Education Secretary Michael Gove says he would like to see the "vast majority" of pupils in England studying maths to the age of 18 within a decade.
He said there were "strong arguments" for "making certain subjects compulsory for longer".
Mr Gove said he did not want to prejudge a national curriculum review, but also suggested that pupils study calculus and algebra at younger ages.
He said the UK was lagging behind its global competitors in the subject.
Speaking at the Royal Society, the education secretary said he was concerned about a post-16 "maths gap", where even pupils who did well at GCSE have forgotten what they knew by the time they start university or work.
The "maths gap" that most pupils now experience after the age of 16 means that even those who did well at GCSE have forgotten much of the maths they learnt by the time they start their degree or a job.
He said not enough students had sufficient maths to be able to study subjects such as physics, engineering and social sciences at university.
"I think we should set a new goal for the education system so that within a decade the vast majority of pupils are studying maths right through to the age of 18," he said.
"Of course, I am not prejudging the [curriculum] review. But there are strong arguments for introducing concepts earlier, for covering some topics more thoroughly, and for making certain subjects compulsory for longer."
Mr Gove said it was possible that England could follow East Asian countries in bringing in "much greater focus on fundamental number concepts, fractions and the building blocks of algebra in primary school".
He said he thought it "genuinely bizarre" that so many children left school "essentially unaware of the development of calculus".
Mr Gove said the review of the national curriculum that the government had commissioned would "set out the essential knowledge that children need to advance in core subjects", but not be "an attempt to prescribe every moment of the school day".
He said it would not spell out how issues and controversies, such as embryo experimentation and energy conservation, should be tackled.
Filling the national curriculum with topical subjects "only encourages a constant tinkering and rewriting which we should stop," Mr Gove said.
According to the Guardian newspaper, the head of the curriculum review panel, Tim Oates, said earlier this month that climate change should not be included in the national curriculum.
Maths is currently compulsory between the ages of 5 and 16.
Mr Gove has already said that teenagers who fail to achieve C grades in English and maths GCSEs by the age of 16 should continue to study the subjects.
Dame Athene Donald, Chair of the Royal Society Education Committee, welcomed Mr Gove's comments.
"The Royal Society's most recent State of the Nation report identified a significant shortage in the numbers of students studying mathematics past GCSE, given the needs of higher education and the economy, and advocates that all students should study some form of mathematics to 18," she said.