Ganesha’s relationship with his wives
The marital status of Lord Ganesha is uncertain based on mythological texts. Lord Ganesha is the Lord of the Brahmins and hence by this virtue a celibate. The vedic mantra- Aum, is believed to be the mantra to lead Brahmins and is synonymous with Lord Ganesha. His celibacy is more commonly known in the South of India (states like Tamil Nadu, Karnataka, Andhra Pradesh and Kerela). Since Lord Ganesha was created out of Goddess Parvati alone and not Lord Shiva, he was born out of the female desire to procreate. Hence the relationship of Lord Ganesha with his mother is believed to be unique and special. This devotion and respect is the reason Lord Ganesha is believed to have never found a woman as perfect as his mother.
However, particularly in northern India, Ganesha is believed to have consorts. He is believed to be married to Brahma’s daughter Buddhi and Siddhi. “Buddhi” means intellect and “Siddhi” means spiritual power. Since Lord Ganesha is believed to be the Lord of wisdom and spiritual knowledge, the consorts are befitting.
The scriptures that are dedicated to Lord Ganesha (the Ganesha Purana and the Mudgala Purana) depict the presence of Siddhi and Buddhi. According to the Ganesha Purana Lord Brahma was performing a ritual in honour of Lord Ganesha and offered his prayers to him. Two of the offerings were his daughters, Buddhi and Siddhi that Lord Ganesha accepted graciously as his wives. Various deities offered gifts to Lord Ganesha in his honour but Lord Brahma offered what was born from his mind. It is also mentioned in the Ganesha Purana that Narada (the son of Brahmin) suggested the nuptials of Ganesha with Riddhi and Siddhi, to Brahma. Some ancient texts indicate that Siddhi and Riddhi are avatars of Shakti, but the Matsayapurana contradicts this claim. The Brahmavaivartapurana also mentions Lord Ganesha’s marriage to Pushti (another name for Siddhi).
Siddhi and Buddhi are known as Siddhi and Riddhi in Shiva Purana. As per the Shiva Purana, Lord Ganesha won his consorts as a prize during a race with his elder brother Skanda (Lord Kartikeyan). The race was declared by their mother Parvati who promised the winner an auspicious marriage that will bring him prosperity. The race was to travel the universe three times. Skanda mounted on his peacock to encircle the world. Lord Ganesha went around his parents instead. For his guile, Lord Ganesha was married to Riddhi and Siddhi.
The consorts of Lord Ganesha are an extension of his existing virtues and accentuate the same. Riddhi accentuates prosperity and intellect and Siddhi highlights spiritual power of Lord Ganesha. It is believed that whoever receives the blessings of Lord Ganesha is also blessed by his wives. Hence one may say that Lord Ganesha’s consorts complete him.