Depending on how you translate his name, Al-Karaji (which is a placename) came from Iran or a suburb of Baghdad. But we know that most of his life was spent in Baghdad.
His work is controversial: for some he merely reworked old problems, while others argue that he made a unique contribution to mathematics. He still used words as his predecessors had done, but many argue that Al-Karaji helped faciliatate the shift in mathematics from the geometric basis of the Greeks. He moved on from the geometrical algebra of al-Khwarizmi and placed arithmetical operations at the heart of algebra as it is today.
He was also believed to be the first to discover the law of formation of the binomial coefficients. This means he proved what we call Pascal’s triangle many centuries before Pascal did.
After setting up a school of algebra in Baghdad which flourished for many years, al-Karaji retired from mathematical life. He went to the mountain regions and spent the rest of his years concentrating on practical problems like drilling wells.