Learn Hardcore German: Wir haben uns im Park nur durch einen Zufall getroffen und seitdem viel Gemeinsames entdeckt. - We met in the park only by chance and have since discovered many things in common.

sein is mainly used with:
- verbs of motion or change of state (e.g. gehen, kommen, sterben)
- and a few others like sein, bleiben, werden.
haben is used with:
- most transitive verbs (verbs that take a direct object)
- many intransitive verbs too.

treffen is a transitive verb: you treffen someone (jemanden treffen). So it always forms the perfect with haben:

Ich habe ihn zufällig getroffen.
Wir haben uns im Park getroffen.

Using sind getroffen would be wrong here.

What does uns do in wir haben uns getroffen? Why not just wir haben getroffen?

treffen normally needs an object: jemanden treffen (to meet someone / to hit someone).

Wir haben getroffen is incomplete: We met/hit... whom?
In wir haben uns getroffen, uns is a reflexive pronoun used with plural subjects to mean each other.

So:

Wir haben uns im Park getroffen.
= We met each other in the park.

This is similar to English each other, but German uses a reflexive pronoun (uns, euch, sich) instead.

You could also say:

Wir haben einander im Park getroffen. (more formal/literary)

But in everyday language uns getroffen is the normal phrase for met each other.

Why is it im Park and not in den Park?

The difference is:

im Park = in dem Park (dative) → location (where?)
in den Park (accusative) → direction (where to?)

German uses:

dative for location (static): wo?
accusative for movement into something: wohin?

In the sentence:

Wir haben uns im Park getroffen.
→ The meeting happened in the park (location) → dative im (in dem) Park.

If you wanted to say We went to the park, then you’d say:

Wir sind in den Park gegangen. (movement → accusative)

Why is it durch einen Zufall and not just durch Zufall or zufällig?

All three are possible in German, but they differ slightly in style and structure:

durch einen Zufall
- literal: through a coincidence
- durch
  - accusative (einen Zufall, masculine)
- sounds a bit more vivid/literal, as if one specific coincidence caused it.
durch Zufall
- more idiomatic expression: by chance
- also very common and natural.
zufällig
- adverb: accidentally, by chance
- e.g. Wir haben uns zufällig im Park getroffen.

Your sentence:

Wir haben uns im Park nur durch einen Zufall getroffen...

could also be said as:

Wir haben uns im Park nur durch Zufall getroffen...
Wir haben uns nur zufällig im Park getroffen...

All are correct; the choice is mostly stylistic. The version with einen Zufall is slightly more concrete and emphatic.

What does nur add in nur durch einen Zufall? Could it be somewhere else in the sentence?

nur means only / just, and here it emphasizes that it was purely a coincidence:

nur durch einen Zufall = only by chance, just by coincidence.

German word order allows some flexibility. You could say:

Wir haben uns nur durch einen Zufall im Park getroffen.
Wir haben uns im Park nur durch einen Zufall getroffen.

Both are correct; the difference in meaning is minimal here. nur usually stands right before what it limits:

nur durch einen Zufall (only by a coincidence)
nur wir haben uns getroffen (only we met)
wir haben uns nur getroffen (we did nothing more than meet)

In your sentence, nur clearly belongs with durch einen Zufall.

Why is there no verb in the second part: ...und seitdem viel Gemeinsames entdeckt? Shouldn’t it be und haben seitdem viel Gemeinsames entdeckt?

Grammatically, the “full” version would be:

Wir haben uns im Park nur durch einen Zufall getroffen und haben seitdem viel Gemeinsames entdeckt.

In your sentence, the second “haben” is simply left out because it’s the same auxiliary as in the first clause. This is a common kind of ellipsis in coordinated clauses in German (and in English too):

English: We met by chance and (have) discovered many things in common since then.
German: Wir haben uns ... getroffen und (haben) seitdem viel Gemeinsames entdeckt.

So the structure is:

[Wir haben] uns ... getroffen und [haben] seitdem viel Gemeinsames entdeckt.

The repeated haben is understood and doesn’t need to be said.
Adding it (... und haben seitdem ...) is also correct, just a bit more explicit.

Is it possible (or better) to write ... und haben seitdem viel Gemeinsames entdeckt?

