"यदम्बा तातो वा द्वयमिदमगादेकतनुतां
तदर्धं चार्धं च क्व नु गतमथार्यः कथयतु" ।
जगत्तत्तज्जातं सकलनरनारीमय"मिति
प्रतीतिं कुर्वाणो जयति शिखिभर्तुर्गजमुखः ॥ (By śrī Maṇḍana kavi)
"yadambā tātō vā dvayamidamagādēkatanutāṁ
tadardhaṁ cārdhaṁ ca kva nu gatamathāryaḥ kathayatu" |
jagattattajjātaṁ sakalanaranārīmaya"miti
pratītiṁ kurvāṇō jayati śikhibharturgajamukhaḥ ||

Once Kārtikēya approached His brother Buddhinātha, the possessor of the greatest intellect in the Cosmos, and asked reverently:

“Arya! I know that when our parents became the arddhanārīśvara mūrti, one half of our Father joined with one half of our Mother. I know half plus half makes one. But there is a puzzle there: what happened to the halves which were left over from the union ? Did those halves also conjoin and form a second arddhanārīśvara mūrti ? If they did, where is that Divine Form ?”

Gaṇēśa simply smiled and gestured to His Younger Brother to follow Him,

They walked in silence and Gaṇēśa led Kārtikēya to the highest point on Mount Kailāsa. From there they could view the whole Cosmos in one panoramic sweep.

The duo saw all the beings in the world, including Men and Women.

Gaṇēśa said, “Do you see all the Male Beings and beside them all the Female Beings ? All the Females Beings are the manifestations of the one left over half of our dear Mother, Goddess Pārvatī and all the Male Beings are the manifestations of the left over half of our dear Father, Paramēśvara.”

Kārtikēya stood there with His tender palms joined together in praise of the grand sight of Pārvatī-Paramēśvara in the Cosmic Expanse and in awe of the peerless Pratibhā śaktī of His own Brother Buddhinātha who could solve any puzzle presented to Him!

Let us also join our palms in praise of the creator of this Muktakaṁ — śrī Maṇḍana kavi who ends the poem by saying, “Glory to the Elephant-faced Deity who created true understanding (प्रतीति = pratīti) in the Lord of the Peacock!”

Note : Relevant Pics