— Carl B. Boyer American mathematician 1906 - 1976
The Rainbow: From Myth to Mathematics (1959), Context: In ancient classical literature the rainbow sometimes was deified as Iris; at other times it was regarded merely as the route traversed by the messenger of Hera. The conception of the rainbow as a pathway or bridge has been widespread. For some it has been the best of all bridges, built out of three colors; for others the phrase "building on the rainbow" has meant a bootless enterprise. North American Indians were among those who thought of the rainbow as the Pathway of Souls, an interpretation found in many other places. Among the Japanese the rainbow is identified as the "Floating Bridge of Heaven"; and Hawaiian and Polynesian myths allude to the bow as the path to the upper world. In the Austrian Alps the souls of the righteous are said to ascend the bow to heaven; and in New Zealand the dead chieftains are believed to pass along it to reach their new home. In parts of France the rainbow is called the pont du St. Esprit, and in many places it is the bridge of St. Bernard or of St. Martin or of St. Peter. Basque pilgrims knew it as the 'puente de Roma'. Sometimes it is called instead the Croy de St. Denis (or of St. Leonard or of St. Bernard or of St. Martin). In Italy the name arcu de Santa Marina is relatively familiar. Associations of the rainbow and the milky way are frequent. The Arabic name for the milky way is equivalent to Gate of Heaven, and in Russia the analogous role was played by the rainbow. Elsewhere also the bow has been called the Gate of Paradise; and by some the rainbow has been thought to be a ray of light which falls on the earth when Peter opens the heavenly gate. In parts of France the rainbow is known as the porte de St. Jacques, while the milky way is called chemin de St. Jacques. In Swabia and Bavaria saints pass by the rainbow from heaven to earth; while in Polynesia this is the route of the gods themselves.
In Eddic literature the bow served as a link between the gods and man — the Bifrost bridge, guarded by Heimdel, over which the gods passed daily. At the time of the Gotterdamerung the sons of Muspell will cross the bridge and then demolish it. Sometimes also in the Eddas the rainbow is interpreted as a necklace worn by Freyja, the "necklace of the Brisings," alluded to in Beowulf; again it is the bow of Thor from which he shoots arrows at evil spirits. Among the Finns it has been an arc which hurls arrows of fire, in Mozambique it is the arm of a conquering god. In the Japanese Ko-Ji-Ki (or Records of Ancient Matters), compiled presumably in 712, the creation of the island of Onogoro is related to the rainbow. Deities, standing upon the "floating bridge of heaven," thrust down a jeweled spear into the brine and stirred with it. When the spear was withdrawn, the brine that dripped down from the end was piled up in the form of the island. In myth and legend the rainbow has been regarded variously as a harbinger of misfortune and as a sign of good luck. Some have held it to be a bad sign if the feet of the bow rest on water, whereas a rainbow arching from dry land to dry land is a good augury. Dreambooks held that when one dreams of seeing a rainbow, he will give or receive a gift according as the bow is seen in the west or the east. The Crown-prince Frederick August took it as a good omen when, upon his receiving the kingdom form Napoleon in 1806, a rainbow appeared; but others interpreted it as boding ill, a view confirmed by the war and destruction of Saxony which ensued. By many, a rainbow appearing at the birth of a child is taken to be a favorable sign; but in Slavonic accounts a glance from the fay who sits at the foot of the rainbow, combing herself, brings death.