There are some Mathematical problems that Hazrat Ali solved while he was Khalifa. He was known for his mathematical genius.

Enjoy reading them:

One Day a person came to Ali (A.S.), thinking that since Ali thinks he is too smart, I'll ask him such a tough question that he won't be able to answer it and I'll have the chance to embarrass him in front of all the Arabs.

He asked "Ali, tell me a number, that if we divide it by any number from 1-10 the answer will always come in the form of a whole number and not as a fraction."
Hazrat Ali Looked back at him and said, "Take the number of days in a year and multiply it with the number of days in a week and you will have your answer."

The person got astonished but as he was a Mushrik he still didn't believe Ali (A.S.). He calculated the answer Ali (AS) gave him. To his amazement he came across the following results:
The number of Days in a Year = 360 (in Arabic Calendar)

The Number of Days in a Week = 7

The product of the two numbers = 2520

Now ... 2520 ? 1 = 2520

2520 ? 2 = 1260

2520 ? 3 = 840

2520 ? 4 = 630

2520 ? 5 = 504

2520 ? 6 = 420

2520 ? 7 = 360

2520 ? 8 = 315

2520 ? 9 = 280

2520 ? 10= 252

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One day a person came to Ali (A.S.). He was planning to ask Ali (A.S.) such a question which would take Ali (A.S.) a long time to answer and because of that his Maghrib Prayers would be
delayed. He asked, "Ali you say you know everything in the world, then tell me which animals
lay eggs and which animals give birth to their young ones"
Hazrat Ali (A.S.) looked back at him smiled and said, "The animals who have their 'EARS' outside their body give birth to their young ones and the animals who have their 'EARS' inside their body lay eggs."

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A person was about to die, and before dying he wrote his Will which went as follows ...
"I have 17 Camels, and I have three sons. Divide my Camels in such a way that My eldest son gets half of them, the second one gets 1/3rd of the total and my youngest son gets 1/9th of the total number of Camels"
After his death when the relatives read his will they got extremely perplexed and said to each other that how can we divide 17 camels like this ?

So after a long hard thought they decided that there was only one man in Arabia who could help them: "Ali Ibne Abi Taalib." So they all came to the door of Ali (A.S.) and put forward their problem.

Hazrat Ali (A.S.) said, "Ok. I will divide the camels as per the man's will."

He said, "I will lend one of my camels to the total which makes it 18 (17+1=18), now lets divide as per his will"
The Eldest gets 1/2 of 18 = 9
The second one gets 1/3 of 18 = 6
and The Youngest gets 1/9 of 18 = 2
Now the total number of camels = 17

Then Hazrat Ali (A.S.) said, "Now I will take my Camel back."

This was the genius that Hazrat Ali was in his time.

Another Example !

The Prophet of Islam worked in Makkah relentlessly for a period of twelve years. His mission had not made any great strides. The converts to Islam were just the oppressed slaves, the downtrodden and those who had no wealth or aristocratic support. In the tenth year of his mission Abu Talib, who had been giving him physical protection from his tormentors, passed away. Soon after, Khadeeja, his beloved wife and companion and the person whose enormous wealth had supported the mission, also passed away. The Prophet was greatly aggrieved; he declared that year as the YEAR OF SORROWS.

Finally, a break came. The Prophet made contact with some tribal leaders of Madinah. They took the message with them back home, and soon, every home in Madinah was buzzing with the news of Islam and its leader. The Prophet advised his companions to proceed to Madinah slowly and gradually.

When the Quraysh got wind of that, they decided to kill the Prophet of Islam. Forty men from different families of the Quraysh came together and surrounded the house of the Prophet one night with the intention of killing him with one stroke of their swords. They surrounded his house and waited for the early morning hours.

In the meantime, Jibreel came and informed the Prophet of the conspiracy. The Prophet called Ali bin Abi Talib and told him about the impending danger. Ali asked as to what the Prophet wanted him (Ali) to do. The Prophet asked him if he (Ali) would sleep in his (Prophet's) bed that night while he (the Prophet) was intending to slip out of Makkah towards Madinah in the darkness of the night. Ali bin Abi Talib asked: "If I sleep in your bed tonight, will you be safe?" The Prophet replied: "Yes, I will be safe." Ali bin Abi Talib immediately did a sajdah of shukr (thanks to Allh) and agreed to do that. The Prophet left all the property that he had been keeping in trust in Ali's charge with the instructions to reimburse those goods to their rightful owners.
So, Ali slept in the Prophet's bed and the Prophet walked out of the house and moved towards the cave of THAWR reciting verses from Sura Yaaseen.

While the Prophet was walking in the darkness of the night, Jibreel came and revealed the following verse of the Qur'an.

Wa minan-naasi man-yashree nafsahu-b-tigha'a maradhaati(A)llahi wa Allahu ra'oofun bil-ibaad(Q-2:207)

Trans: And among men is he who sells himself to seek the pleasure of Allah; and Allah is affectionate to the servants.

This has been variously reported by the following scholars:

1. Hakim Nayshapoori in his Mustdarak reports from Ibn Abbas.
2. Muhammad bin Sa'ib Kalbi in his Tafseer Tas-heel al-Uloom at-Tanzeel
3. Abu Abdullah Muhammad bin Ahmad bin Abi Bakr Ansari in his Tafseer Qurtabi
4. Ibn Atheer in his Usud al-Ghaaba
5. Abu Bakt Nayshapoori in his Tafseer
6. Allama Kanji in his Kifayat- Talib
7. Allama Abdur-Rahman Safoori in his Nuzhat al-Majaalis
8. Muhib-ud-Deen Tabari in his Zakha'ir Uqba
9. Abul Hasan Wahidi in his Asbabb an-Nuzool as a commentary on Tafseer Jaalalayn
10. Allama Shablanji in his Noor al-Absaar

The most interesting commentary on this verse is given by Imam Ghazaali in his Ihya Fi Uloom ad-Deen, under the topic AL-EESAAR AL-AN NAFS.

Ghazaali writes that Allah sent called two of the great angels, Jibreel and Meekaa-eel and said: "I make you two brothers of each other. Now can one of you sacrifice his life for the other." Both declined to do that. Allah then pointed to Ali bin Abi Talib sleeping in the Prophet's bed and said: "There is a brother ready to sacrifice his life for another brother."

MY NOTE: I suppose Allama Iqbal had that story related by Ghazaali when he said:
Farishton se behtar hai insaan ban-na,
Magar ismen lagti hai mehnat ziyada.
Trans: It is better to be a human being than an angel, but it takes a lot of doing.

Allah then commanded the two angels to go down and protect Ali bin Talib from the enemies. Thus the two angels came and Jibreel stood by Ali's headrest and Meekaa'eel by his feet. And they both were saying: "Bravo, bravo, O son of Abu Talib, Allah is taking pride in your act of self-sacrifice and showing your glory over the angels."

There are some five hundred verses in the Holy Qur'an which either relate the glories of Ali bin Abi Talib or record one of his good deeds that he performed in the service of Islam.

This was one of those verses.