Was Vipassana discovered by the Buddha (Siddhartha)? I read somewhere that samatha (and jhana) was discovered by the Buddha, but how about vipassana? Is there any evidence either way (i.e. suttas)?

The reason I'm asking is because I am more proficient at practicing vipassana meditation than samatha, but I have some doubt about vipassana itself. Perhaps, if there were some proof that this method was founded by the Buddha himself, my doubt would be gone.

Note: I would prefer answers based on Theravada suttas.
The orthodox view is that samatha meditation was not discovered by the Buddha and vipassana meditation was.

On the origins of samatha meditation:
Besides the fact that other teachers at the time of the Buddha and before were practicing what appears to be samatha and jhana, we have the fact that the Bodhisatta went into the first jhana as a young boy, and the fact that he learned jhana from two teachers before his enlightenment:

“I considered: ‘I recall that when my father the Sakyan was occupied, while I was sitting in the cool shade of a rose-apple tree, quite secluded from sensual pleasures, secluded from unwholesome states, I entered upon and abided in the first jhāna, which is accompanied by applied and sustained thought, with rapture and pleasure born of seclusion. Could that be the path to enlightenment?’ Then, following on that memory, came the realisation: ‘That is indeed the path to enlightenment.’
-- MN 36 (Bodhi, trans)

and

“I considered: ‘It was not through mere faith alone that Rāma declared: “By realising for myself with direct knowledge, I enter upon and abide in this Dhamma.” Certainly Rāma abided knowing and seeing this Dhamma.’ Then I went to Uddaka Rāmaputta and asked him: ‘Friend, in what way did Rāma declare that by realising for himself with direct knowledge he entered upon and abided in this Dhamma?ʹ In reply Uddaka Rāmaputta declared the base of neither-perception-nor-non-perception.
-- MN 26 (Bodhi, trans)

The confusion seems to stem from some poorly constructed arguments from proponents of the necessity of practicing samatha meditation that what the Bodhisatta's teachers taught was not jhana, but something else. For example:

Some might raise an objection that the teachers Alara Kalama and Udaka Ramaputta preached on Jhana, because the texts state that they taught the Bodhisatta (the Buddha-to-be) the attainment of the state of nothingness and the attainment of the state of neither perception nor non-perception. However, those two attainments could not have been connected to Jhana, because the Bodhisatta recalled, just prior to sitting under the Bodhi Tree, that the only time in his life that he had experienced any Jhana was as a young boy, while sitting under a Rose Apple Tree as his father conducted the first-ploughing ceremony (MN 36). That spontaneous early experience of Jhana had been untaught, unplanned and since forgotten. If that was the only Jhana experienced by the Bodhisatta prior to his experience under the Bodhi Tree, then the two teachers Alara Kalama and Udaka Ramaputta could not have taught Jhana at all.
http://www.dhammatalks.net/Books/Ajahn_Brahm_The_Jhanas.htm

The problem with this argument is that it misrepresents the Buddha (the part in bold). I have already quoted above what the Buddha actually said, and he is clearly not suggesting that he only experienced jhana once under the rose apple tree.
The orthodox view is that the Bodhisatta cultivated samatha meditation countless times in his past lives before finally discovering vipassana.

On the origins of vipassana meditation:
There are many references to vipassana in the suttas; the word itself is most often used in conjunction with samatha, as in:

“Bhikkhus, these two things pertain to true knowledge. What two? Serenity and insight. When serenity is developed, what benefit does one experience? The mind is developed. When the mind is developed, what benefit does one experience? Lust is abandoned. When insight is developed, what benefit does one experience? Wisdom is developed. When wisdom is developed, what benefit does one experience? Ignorance is abandoned.
-- AN 2.31 (Bodhi, trans)

(The word for serenity is samatha, and insight is vipassana)
But what is less acknowledged is the frequent use of other forms of the root √pas with the prefix vi, e.g.:

paccuppannañca yo dhammaṃ, tattha tattha vipassati.
And what ever dhammas arise in the present, one sees clearly therein.
-- MN 131

or

andhabhūto ayaṃ loko, tanukettha vipassati.
Blind is this world; few here see clearly.
-- Dhp. 174

Further, the root √pas is used together with the noun paññā in a way that leaves no doubt as to the meaning being the same as vipassana:

evametaṃ yathābhūtaṃ sammappaññāya passati
Thus one sees this as it is with right wisdom.
-- MN 35

So, the question of whether vipassana was something the Buddha taught is easy to answer.
The question of whether the Buddha discovered vipassana is a bit more complicated. What do you mean by vipassana? It is a term that means &quot;clear seeing&quot;. If, by clear seeing, you include seeing shapes in front of your eyes, or being able to understand logical arguments, or empathizing with others, or any number of things that are called clear seeing by the world, then of course no, the Buddha didn't discover that for himself.
The clear seeing that the Buddha discovered was in regards to the three characteristics and the four noble truths; this is something he discovered that had been hidden to the world, and was the core of his teaching, for example:

“sabbe saṅkhārā dukkhā”ti, yadā paññāya passati.
atha nibbindati dukkhe, esa maggo visuddhiyā.
'All formations are suffering.' When one sees this with wisdom,
Becoming thereupon disenchanted in regards to what is suffering, this is the path to purity.
-- Dhp. 278

Notice the use of a construct similar to vipassati.  As to the Buddha discovering this fact, we have:

uppādā vā, bhikkhave, tathāgatānaṃ anuppādā vā tathāgatānaṃ ṭhitāva sā dhātu dhammaṭṭhitatā dhammaniyāmatā. sabbe saṅkhārā dukkhā. taṃ tathāgato abhisambujjhati abhisameti. abhisambujjhitvā abhisametvā ācikkhati deseti paññāpeti paṭṭhapeti vivarati vibhajati uttānīkaroti — ‘sabbe saṅkhārā dukkhā’ti.
“Bhikkhus, whether Tathāgatas arise or not, there persists that law, that stableness of the Dhamma, that fixed course of the Dhamma: ‘All conditioned phenomena are suffering.’ A Tathāgata awakens to this and breaks through to it, and then he explains it, teaches it, proclaims it, establishes it, discloses it, analyzes it, and elucidates it thus: ‘All conditioned phenomena are suffering.’
-- AN 3.136 (Bodhi, trans)

And finally, in relation to seeing the four noble truths:

“‘idaṃ dukkhaṃ ariyasaccan’ti me, bhikkhave, pubbe ananussutesu dhammesu cakkhuṃ udapādi, ñāṇaṃ udapādi, paññā udapādi, vijjā udapādi, āloko udapādi.
'This is the noble truth of suffering.&quot; arose for me, bhikkhus, in regards to previously unheard dhammas; an eye arose, knowledge arose, wisdom arose, understanding arose, light arose.
-- SN. 56.11

All of this refers to the type of vipassana that the Buddha realized for himself before anyone else in the world.