Yes, that’s perfectly correct:

Wir haben uns im Park nur durch einen Zufall getroffen und haben seitdem viel Gemeinsames entdeckt.

Both versions are fine:

With repeated haben: slightly more explicit, maybe a bit clearer for learners.
Without repeated haben: a bit more compact and very natural in fluent speech and writing.

There is no change in meaning; it’s just a stylistic choice.

Why is the perfect tense used (wir haben uns getroffen, wir haben ... entdeckt) instead of the simple past?

In spoken German, the Perfekt (present perfect) is the normal tense for past events in everyday conversation:

Wir haben uns im Park getroffen.
Wir haben seitdem viel Gemeinsames entdeckt.

The Präteritum (simple past) is used more in:

written narratives (books, reports)
and with a few very common verbs even in speech (war, hatte, konnte, musste, etc.).

You could say in written style:

Wir trafen uns im Park nur durch einen Zufall und entdeckten seitdem viel Gemeinsames.

But in normal conversation, Perfekt is far more natural:

Wir haben uns ... getroffen und seitdem viel Gemeinsames entdeckt.

What exactly is seitdem doing here? How is it different from seit or dann?

seitdem in this sentence is an adverb meaning since then:

... und seitdem viel Gemeinsames entdeckt.
→ ... and (have) discovered many things in common since then.

Compare:

seitdem = since then (adverb of time)
- Wir haben uns kennengelernt, und seitdem telefonieren wir jeden Tag.
seit
- time expression = since (preposition)
- Wir kennen uns seit 2020. (since 2020)
seitdem can also be a subordinating conjunction:
- Seitdem wir uns kennengelernt haben, telefonieren wir jeden Tag.
dann = then (at that time / afterwards), not since then:
- Wir haben uns getroffen, und dann sind wir ins Kino gegangen.

So here, seitdem marks the period starting from the meeting up to now.

Why is Gemeinsames capitalized?

Gemeinsames is originally an adjective (gemeinsam = common, shared), but here it is used as a noun:

viel Gemeinsames entdecken
literally: to discover much that is common
natural English: to discover many things in common / a lot in common.

In German, when an adjective is used as a noun, it is:

capitalized
and gets adjective endings depending on case, gender, and number.

So:

das Gemeinsame = the thing(s) that are common
viel Gemeinsames = much that is common / a lot in common

That’s why Gemeinsames has a capital G.

Why is it viel Gemeinsames and not viele Gemeinsame?

Here, viel is used because the idea is more mass/abstract (a lot of “commonness”) rather than counting individual items:

viel Gemeinsames ≈ a lot in common (uncountable idea)
viele gemeinsame Dinge = many common things (countable plural noun)

Both structures are correct, but they have slightly different flavors:

Wir haben seitdem viel Gemeinsames entdeckt.
→ stylistically smooth, slightly abstract: We’ve discovered we have a lot in common.
Wir haben seitdem viele gemeinsame Interessen entdeckt.
→ concrete: We’ve discovered many common interests.

viele Gemeinsame would sound wrong here because Gemeinsame isn’t used as a regular plural noun in this context.

What case and ending does Gemeinsames have in viel Gemeinsames entdeckt?

Gemeinsames here is:

accusative singular
neuter
strong declension (no article before it, only viel).

Why?

It is the direct object of entdeckt → accusative.
Abstract “something common” is treated as neuter: das Gemeinsame.
With no article (like das, ein, kein) and just a quantity word like viel, the adjective takes strong endings.
For neuter accusative singular, the strong ending is -es:
- etwas Neues (something new)
- nichts Interessantes (nothing interesting)
- viel Gemeinsames (a lot in common)

So Gemeinsames is: neuter, accusative, singular, strong ending -es.

Could you also say viele gemeinsame Dinge entdeckt instead of viel Gemeinsames entdeckt?

Yes, and it’s very natural:

Wir haben seitdem viele gemeinsame Dinge entdeckt.
Wir haben seitdem viele gemeinsame Interessen entdeckt.

These are a bit more concrete: you’re explicitly talking about things or interests.

viel Gemeinsames is a bit more compact and abstract, like:

We’ve discovered we have a lot in common.

Both are idiomatic; the original sentence just chooses the more compact, adjective-noun form.