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Prosperity in the Gupta Empire initiated a period known as the Golden Age of India, marked by extensive inventions and discoveries in science, technology, engineering, art, dialectic, literature, logic, mathematics, astronomy, religion, and philosophy. The Gupta Empire saw a vast range of scientific and cultural achievements. To the chagrin of many high school math students, trigonometry and geometry got their start during this golden age. And Guptan mathematicians developed the concept of zero and the number system. Other major contributions from this era helped improve human health. Not only did scientists and doctors expand the alternative system of medicine called Ayurveda, but they also improved surgical practices and helped popularize vaccinations. Gupta Emperors followed a model of decentralized administration. They organized a hierarchy of officials exercising imperial authority in different parts of the country to help them systematically control their territories. There was a five tiered administration system in the regions which were under the direct control of the Gupta Empire. The hierarchy began at the imperial level with the Emperor and his Mantriparishad, or Council of Ministers; led by a Pradhan Mantri, or Prime Minister. The Gupta Period, among other things, was marked by economic prosperity and stable governance. There was abundant food with crops harvested twice a year. Several industries flourished and goods were exchanged within the empire as well as exported to other regions around the world. Urban centres; like Ujjian, Prayaga, Banaras, Gaya, Pataliputra and Ayodhya; experienced bustling trade and prosperity with people maintaining a high standard of living. Law and order was maintained through the empire. The Gupta period thus is generally regarded as a classic peak and golden age of North Indian art for all the major religious groups. The vast majority of surviving works from the period are religious sculpture; mostly in stone but some also in metal or terracotta. These sculptures include beautiful depictions of Hindu Gods and Goddesses; large scale depictions of Buddha; and Jain tirthankara figures. The Indian numerals, the first positional base 10 numeral system in the world, was transferred to China and back to the Middle East, and continued to migrate for another few centuries before finally reaching Europe. Much of the mathematical achievements in the world have come about due to the Indian numeral system and the concept of zero that it uses. Aryabhatta, a mathematician and astronomer active during the Gupta Period, is usually credited with this invention. Aryabhatta made numerous other contributions to mathematics.