[3] Joshi is also the Vice-President of the International Mathematical Union, and is the first Australian to hold this position.

I had the freedom to explore all day long so long as I went to school and that's what I actually seek every time I look at mathematics; it's an adventure, an exploration, forging new paths into territories nobody else has looked at before.Joshi attended Fort Street High School and gained her Bachelor of Science with honours in 1980 at the University of Sydney, and her PhD at Princeton University under the supervision of Martin David Kruskal.

[7] In 2015, Joshi co-founded and co-chaired the Science in Australia Gender Equity (SAGE) program, which works to increase retention of women in STEM fields using Athena SWAN principles.

[7] In 2012, Joshi became a Georgina Sweet Australian Laureate Fellow, which involves the five-year project, Geometric construction of critical solutions of nonlinear systems.

She was recognised in the October 2019 NSW Premier's Prizes for "Excellence in Mathematics, Earth Sciences, Chemistry or Physics".