A number of famous names are among the 13 firms in the running to design new galleries at London’s Science Museum as the site looks to evolve.

Zaha Hadid, Amanda Levete and Haworth Tompkins are all vying for a shot at shaping the two new galleries – a maths area due to open in 2016 and a medicine offering to follow two years later.

Hadid has been shortlisted for the maths gallery along with five others including Hugh Broughton and Carmody Groarke. The new mathematics gallery will bid to illustrate the subject’s vital role in all aspects of life, recounting stories of mathematicians, their tools and ideas, and the wider world their work has underpinned, from the turn of the 17th century to the present.

The brief for the medicine galleries is to “create the world’s greatest centre for the understanding of medicine through a ground-breaking suite of new galleries,” set to be double the size of the existing offering. The galleries will reveal personal stories about how our lives have been transformed by changes in medicine and health over the last 400 years. Seven practices have been shortlisted for the medicines galleries, including Rick Mather and Wilkinson Eyre.

Appointments for both projects will be made in early August.

Mathematics gallery shortlist:

Casper Mueller KneerZaha Hadid

Hugh BroughtonCarmody Groarke

Adam RichardsUniversal Design Studio

Medicine galleries shortlist:

Muma AL_A

Rick MatherHaworth Tompkins

Caruso St JohnGareth Hoskins

Wilkinson Eyre