Grímnismal 31 informs us that the world-tree Yggdrasil is fed by three roots:

Historically, this verse has been interpreted in three ways:

1. Modern scholars read this verse literally. Yet, doing so has logical consequences that no one seems to consider. A literal reading does not agree with Snorri's text. Reading the verse literally places one root in the underworld (Hel), one in Jotunheim (with frost-giants) and one on earth/Midgard (with human men). Jotunheim lies on the outskirts of Midgard. That leaves no root in heaven, as Snorri says.
 
2. Snorri's interpretation of this verse, contained in Gylfaginning 15, takes the "human men" as the Aesir, Odin's people, which is consistent with his portrayal of the gods as human beings from Asia. Snorri himself places Asgard in modern day Turkey. But surely a heathen poet would not call the gods human men (cp. Sigurdrífumál 18), so that cannot be the meaning of the heathen verse. Snorri's view expressed in the Prologue to Gylfaginning conforms to a Christian understanding of the universe as three-tiered structure consisting of heaven, earth and hell.
 
3. The genuine heathen perspective placed all three roots in the underworld. In other words, Mimir's and Urd's well were located in the oldest part of creation, not in Jotunheim and in Heaven (respectively), as Snorri says. We find ample evidence from the Eddic and skaldic poems in support of this view. Accordingly, Urd's well is located in the warm southern part of the underworld. Mimir's well is located in the center of the lower world ("where Ginnungagap once was", Gylf 15) and Hvergelmir is located in Niflhel, the cold northern part of Hel.

THE SQUARE ROOT OF THREE

Surely no one will be surprised if I bring into play a fourth possibility along with the three summarized above. It is my belief that:

4. All three roots and ways can be found in heaven.

Why do I think so?

If, for the moment, we look beyond the roots and focus on the ways, what  three 'ways' might be meant? Looking into the Phainomena of Aratus we find 5 celestial paths described:

The Milky Way   The Tropic of Cancer   The Tropic of Capricorn   The Celestial Equator

To get an impression of how these circles were depicted in Greek and Roman times, it's interesting to look at the images on the Farnese globe (left) and the Mainz globe (right), and ask,  "Do any three of these circles fit  the description of Grimnismal 31?"

The stanza tells us that Hel dwells under one way root. I have previously identified Hel as the constellation Lyra with the bright blue star Vega. Lyra is located next to the Milky Way and nearly touches the Tropic of Cancer. Now compare this stanza with Snorri's version. Surprisingly he connects the way or root with Niflheim and Nidhöggr instead of Hel in Gylfaginning 15: .

I have already identified Nidhöggr with Cygnus, and Niflheim in general with the region around Sagitta, a lost constellation known as the 'Deadman' surrounded by many raptors. Indeed the beak of Cygnus also touches  the Tropic of Cancer in the area of the Milky Way directly next to Lyra.

Thor's many conflicts with the giants point to a location for 'berg-risar' (mountain-giants) and 'hrim-thursar' (frost-giants)  in the southern regions of the Milky Way, i.e. Sagittarius, Scorpio and Centaur. In this region we find the Tropic of Capricorn.

So, what about the third way connected with mankind  in Grímnismál and  with the Æsir in Gylfaginning? I assume this is the celestial equator touching the legs of the constellation Taurus (which I identify with Thor, along with and his hammer Mjöllnir found in the Pleiades.)

Surprisingly this would mean that we find three parallel (!) ways - I admit this sounds a little strange, however, it would explain why the three ways are said to be afarbreitt, 'far apart' as the two tropics are 23.5° away from the celestial equator. They are connected by the circle of the Milky Way, which has been brought into connection with the ash Yggdrasil by many previous scholars.

Personally, I'm convinced that the three 'ways' are described in Völuspá in much more detail: particularly in Dvergatal, the so-called 'dwarf-list'. I will present some decodings in another essay.