Thus, for many centuries, Central Asia — not the Arab Middle East — was the intellectual and political center of the Muslim world. The second holiest book of Islam, “Sayings of the Prophet,” was assembled by a scholar from Bukhara, in present-day Uzbekistan. It was in places like Kazakhstan, Tajikistan and Uzbekistan that Islam’s powerful mystical movement, Sufism, found its greatest exponents, and it was from there that Sufism spread across the Muslim world. And among medieval theologians, few thinkers stood higher than Abu Hamid al-Ghazali, from the city of Tus on the borderland between Iran, Turkmenistan and Afghanistan, who exerted a profound influence on St. Thomas Aquinas.

Central Asia can also claim a lion’s share of the greatest names in Islamic science and philosophy. The codifier of algebra, to whom Mr. Obama referred his “new beginning” speech at Cairo University in 2009, was also from Khwarazm, in what is now Uzbekistan. Called Al-Khwarazmi in Arabic, he gave his name to algorithms, which lie at the heart of modern computer science. Also from Uzbekistan was Ibn Sina, known as Avicenna to the West, whose great “Canon of Medicine” gave rise to the medical sciences in the Middle East, Europe and India. Another great intellectual, Al-Farabi, who revived and greatly added to Aristotle’s logic and who wrote the greatest medieval study of music, was from what is now Kazakhstan. And the pioneering astronomer Abu-Mahmud Khojandi was from Khujand, now in Tajikistan.

True, all these people wrote in Arabic. But a Japanese who writes in English is not an Englishman. All of them — and scores of other innovators from the Muslim world whom we are accustomed to think of as Arabs — belonged to various Central Asian branches of the Persian peoples, or were Turks, not Arabs.

Today, the countries that are heirs to the old Silk Road are struggling to reclaim their heritage. The task is not easy. Many of their leaders are attracted to the authoritarianism that has brought relative stability to Russia and tremendous prosperity to China. The people of Central Asia have no prior experience with democracy, ethnic tensions persist, and many of their leaders rule with a heavy hand. Yet these countries remain secular states and are more tolerant of other religions than most of their counterparts in the Middle East. Their economies have grown steadily and they have embraced modern secular education, sending tens of thousands of youths to study abroad. They are developing new universities of their own, largely on the American pattern. Many use English as the language of instruction. And all can boast a rising generation of men and women drawn to the ideals of an open society.

Unfortunately, in the eyes of many Central Asians, America’s interest does not extend beyond gas and oil. Washington’s decision to pull back from Afghanistan in 2014 will likely erode American influence at the very moment when it could do the most good — especially as rising prosperity increases pressure for governments to loosen their grip. Greater freedom presents great dangers, as the disillusions of the Arab Spring have so sadly demonstrated.