The government is to spend an extra £600m on building 100 new free schools in England over the next three years.
The BBC's Ben Wright said the money will not come from the existing education budget, although the Treasury will explain the source in Tuesday's autumn statement on the economy.
Some 12 selective specialist maths schools will be among the 100 schools.
Free schools are run by independent education providers that are funded directly by central government.
They can be set up by groups of parents, teachers, charities, businesses, universities, trusts, religious or voluntary groups.
They are established as academies, independent of local authorities and with increased control over their curriculum, teachers' pay and conditions, and the length of school terms and days.
The specialist maths schools being proposed would be for pupils aged between 16 and 18.
The schools, which will be the subject of a special application process outside the regular free school application process, will be connected to strong university maths departments.
Ministers say maths is a "fundamental strategic priority in education", adding that these schools are not being created just to accelerate pupils through the normal exams faster.
The schools will have their own curricula and are intended to produce outstanding mathematicians who can work in digital technologies, produce breakthroughs in applied maths or develop innovative companies.
Chancellor George Osborne is expected to announce the new free schools when he delivers his autumn statement on the economy on Tuesday.
The autumn statement replaced the pre-Budget report, which under the previous Labour government was seen as a mini-Budget in which draft tax and spending decisions were outlined.