Is Ali mentioned in the Quran?

Question

Assalamu alaikum warahmatullaahi wabarakaatuh

If Shia revere and follow Ali so much, is he mentioned in the Quran?

Answer 1

If he was mentioned by name many people would name themselves ali. Mentioning by name is not a solution to remove ambiguity. as @ali has mentioned he is referred in several verses. Quoting from Tarikh Khulafa by Suyuti:

اخرج ابن عساکر عن ابن عباس قال: ما نزل فی کتاب الله تعالی ما نزل فی علی

اخرج ابن عساکر عن ابن عباس قال: نزلت فی علی ثمانمائه آیه

Also refer to almusnad by ahmad hanbal where he speaks about imam ali. According to him Imam ali is referred in quran 300 times.

Answer 2

Is the name of any of Khulafa in Quran?

Is the name of "Harun" somewhere in 10 orders of Musa? If Ali was mentioned by his "name", you could raise the question: "Are Hassan and Hussain and Ali-ibn Hussain mentioned in quran"?

Although the name of Ali is not in Quran, he is mentioned several times:

قُلْ لَا أَسْأَلُكُمْ عَلَيْهِ أَجْرًا إِلَّا الْمَوَدَّةَ فِي الْقُرْبَى - شوری 23

روى السيوطي وغيره في تفسير هذه الآية بالاسناد إلى ابن عباس ، قال: لما نزلت هذه الآية ﴿ قُل لا أسألُكُم عَليه أجراً إلاّ المودَّةَ في القُربى ﴾ قالوا : يارسول الله ، من قرابتك هؤلاء الذين وجّبت علينا مودتهم ؟ قال صلى الله عليه وآله وسلم :علي وفاطمة وولداهما

Al-Suyuti has provided a Hadith of prophet Muhammad by Ibn-Abbas that informs us the above Ayah is about Ali, Fatima - the daughter of prophet Muhammad - and their children Hassan and Hussain - the offsprings of prophet Muhammad.

إِنَّمَا وَلِيُّكُمُ ٱللَّهُ وَرَسُولُهُ وَٱلَّذِينَ آمَنُواْ ٱلَّذِينَ يُقِيمُونَ ٱلصَّلاَةَ وَيُؤْتُونَ ٱلزَّكَاةَ وَهُمْ رَاكِعُونَ -المائدة: 55

This ayah says: Your "wali" are Allah, prophet, and the people who believe in Allah, who pray and pay Zakah while they are doing prayers (وَهُمْ رَاكِعُونَ). But how can someone pay Zakah at the same time that he is doing prayers? According to Asbab Al-Nuzul by Al-Wahidi:

Al-Kalbi ... added that the end of the verse was revealed about ‘Ali ibn Abi Talib, for he gave his ring to a beggar while he was bowing during prayer

This happened while some poor man arrived the mosque and asked the people, no one replied him, but Ali - who was at prayers, drew his hand wearing a ring, and let the poor man to take the ring as charity.

وَ مِنَ النَّاسِ مَن يَشْرِي نَفْسَهُ ابْتِغَاء مَرْضَاتِ اللّهِ وَاللّهُ رَؤُوفٌ بِالْعِبَاد - البقره 207

In the night that prophet Muhammad (PBUH) wanted to leave Mecca towards Medina, 40 men of Mecca were ready to attack and kill prophet. Although very dangerous, Ali readily slept in bed of prophet such that the enemies did not mention Prophet has left. Several famous books of sunnah have linked this ayah to Ali.

There are several other Ayahs also related to Ali ibn Abi Talib (Karramallahu Wajhah), you can easily find by googling.