One can find various quotes like this by Muslim philosopher Ibn Khaldun:

Thus the founders of grammar were Sibawaih and after him, al-Farisi and Az-Zajjaj. All of them were of Persian descent… they invented rules of (Arabic) grammar … great jurists were Persians … only the Persians engaged in the task of preserving knowledge and writing systematic scholarly works. Thus the truth of the statement of the prophet becomes apparent, ‘If learning were suspended in the highest parts of heaven the Persians would attain it’ … The intellectual sciences were also the preserve of the Persians, left alone by the Arabs, who did not cultivate them … as was the case with all crafts … This situation continued in the cities as long as the Persians and Persian countries, Iraq, Khorasan and Transoxiana [=modern Central Asia], retained their sedentary culture.

Stereotypes are not always true, but usually. So given persistent stereotypes about Persian intellectual superiority among peoples of the region, I tried some quantitative analyses.

Wikipedia: Founders of schools/fields

This list has 16 people. I checked their ancestry.

Wiki Description Ancestry Ancestry text https://en.wikipedia.org/wiki/Al-Zahrawi Abu al-Qasim al-Zahrawi, also known as Abulcasis, has been called the “father of modern surgery”[1] and the “father of operative surgery”.[2] Arab (Spain) “Al-Zahrawi was born in the city of Azahara, 8 kilometers northwest of Cordoba, Andalusia. His birth date is not known for sure, however, scholars agree that it was after 936, the year his birthplace city of Azahara was founded. The nisba (attributive title), Al-Ansari, in his name, suggests origin from the Medinian tribe of Al-Ansar,[9] thus, tracing his ancestry back to Medina in the Arabian peninsula.[10]” https://en.wikipedia.org/wiki/%27Ali_ibn_al-%27Abbas_al-Majusi Ali ibn al-‘Abbas al-Majusi, also known as Haly Abbas is ranked among the top three of most eminent doctors of medieval Islam. One scholar asserts that he “must be acknowledged as a founder of anatomic physiology”.[3] In addition, the section on dermatology in his Kamil as-sina’ah at-tibbiyah (Royal book-Liber Regius) has one scholar to regard him as the “father of Arabic dermatology”.[4] Persian “He was born in Ahvaz, southwestern Persia” https://en.wikipedia.org/wiki/Ibn_al-Haytham Alhazen: is considered the “father of modern optics”,[5][6] the “father of physiological optics”,[7] and the “father of optics”.[8][9] Arab (Iraq) “Ibn al-Haytham (Alhazen) was born c. 965 to an Arab[17][13] family in Basra, Iraq, which was at the time part of the Buyid emirate. “ https://en.wikipedia.org/wiki/Al-Biruni Al-Biruni: According to Francis Robinson, Al-Biruni earned the “founder of Indology” and “first anthropologist” titles for his remarkable description of early 11th-century India.[10] Georg Morgenstierne regarded him as “the founder of comparative studies in human culture”.[11] Al-Biruni is also known as the “father of Islamic pharmacy”.[12][13] Persian “He was born in the outer district of Kath, the capital of the Afrighid dynasty of Khwarezm in Central Asia” https://en.wikipedia.org/wiki/Al-Farabi Al-Farabi: regarded as the “founder of Islamic/Arab Neoplatonism”[14][15] and by some as the “father of formal logic in the Islamic world”.[16] Unknown (Arab/Persian) “Scholars largely agree that Farabi’s ethnic background is not knowable.” https://en.wikipedia.org/wiki/Al-Khalil_ibn_Ahmad_al-Farahidi Al-Khalil ibn Ahmad al-Farahidi: has been called the father of Arabic lexicography (‘ilm al-lugha) and prosody (al-ʿarūḍ).[19] Arab (Oman) “Born in 718 in Oman, southern Arabia, to Azdi parents of modest means al-Farahidi became a leading grammarian of Basra in Iraq.” https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi Al-Khawarizmi: most renowned as the “father of algebra”. Solomon Gandz states: “In a sense, Khwarizmi is more entitled to be called “the father of algebra” than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers”.[20] Persian “He was born into a Persian[6] family and Ibn al-Nadim gives his birthplace as Khwarezm[24] in Greater Khorasan (modern Khiva, Xorazm Region, Uzbekistan). “ https://en.wikipedia.org/wiki/Al-Kindi Al-Kindi, known as “the Philosopher of the Arabs”, is unanimously hailed as the “father of Islamic/Arab philosophy”.[17][21][22] Arab (Saudi) “Al-Kindi was born in Kufa to an aristocratic family of the Kinda tribe, descended from the chieftain al-Ash’ath ibn Qays, a contemporary of Muhammad.” https://en.wikipedia.org/wiki/Averroes Averroes (1126-1198): known in Arabic as Ibn Rushd, was an Andalusian polymath born in Córdoba, al andalus Spain now. Averroes was regarded by some (medieval ?) Christian bishops as the “father of free thought and unbelief”[23][24] and has been described by some as the “father of rationalism”[25] and the “founding father of secular thought in Western Europe”.[26][27] Ernest Renan called Averroes the absolute rationalist, and regarded him as the father of freethought and dissent.[28] Arab (Spain) “Muhammad ibn Ahmad ibn Muhammad ibn Rushd was born in 1126 (520 AH[2]) in Córdoba.” https://en.wikipedia.org/wiki/Ibn_Hazm Ibn Hazm: author of one of the earliest works on comparative religion and “honoured in the West as that of the founder of the science of comparative religion”.[29] Alfred Guillaume refers to him the composer of “the first systematic higher critical study of the Old and New testaments”.[30] However, William Montgomery Watt disputes the claim, stating that Ibn Hazm’s work was preceded by earlier works in Arabic and that “the aim was polemical and not descriptive”.[31] European Muslim “Ibn Hazm’s grandfather Sa’id and his father Ahmad both held high advisory positions in the court of the Umayyad Caliph Hisham II.[9] Scholars believe that they were Iberian Christians who converted to Islam.” https://en.wikipedia.org/wiki/Ibn_Khaldun Ibn Khaldun is regarded by many as the father of sociology, historiography and modern economics. He is best known for his Muqaddimah. Arab (Spain) “was born in Tunis in AD 1332 (732 AH) into an upper-class Andalusian family of Arab descent” https://en.wikipedia.org/wiki/Avicenna Ibn Sina is regarded as the father of early modern medicine.[32] Persian “Avicenna was born c. 980 in Afshana, a village near Bukhara (in present-day Uzbekistan), the capital of the Samanids, a Persian dynasty in Central Asia and Greater Khorasan.” https://en.wikipedia.org/wiki/Jabir_ibn_Hayyan Jabir ibn Hayyan was a prominent Persian or Arab alchemist who is praised as the “father of Islamic/Arabic alchemy”[33] and who has often been referred to as “the father of chemistry” and is widely credited with the introduction of the experimental method into alchemy, as well as with the invention of numerous important processes that are still used in chemistry today.[34][35] Persian? “he was born in Tus, Khorasan, in Persia,[2] well known as Iran then ruled by the Umayyad Caliphate.” https://en.wikipedia.org/wiki/Muhammad_ibn_Zakariya_al-Razi Rhazes: His treatise on Diseases in Children has led many to consider him the “father of pediatrics”.[36][37][38] He has also been praised as the “real founder of clinical medicine in Islam”.[39] Persian “Razi was born in the city of Ray (modern Rey) situated on the Great Silk Road that for centuries facilitated trade and cultural exchanges between East and West.[18] His nisba, Râzī (رازی), means “from the city of Ray” in Persian.[19] It is located on the southern slopes of the Alborz mountain range situated near Tehran, Iran. “ https://en.wikipedia.org/wiki/Muhammad_al-Shaybani Muhammad al-Shaybani: the father of Muslim international law.[40] Arab (Iraq) “Muḥammad b. al-Ḥasan was born in Wāsiṭ, Iraq, in 750; soon, however, he moved to Kufa, the home town of Abū Ḥanīfa, and grew there.” https://en.wikipedia.org/wiki/Shahab_al-Din_Yahya_ibn_Habash_Suhrawardi Suhrawardi: founder of the Illuminationist school of Islamic philosophy.[41][42] Persian “Suhraward is a village located between the present-day towns of Zanjan and Bijar Garrus in Iran, where Suhrawardi was born in 1154.”

