When, as a time-pressed traveller, I visit some place that moves me deeply, I long to be able to spend days there in order to soak in its atmosphere at leisure... to see the sun weave slow shadows through the cloisters of Monreale, or wake at morning above the ruins at Delphi and feel the air vibrate to the first beams of the sun, or live in the square courtyard of a Samarkand madrasah... and behold... the dream has turned into reality. What more lovely present could a traveller have in return for having come so far?

"Turkestan Solo" by Dervla Murphy

While his grandfather is remembered for monumental mosques and mausoleums, Ulug Beg's legacy is appropriately educational. Ulugbek Medressa, on the west side of the Registan, is the original medressa, finished in 1420 under Ulugbek (who is said to have taught mathematics here; other subjects included theology, astronomy and philosophy). The madrassa itself measure 56m by 81m and is built around a large, open courtyard. Beneath the little corner domes were lecture halls, and at the rear a large mosque with a beautiful interior and an austere teaching room to one side.

The Ulugh Beg Madrasah has an imposing iwan with a lancet-arch pishtaq or portal facing the square. The corners are flanked by high minarets. The mosaic panel over the iwan's entrance arch is decorated by geometrical stylized ornaments. The square courtyard includes a mosque and lecture rooms, and is fringed by the dormitory cells in which students lived. There are deep galleries along the axes. Originally the Ulugh Beg Madrasah was a two-storied building with four domed darskhonas (lecture rooms) at the corners.

The madrassah housed at least 100 students in the 50 cells under the tutelage of the finest scholars of the age both in Islamic and secular sciences, many of them making use of the astronomical instruments housed here before the construction of Ulug Begs observatory. His lecturing of astronomy - his greatest passion, is reflected in the panoply of azure-blue stars on the 35-metre pishtak (portal). A Kufic inscription reads: "This magnificent facade is of such a height it is twice the heavens and of such weight that the spine of the earth is about to crumble". Yet its size is more than balanced by the sheer elegance of its design and ceramic tile coating. A yellow-brown background, the colour of the earth, highlights glazed green, turquoise, yellow and light and dark blue. Mosaic and majolica panels shine with floral motifs and Kufic calligraphy, but dominant are geometric girikh patterns stretching across the walls and up the minarets flanking the fagade. These 33-metre columns, still flouting the perpendicular, terminate in muqarna honeycomb decoration.

The Ulugh Beg Madrasah was one of the best clergy universities of the Muslim Orient in the 15th Century CE. Islamic scholar Abdurakhman Djami, a prominent poet, scientist and philosopher studied at the madrasah. Ulugh Beg himself gave lectures there. During Ulugh Beg's government the madrasah was a centre of secular science.

If you tip the security guard you can climb over the dust and builders' rubble and up the steep and narrow staircase to the top of the right-hand minaret, finally pulling yourself up through the metal hatch and onto the rooftop. There's scarcely any room to move and you sit in a precarious position with an awfully long drop below, but if you can overcome any fear of heights, this is an exhilarating place from which to view the tiger mosaic on the Sher Dor madrassa opposite and you feel like you're on top of the world.

Ulug Beg's 600th anniversary in 1994 accelerated the pace of restoration, so that the interior too resembles the building of Samarkand's heyday. Through the pishtak entrance is a square courtyard, from which four large iwans (vaulted arches) give onto 50 hujra (student cells) on two storeys. Under the corner domes lie spacious darskhana (lecture halls), while the western axis conceals a five-bayed mosque, whose exhibits include copies of 17th century European documents and engravings featuring a very European-looking Ulug Beg.