A-levels should be axed in favour of a new "baccalaureate"-style qualification that requires teenagers to study maths and science up the age of 18, experts have said.
Too many people in the UK are "mathematically and scientifically illiterate", according to the Royal Society, the UK's national academy of science.
In a new report, it warns that there is persistent lack of youngsters taking science and maths-based courses past the age of 16 across the UK at a time when the nation needs more workers with skills in these areas.
A million more science, technology and engineering professionals will be needed by 2020, the study says, but the UK is falling far short of this target.
The major new report, drawn up by a committee of leading scientists and mathematicians, calls for radical changes to the UK's education systems.
Sir Martin Taylor, chair of the Royal Society's vision committee said: "The current education system will not meet the needs of the UK over the next 15 to 20 years, so we need to start building a stable education system that produces scientifically literate citizens now, before it is too late."
He added: "We all know that we have significant problems with the demand for science, mathematics and engineering skills and their supply. Employers tell us this. We know that only one in eight 16-year-olds goes on to do A-level mathematics. That's just not enough for a vibrant knowledge economy."
The leading mathematician later said: "We should bear in mind for instance that one million new science, engineering and technology professionals are going to be needed by 2020 and at the current rate we're falling 40,000 shy of this each year."
"If we get this right then we will continue to contribute to scientific discovery and technological innovation," Sir Martin said.
"The UK will provide a leading role in providing solutions to some of the great global challenges that the world is now facing - things like climate change, food and energy security and the ageing population issue."
The report sets out a "road map for radically transforming our education system" with a particular focus on maths and science over the next 20 years.
It calls for the creation of tough new courses and qualifications for sixth-formers in science, maths, engineering and technology (STEM) that will interest teenagers who want to study arts and humanities subjects and those who are training in the workplace.
A-levels should be ditched in favour of a "baccalaureate" system with science and maths at the centre, it suggests.
Under the current system, sixth-formers taking A-levels usually study three or four subjects. A baccalaureate system, such as the International Baccalaureate, tends to be broader - typically involving studying around six subjects from different areas.
Sir Martin said: " All students should study mathematics and science to the age of 18 alongside the arts and humanities as part of a new baccalaureate that provides a broad education for all.
"We believe that this means changing our current educational framework, gradually replacing the current A-level system with a broader framework that places emphasis both on vocational and academic learning."
The committee's vice-chair, Professor Dame Julia Higgins, said: "Eventually, we believe that there should not be A-levels, there will be something like a baccalaureate.
"What we're looking at is a broad exam framework, with specialist subjects."
The report calls for every primary school to have access to at least one specialist teacher in both maths and science, and argues that all secondary school lessons in these subjects should be taught by suitably qualified specialists.
At the same time, all school and college teachers should be required to work towards a teaching qualification to ensure they are experts in teaching as well as their specialist subject.
The study also suggests that new independent expert bodies should be set up in England and Wales, and existing structures in Scotland and Northern Ireland strengthened, to oversee the curriculum and exams in STEM subjects.
The report comes amid major reform of A-levels as part of a bid by ministers to toughen up the qualifications, and continuing moves by Government to encourage youngsters to continue studying maths and science past GCSE.
A Department for Education spokeswoman said: "We agree with the Royal Society about the importance of science and maths. That is why we have already announced major reforms to the qualifications system which will mean thousands more young people are studying courses in maths, sciences and vocational education that will give them the chance to compete for good jobs."