In mathematics, specifically in local class field theory, the Hasse–Arf theorem is a result concerning jumps of the upper numbering filtration of the Galois group of a finite Galois extension.
 A special case of it when the residue fields are finite was originally proved by Helmut Hasse, and the general result was proved by Cahit Arf.
Cahit Arf (] ; 11 October 1910 – 26 December 1997) was a Turkish mathematician.
 He is known for the Arf invariant of a quadratic form in characteristic 2 (applied in knot theory and surgery theory) in topology, the Hasse–Arf theorem in ramification theory, Arf semigroups, and Arf rings.
Yahya ibn Umar ibn Yahya ibn Husayn ibn Zayd ibn Ali Zayn al-Abidin ibn Al-Husayn ibn Ali al-Murtada was an Alid Imam.
 His mother was Umm al-Husayn Fatimah bint al-Husayn ibn Abdallah ibn Ismail ibn Abdullah ibn Ja`far ibn Abī Tālib.
 In the days of the Abbasid Caliph Al-Musta'in, he marched out from Kufa and lead an abortive uprising from Kufa in 250 A.H. (864-65 C.E.), but was killed by the Abbasid forces led by Hussain ibn Isma’il, who had been sent to deal with him.
Habīb ibn Madhāhir al-Asadi (Arabic: حبيب بن مظاهر الأسدي‎ ‎ ) was of the Banu Asad clan, and one of the companions of Ali, Hasan ibn Ali and Husayn ibn Ali.
 He was one of the people of Kufa who sent letters to Husayn ibn Ali (grandson of Muhammad) and invited him to Kufa.
 Though, when he realized that people of Kufa have broken their allegiance to Husayn, he left Kufa, joined Husayn, and was martyred at the age of 75 while fighting in Husayn's army, in Karbala.
Bibi Pāk Dāman (Urdu: بی بی پاکدامن) is the mausoleum of Ruqayyah bint Ali located in Lahore, Punjab, Pakistan.
 Legend has it that it holds the graves of six ladies from Muhammad's household (Ahl Al-Bayt).
 Ruqayyah bint Ali ibn Abu Talib was the daughter of Muhammad's cousin and son-in-law Ali ibn Abu Talib with his wife Umm al banin bint Huzaam.
 Ruqayah bint Ali was the full sister of Al-Abbas ibn Ali and also the wife of Muslim ibn Aqeel (emissary of third Shi'a Imam Husayn ibn Ali to Kufah).
 Others are said to be Muslim ibn Aqil's sister and daughters.
 It is said that these ladies came here after the event of the battle of Karbala on the 10th day of the month of Muharram in 61 AH (October 10, AD 680).
 Bibi Pak Daman, which means the "chaste lady", is the collective name of the six ladies believed to interred at this mausoleum, though it is also (mistakenly) popularly used to refer to the personage of Ruqayyah bint Ali alone.
 They were among the women who brought Islam to South Asia, preaching and engaging in missionary activity in the environs of Lahore.
 It is said that Data Ganj Bakhsh, considered a great Sufi saint of the South Asia, was himself a devotee of the Bibi Pak Daman shrine and received holy knowledge from this auspicious shrine.
Abbas (Abbass, Arabic: عباس‎ ‎ means "lion" in Arabic The name traces back to Al-‘Abbas ibn ‘Abd al-Muttalib (an uncle of Muhammad) and Abbas ibn Ali, a son of Ali ibn Abi Talib, who participated in the battle of Karbala alongside his half-brother Hussain ibn Ali.
 Abbas ibn Ali is revered by Shia Muslims, some of whom are named Abbas in remembrance and tribute to him.
 There is an Arabian tribe of the same name, the Banu Abbas.
 In Arabic language it literally means "grouchy face" or "frown" referring to a Mean-spirited or a Stern person mainly male.
People with the surname Zaidi trace their origins to the Islamic Holy City of Mecca, located in present-day Saudi Arabia.
 Descendants of Zaid ibn Ali are known as Sayyid, an honorific title bestowed upon to the descendants of Muhammad.
 The Zaidi surname is derived from Zaid ibn Ali, the son of Ali ibn al-Husayn Zayn al-'Abidin, who was the great grandson of the Prophet Muhammad.
 Descendants of Zaid ibn Ali who chose to move away from the Arabian Peninsula and have the surname Zaidi are commonly located in Iraq, Iran, Afghanistan and Pakistan.
This is a simplified family tree of Husayn ibn Ali.
 For the ancestors of ibn Ali see the family tree of Muhammad and the family tree of Ali.
 People in "italics" are considered by the majority of Shia and Sunni Muslims to be "Ahl al-Bayt" ("People of the House").
 Twelver Shia also see the 4th to 12th Imamah as Ahl al-Bayt. "
(Ali is an imam in Mustaali but no number is assigned for this position, and Hasan ibn Ali is not an imam in Nizari Imamah.)"
In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated to a Seifert surface.
 If "F" is a Seifert surface of a knot, then the homology group H("F", Z/2Z) has a quadratic form whose value is the number of full twists mod 2 in a neighborhood of an imbedded circle representing an element of the homology group.
 The Arf invariant of this quadratic form is the Arf invariant of the knot.
He is known to have translated and modified the Zij al-Sindhind.
 The Zij al-Sindhind was the first astronomical table ever introduced in the Muslim World.
 As a mathematician Sind ibn ʿAlī was a colleague of al-Khwarizmi and worked closely with Yaqūb ibn Tāriq together they calculated the diameter of the Earth and other astronomical bodies.
 He also wrote a commentary on "Kitāb al-ğabr wa-l-muqābala" and helped prove the works of al-Khwarizmi.
 The decimal point notation to the Arabic numerals was introduced by Sind ibn Ali.

Question: Who did more ring theory, Cahit Arf or Sind ibn Ali?
Answer: Cahit Arf