi for where, but in qua is more tightly connected to the noun scholam.

Compare:

• scholam, in qua discant = a school in which they learn
• scholam, ubi discant = also possible in sense, but less explicitly tied to the noun by agreement

Using in qua makes the relationship especially clear: it is the school in which they learn.

The main verb is sunt.

Everything after it explains who exists:

• Sunt = There are
• qui putent ... = those who think...

So the skeleton of the sentence is:

• Sunt qui putent
• There are those who think

Then Latin adds what they think:

• forum esse scholam viventem
• that the forum is a living school

And then it further describes that school:

• in qua pueri et puellae non minus quam in libris discant