Plato puts the following words in the mouth of Socrates at Theaeteus 155 d (tr. Benjamin Jowett): "I see, my dear Theaetetus, that Theodorus had a true insight into your nature when he said that you were a philosopher, for wonder is the feeling of a philosopher, and philosophy begins in wonder."
Aristotle echoes the Theaetetus passage at 982b12 of his Metaphysics: "It was their wonder, astonishment, that first led men to philosophize and still leads them." Martin Heidegger, commenting on both passages, writes in Was ist das — die Philosophie?:
Das Erstaunen ist als pathos die arche der Philosophie. Das griechische Wort arche muessen wir im vollen Sinne verstehen. Es nennt dasjenige, von woher etwas ausgeht. Aber dieses "von woher" wird im Ausgehen nicht zurueckgelassen, vielmehr wird die arche zu dem, was das Verbum archein sagt, zu solchem, was herrscht. Das pathos des Erstaunens steht nicht einfach so am Beginn der Philosophie wie z. B. der Operation des Chirurgen das Waschen der Haende voraufgeht. Das Erstaunen traegt und durchherrscht die Philosophie.
Heidegger's point is that philosophy's beginning, the pathos of astonishment, is also its principle. As such, it is not something left behind as philosophy progresses, but something that pervades and guides her at every step. This, I would add, is one of the differences between philosophy and (positive) science. The aim of the sciences is to dispel wonder, perplexity, astonishment and replace them with understanding, an understanding that makes possible the prediction and control of that which is understood. Philosophy, by contrast, not only begins in wonder but is sustained by it and never succeeds in dispelling it.
Note that Jowett translates pathos as 'feeling.' But as Heidegger remarks, passion, Leidenschaft, Gefuehlswallung, are too superficial to convey the Greek pathos. Heidegger prefers Stimmung, mood, with the connotations of Gestimmtheit, disposition, attunement, and Bestimmtheit, determination.
I would add — and I am surprised that Heidegger didn't notice this connection — that Stimmung resonates in the semantic vicinity of Bestimmung which can convey the sense of vocation, calling, as in Fichte's title Die Bestimmung des Menschen, The Vocation of Man. Accordingly, wonder is the mood or disposition of the philosopher whereby he responds to the call of Being (Ruf des Seins), thereby finding his calling, Beruf.
For further rumination: Is there any connection between wonder, Wunder, and wound? Perplexed, we are put out of commission. The daily round is suspended and things stand forth in their strangeness. The broken hammer und das Nichts.
And if philosophy begins in wonder, where does it end? End not in the sense of cessation, but in the sense of completion, perfection. Some will say that the end of philosophy's erothetic striving is in Silence.
Curously, this not what Heidegger says, He speaks of Das Ende der Philosophie und die Aufgabe des Denkens. Denken is not contemplative repose, but a further working of the fields of language. Heidegger, I would say, is in the end no mystic. But this is a huge topic best postponed.