Maths and science experts say that the lack of geometry study in school sixth forms means that teenagers studying science and engineering courses at university are floundering.
A report for The Royal Society puts most of the blame for a "drastic reduction" in the study of shape, space and measures on the problems of recruiting and retaining maths teachers.
At the beginning of the year, there were 410 maths teacher vacancies in England and the latest teacher training figures show that 86 of the 96 maths courses have empty places.
Professor Adrian Oldknow, from University College, Chichester, said:
"Architecture to drug design and the human genome requires a thorough understanding of geometrical principles but many students struggle to understand shapes, even after gaining A-levels. But he also criticised ministers' "obsession" with mumeracy. "The Government needs to recognise there is more to maths than numbers," he said.
Geometry at AS and A-level has limited compulsory study of lines and circles, some trigonometry and basic work with vectors.
The Royal Society report claims some teachers have a gap in their geometry knowledge, particularly non-maths graduates forced to teach the subject because of staff shortages.
And it says computer programmes with the ability to revolutionise the teaching of geometry were underused because of lack of teacher skills.