Ayse Soysal was born on June 24th, 1948. She graduated from the American College for Girls in Arnavutköy, Istanbul in 1967 with first-place honors. She then went to Robert College, from which she received a BS degree in the double-major program in physics and mathematics in 1971, again as the valedictorian in her graduating class. She received a travel grant from the Fulbright Commission to do graduate work in the University of Michigan, Ann Arbor, where she received an MS in mathematics in 1973 and a PhD in mathematics in 1976.

In 1973 Ayse Soysal became the first Turkish student to be awarded with the Betsy Barbour prize, a prestigious scholarship awarded to Asian women doing graduate work in the University of Michigan. After completing her dissertation in group theory, Soysal returned to Turkey and joined the staff of the department of mathematics in her alma mater, which had transformed itself into a university called Bogazici University during her absence. During her tenure as a faculty member in this university, she was promoted to the position of associate professor in 1981 and became a full professor in 1991.

While working in Bogazici University, Ayse Soysal served as vice dean of the School of Arts and Sciences from 1984 to 1988, as the chair of the mathematics department from 1991 to 1992, and as the dean of the School from 1992 until the year 2004, when she became the president of the university, a post she held until 2008. She was the the first woman to be appointed to that position.

Ayse Soysal served on the Science Board of TÜBİTAK (Scientific and Technological Council of Turkey) between 2008 – 2012, and on the board of the Higher Education Council of Turkey between 2009 – 2013.

Soysal was a board member of the UNESCO Turkish National Commission between 1993 and 2000, member of the advisory board of the Turkish chapter of the Open Society Institute between 2004 – 2006, and member of the board of advisors of the Duke University Islamic Studies Center between 2008 – 2014. Presently she is an honorary member of the Turkish Mathematical Association, member of the board of trustees of the Boğaziçi University Foundation, member of the board of advisors of KAGIDER (Association of Women Entrepreneurs), member of the Galatasaray sports club, and chair of the board of advisors of the International Hrant Dink Foundation.

Soysal has taught courses in a wide range of topics, including group theory, ring theory and theory of fields, vector spaces and modules, topology, algebraic topology, group cohomology, differential equations, linear algebra, matrix theory, real analysis, complex analysis, probability theory, commutative algebra, geometric algebra, and group representations. She received the excellence in teaching award from Boğaziçi University in 2012. In 2014 she chose to retire from her alma mater, Boğaziçi University, after more than 40 years of service. Soysal is presently working as a part-time faculty member in Istanbul Şehir University.