Presence

Kiddushin 71B.

Rashi, s.v. "Until the River Azak..."

From the context it appears that Bavel is between two great rivers, Tigris and Euphrates; it is found between them, one from the west, the other from the east, and [the rivers] flow from south to north, and the end of the Euphrates empties into the Tigris. All this can be learned from: "The Land of Israel is south of Bavel, as it says, 'From the north will evil will come forth,'" meaning Bavel is in the north, the Euphrates descends from the Land of Israel to Bavel...

Tosofos, s.v. "Until where is Bavel?"

Rabbenu Tam explains that the Euphrates flows from north to south, since the Euphrates comes, "from the east of Eden," and Gan Eden is in the northern part of the world, while the Land of Israel is in the south. The Euphrates begins in Eden, and flows from north to south.

This exchange is interesting for a number of reasons. First off, as both Rashi and Rabbenu Tam are basing their geological estimations on statements of Chazal, it appears neither of them had access to a map of the region (and, although neither of them were exactly correct, R. Tam was more correct; the right answer is south-east). Rashi bases his position on the fact that Israel is called "higher than all other lands," a statement that is certainly meant to be taken in a spiritual sense, not a topographic one. R. Tam, it would appear, understood this to be a figurative statement (unless he felt water could flow uphill), instead basing his estimation on the purported location of Gan Eden and the text from Genesis 2.

From a halachic perspective, which direction the Tigris and the Euphrates actually flow makes little difference. This also gives you a good idea of the state of science/geography/cartogrophy available in Rashi's time (unless the information was in fact available, but was not relied upon), as well as indicating that the Rishonim took a hyper-literal interpretation of not only the text of Genesis 2, but many ancillary statements of Chazal.