One thing that seems to have been emphasised in the Samarqand School was the importance of the mathematical sciences. Biographical accounts of Qadi Zada al-Rumi, for example, highlight his difficulties with his teacher al-Sayyid al-Sharlf al-Jurjani, who thought his student overly interested in mathematics at the expense of philosophy. Jamshid al-Kashi is also noted for his embrace of the mathematical sciences, as we can see from his letters to his father, and Ulugh Beg, like a number of Mongol/Turkic rulers, was predisposed to support the mathematical sciences; in addition, he himself became proficient in them. It was in this atmosphere that the young Ali Qushji was raised, and this seems to have had a profound effect upon his intellectual outlook.

The so-called "sextant" obviously would have extended well above the ground ... and likely was closer to being a quadrant. ... the instrument "was by far the largest meridian instrument ever built." Fragments of the curved measuring track have survived with markings for around 20 degrees; this is about the highest point that observations likely would have been made. The "sextant" would have been used to measure the angle of elevation of major heavenly bodies, especially at the time of the winter and summer solstices. Light from the given body, passing through a controlled opening, would have shone on the curved track, which is marked very precisely with degrees and minutes. "It could achieve a resolution of several seconds of arc - on the order of a six-hundredth of a degree ... . It is not clear whether more than the sun and moon could have been measured in this fashion, since planets, for example, would not have cast sufficient light. The observatory was equipped with a variety of other instruments, which probably accounted for the largest part of its scientific measurement.

I would like to go back to Tabriz if you let me. The true reason of my existence here is to be the good-will Messenger of Akkoyunlu Ruler, Sultan Hasan. It is necessary for me before I accept the gracious invitation of my Sultan to turn back and inform the person who sent me here and who trusted me that I carried my duty with a good result ...

... around 1472 Ali Qushi, together with his family and students, left permanently for Constantinople ... When Ali Qushji and his entourage approached Constantinople, Sultan Mehmed sent a group of scholars to welcome them. Sources say that in crossing the Bosporus to Constantinople, a discussion ensued about the causes of its ebb and flow. Upon arrival in Constantinople, Ali Qushji presented his mathematical work 'al-Muhammadiyya fi al-hisab' to the sultan, which was named in his honour.

In this brief period Ali Qushji educated and influenced a large number of students, who, along with his writings, were to have an enormous impact on future generations.

In 1973, Noel Swerdlow presented a new and significant reconstruction of how Copernicus arrived at the heliocentric theory. This reconstruction was based upon several bits of newly-interpreted information, most importantly a set of notes in Copernicus's hand contained in an Uppsala University manuscript. These notes provided compelling evidence that Copernicus had transformed Ptolemy's epicyclic models of the planets into eccentric models as a first step in developing a Sun-centred astronomy. But this transformation depended upon a general proposition that one could indeed convert all the epicycle models into eccentric ones. Curiously, Ptolemy denied this, claiming in Book XII of the Almagest that this was possible only for the outer planets (Mars, Jupiter, and Saturn) but not the inner ones (Mercury and Venus). ...

... it would seem that no one else recognised this until the fifteenth century. Swerdlow found what he believed to be the source for the propositions Copernicus needed to begin his conversions, namely Book XII, Chapters I and 2 of Regiomontanus's 'Epitome of the Almagest'. In Chapter 2, Regiomontanus gives a brief sketch and proof of the crucial theory for the inner planets, which would allow Copernicus to convert all the planets from epicyclic to eccentric models. Though Copernicus is sparing in his references and nowhere cites Regiomontanus for these propositions, his use of the 'Epitome' is well-documented, and there would seem to have been no other European source that he could have depended upon.

Whatever subsequent use was made of them, Regiomontanus's own motivation for including these propositions at the beginning of Book XII has remained unclear. ... What is especially odd about Regiomontanus's interest is that it is apparently so unprecedented. Neither in Europe nor in the Islamic world does this eccentric alternative alluded to by Ptolemy seem to have generated much interest. And the motivation to extend this alternative to the lower planets, after being rejected by the great authority himself, is even more puzzling. Finally, there is the odd way in which Regiomontanus presents the two propositions. He himself gives no motivation - he just presents them. There is no mention of Ptolemy, no statement that Ptolemy was wrong, no explanation of why Ptolemy made his mistake, no claim of credit.

One possibility is that Regiomontanus does not claim credit because he was not in fact the originator of the proposition. Indeed, it would seem, based on evidence presented in the sequel, that an older contemporary of Regiomontanus named Ali Qushji may well have been the discoverer of this crucial proposition and that Regiomontanus learned of it either while in Italy or through the intermediation of Cardinal Bessarion , who had originally suggested to Regiomontanus and his collaborator Georg Peurbach that they write the 'Epitome'.

Most readers of this journal will be acquainted with Regiomontanus and Peurbach, and perhaps even Bessarion, but Ali Qushji is most likely an unknown figure. This is regrettable since he is, at least in my opinion, one of the major figures in astronomy of the fifteenth century.

... conception of existence, existents, nature, knowledge, and language. As for the mathematical sciences, Ali Qushji in general tried to free them from Hermetic-Pythagorean mysticism and to provide an alternative to Aristotelian physics as the basis for astronomy and optics.

... mathematical entities are not abstracted from sensory data, but are rather attained through human activity such as counting, ordering, comparing, etc.

Ali Qushji's views were debated for centuries after his death, and he exerted a profound influence on Ottoman-Turkish thought and scientific inquiry, in particular through the madrasa and its curriculum. His influence also extended to Central Asia and Iran, and it has been argued that he may well have had an influence, either directly or indirectly, upon early modern European science, to which his ideas bear a striking resemblance.