The Persian mathematicians living in Persia in the times after the Islamic conquest simply weren't Arabs, exactly like the Greeks weren't Romans after the Roman conquest.
One doesn't get the new ethnicity by being occupied.
We unfortunately don’t have too many biographical details about most of the famous “Greek” mathematicians, so it’s generally not precisely known what their background was.
In the middle ages, there was greater Persia and two Iraqs (Iraq al-Arab to the west and Iraq al-Ajman to the east which is today's western and central Iran).
If we are being pedantic, either the polymaths in question were Persian (which they are) or Iraqi Arabs, not Iranians. In fact, Persian empire also encompassed parts of modern day Uzbekistan, Kyrgyzstan, Turkmenistan, Afghanistan, Pakistan, and Kazakhstan, until they came under the Turcko-Mongol rule.
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Anyway, “Persia” (Persis) comes from the Greek version of “Pars”. Persians call their language “Farsi”, from the Arabic version, “Fars”. These all have the same origin, and date back millennia.
It’s similar to the way we call all of the mathematicians of ~ 500 BCE – 500 CE “Greek”, even though most of the later ones were Roman citizens living in Egypt or elsewhere.
Or the way we call Mesopotamian mathematics generically “Babylonian”, even though most of it was from other cities, and some of the relevant developments lumped in are from before Babylon per se existed, done by people of a different ethnic group who spoke a different language.
Or the way Soviet scientists are often called “Russian”.