Yajnavalkya was so confident he would win, however, he had the cows delivered to his place in advance. He had mastered the art of Kundalini Yoga, “the yoga of awareness,” and no one he felt, could challenge his knowledge and win. Of course, this made everyone all the more determined to try, but only eight sages volunteered. Gargi was one of them.
One by one the different sages lost the debate, until it was finally Gargi’s turn. Gargi forged ahead pounding him with questions one after another concerning the status of the soul and the origin of the world. Yajnavalkya answered each question masterfully. She changed her tactic and asked one final question, but her new line of questioning angered the sage. She had asked what exactly exists above Brahmalok (Hindu heaven).
He replied, “Beware Gargi! You dare to ask who is above Brahman (God). Beware of the limits of your questions; otherwise you will lose your head!”
Gargi respectfully sat back in silence for a moment, thinking about what to say. Finally, she asked two more questions, both of which he answered correctly:
Gargi's first question: “That, O Yagyavalkya, which is above the sky, that which is beneath the earth, that which is between these two, sky and earth, that which people call the past and the present and the future—across what is that woven that ‘permeates’ it?
Yagyavalky: “That, O Gargi, which is above the sky, that which is beneath the earth, that which is between these two, sky and earth, that which people call the past and the present and the future—across space is that woven, (which) permeates it.”
Gargi: “Adoration to you, Yagyavalkya, in that you have solved this question for me. Prepare yourself for the other.”
Gargi's second question: “Yajnavalkya, what pervades that Sutra which is above heaven and below the earth, which is heaven and earth as well as what is between them and which—they say—was, is and will be?”\
Yajnavalkya: “That, O Gargi, which is above heaven and below the earth, which is heaven and earth as well as what is between them and which—they say—was, is and will be, is pervaded by the un-manifested akasha.”
Gargi: “What pervades the akasha?"
Yagyavalkya: “That, O Gargi, the knowers of Brahman call the Imperishable. It is neither gross nor subtle, neither short nor long, neither red nor moist; It is neither shadow nor darkness, neither air nor akasha; It is unattached; It is without taste or smell, without eyes or ears, without tongue or mind; It is non—effulgent, without vital breath or mouth, without measure and without exterior or interior. It does not eat anything, nor is it eaten by anyone.
At this point in the debate, hours had passed. There were probably those sitting in the crowd swaying as they dozed. Yagyavalkya was concerned about Gargi's stamina and suggested they end the debate. My guess is he was pretty exhausted too. The debate ended with praise from Gargi that Yagyavalkya was indeed the greatest brahmanishtha (yoga).
Reading this story at other sites online, I noticed that some neglect to tell the outcome of the debate, emphasizing Gargi’s strength as a woman only. She was certainly strong, but I think her performance in the debate also demonstrated her courage, humility, and wisdom.
Source: https://kids.baps.org/storytime/gargi.htm; https://en.wikipedia.org/wiki/Gargi_Vachaknavi