Sorry, but there aren't a lot of VORs (effectively a VHF transmitter, with comparable range to FM radio, accepted range at cruising altitude about 130 nautical miles) up at the North Pole, nor in the middle of the ocean.

Navigation up near the pole is indeed a mathematical challenge, even to GPS (which effectively lets you work out your lat/long coordinates, but those become imprecise as they converge at the pole) and there needed to be a lot of development to validate both GPS and its predecessors like INS above about 80 degrees north. It was cracked, but it took time.

Do not confuse polar north with magnetic north in compasses, they are not at the same place and thus there always needs to be a compensating adjustment dependent on where you are, known as Magnetic Deviation. Runway headings are always given in magnetic, which is why at places like Anchorage, Alaska, where the deviation is more than 20 degrees, the runway numbers appear quite different to what you might expect looking at a correctly oriented runway diagram.

Polar navigation has always been difficult. The first such flights back in the 1950s, when celestial navigation was the main approach (ie sextant and shooting the sun or stars), had to develop special optical instruments because they spent hours in twilight with the sun just beneath the horizon, so unable to get an accurate fix on the sun, but the sky too light to see any stars. A special sextant variation and a lot of mathematics (and a full-time navigator on board) finally overcame this. SAS were the pioneers with this kit, operating DC7Cs from Copenhagen to Seatle.