Mahabharata contains one lakh shlokas having 1.8 million words. In the beginning, it has 24,000 shlokas which kept on growing to 100,000 later.
Technically this was Lord Ganesha who wrote down the text to Vyasa’s dictation. There is one interesting story about this. Veda Vyasa wanted to write Mahabharata, which was like an ocean in his mind floating with huge & small waves. It was a composition of hundreds of stories and sub-stories. He wanted to write it, but he knew that he couldn’t write it alone, as this was a very time-consuming.
So he approached Lord Ganesha by meditating. Ved Vyas explain the reason of his meditation to Lord Ganesha. Ganesha agreed but put one condition to Ved Vyas i.e., he could not wait for him to compose his words and would write extremely fast. Though Veda Vyasa was confident upon himself that he could compose very fast. But at the same time, he was also confused whether he could match the speed of Lord Ganesha.
He said that Lord Ganesha was not to write anything unless he understood the meaning of what was narrated to him. Lord Ganesha accepted the condition and the writing of epic starts this way. Veda Vyasa knew that Lord Ganesha is the God of literature and it would be a very tough competition. But he used one trick against Lord Ganesha. After few shlokas, Veda Vyasa used to say a very tough one that Lord Ganesha would take some time to understand. Due to this Veda Vyasa would get some time and would make new shlokas.
Lord Ganesha was writing the story so fast that the pen broke suddenly. As per his agreement with Veda Vyasa, he could not pause, and neither could ask him to pause. How was he to continue writing without a pen?
But Lord found a quick solution; he broke off one of his tusks and start writing again with his tusk. This was the written story of Mahabharat and Lord Ganesha also came to be known as Ekadanta – The Lord with the single tusk!
That is the reason Lord Ganesha is seen in most of the pictures with only one tusk and the broken tusk in his hand.
There is also another story behind the broken tusk that is of Parshurama. From the excerpts of Upogatha Pada of Brahmanda Purana, Parashurama, the axe-wielding incarnation of Vishnu, had sucessfully defeated his enemy Kartavirya Arjuna and the kings allied with him, and so he wanted to thank Shiva for giving him the power to fight these enemies.
Parashurama went to Mount Kailash to pay his homage to Shiva where Ganesha stopped him, saying his father was sleeping along with his mother, and he didn’t want Parashurama intruding on them in case they might be engaged in amorous pursuits. Parashurama was enraged that he was being prevented from seeing Shiva, and so he started fighting Ganesha.
Ganesha was winning handily, but then Parashurama threw his axe at Ganesha and Ganesha didn’t fight back against it, because the axe was a gift from Shiva. Perceiving that the axe had been given to him by his father, Ganesha became desirous of meaning it not to go in vain. Hence he received it with his left tooth (tusk). Chopped off by the axe, the tusk fell on the ground, covered with blood like a mountain that fell on the ground when struck by Indra’s thunderbolt.
In either case of the story, the more important symbolic meaning behind the broken tusk is that Buddhi(symbolized broken tusk) should always be less than Shraddha or faith(symbolized by full tusk). This is one of the many symbolisms attributed to the broken tusk.