
auftauchen
to appear
To suddenly and often unexpectedly become visible or appear in a place.
Nach drei Jahren ist mein verschwundener Schlüssel plötzlich wieder aufgetaucht.
After three years, my missing key suddenly appeared again.
to appear / surface
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to appear
To suddenly and often unexpectedly become visible or appear in a place.
Nach drei Jahren ist mein verschwundener Schlüssel plötzlich wieder aufgetaucht.
After three years, my missing key suddenly appeared again.

to surface
To come to the surface from the water.
Der Wal tauchte nur wenige Meter vom Boot entfernt auf.
The whale surfaced only a few meters from the boat.

to arise
To come up or become apparent, usually in reference to abstract things such as problems, questions, or ideas.
Während der Diskussion sind einige unerwartete Schwierigkeiten aufgetaucht.
During the discussion, some unexpected difficulties arose.
'Auftauchen' is a separable verb. The prefix 'auf-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Plötzlich tauchte eine alte Freundin auf der Party auf.
Suddenly an old friend appeared at the party.
The word consists of 'auf' and 'tauchen' (to dive). The literal meaning is 'to come to the surface'. This idea is also used metaphorically when problems or people unexpectedly come 'to the surface' of awareness.
Der Taucher musste langsam wieder auftauchen.
The diver had to surface slowly.
Because 'auftauchen' describes a change of place or state, the perfect tense is always formed with the auxiliary verb 'sein'.
Gestern ist eine neue Frage in unserem Projekt aufgetaucht.
Yesterday a new question arose in our project.
In the abstract meaning, 'auftauchen' is often combined with problems, questions, doubts, or ideas. The subject is then usually something abstract.
Wenn neue Zweifel auftauchen, sollten wir darüber sprechen.
If new doubts arise, we should talk about them.
to arise
When referring to a new problem, both words can fit. „Entstehen“ says that the problem was newly formed or caused, whereas „auftauchen“ emphasizes that it becomes visible or noticeable without specifying how it originated. Use „entstehen“ when focusing on the cause and „auftauchen“ when focusing on noticing it later.

Nach dem Update tauchte ein neues Problem auf.
A new problem appeared after the update.
Durch den Fehler entstand ein neues Problem.
The mistake caused a new problem to arise.