So, we count 7.5ish Persians, and 7.5ish Arabs, and 1 European convert. 3 of the Arabs are listed as born in Spain, which is curious because that was a tiny part of the empire, so maybe these are more converts (crypto-Europeans), or were somehow influenced by European culture in Spain.

So it’s a little unclear what the demographics of the Islamic empire were, but only 2 of the 16 were born before 750 CE and the maximum expansion of the population. Thus, we might estimate that Persians were maybe 20% of the population at the time, but contributed ~50% of the thinkers on the list, so they were over-represented by factor of 2.5. Note that in Iran today, Persians are only about ~60% of population.

Pre-modern scientists and scholars

Wikipedia provides us with parallel lists for these:

A quick count gives us 354 and 245. So ~600 total and 41% Iranian. If we ignore the Persian/Iranian difference, and use the 20% population from before, we get about factor 2.

So, they are a tiny (~70k) Iranian diaspora population living in mostly in India. Despite this, there’s a list of 454 famous ones here. As Peter Frost noted in 2013, this makes them hugely disproportionately represented. Unfortunately, like other great peoples, they are dying out, killed by modernity:

Whatever eventually happens, such research may become a race against time. You see, the Parsis are dying out. They have long had high rates of late marriage and non-marriage, and both trends have worsened in recent decades. By 1980-82, their total fertility rate was already down to 1.12, i.e., half the replacement rate. By 2000, it was 0.94. The latest data, from 2001-2006, indicate a total fertility rate of 0.88 (Patel, 2011).

More research needed

The above considerations are probably sufficient to support a claim that Persians and Parsis are more intellectually successful than their neighbors in the Middle East (and India), but a more systematic study is needed for proper quantification. In many cases, we don’t know from history the ancestry of the famous person in question. However, with the advent of archaeogenomics, we will probably find out in the coming decades as people lose their inhibitions to sequencing old letters, graveyards, tombs etc. We have already made good progress on some questions, but we can go much, much further. We need to go full cliodynamics, combined with genomics with cross-ethnic valid polygenic scores. This can finally throw light on the role of eugenic-dysgenic selection cycles in the rise and fall of empires. I believe this idea has been invented a few times already independently (e.g. Volkmar Weiss 2007 in MQ).