Education in England is no better than mediocre, and billions of pounds have been wasted on pointless university courses and Sure Start schemes for young children, Michael Gove's special adviser has said in an outspoken private thesis written a few weeks before he is due to step down from his post.

Dominic Cummings, the most influential adviser to the education secretary in the past five years, also argues in a revealing 250-page paper that "real talent" is rare among the nation's teachers – and, eye-catchingly, says educationists need to better understand the impact of genetics on children. The adviser, known for making fierce demands of civil servants, writes that the endgame for the Department for Education should be to reduce its role to acting as accountants and inspectors, employing hundreds and not thousands of civil servants – and creating an environment in which private and state education would be indistinguishable.

The Cummings manifesto claims that "the education of the majority even in rich countries is between awful and mediocre", and that the quality of maths education, in particular, is poor.

"In England, few are well trained in the basics of extended writing or mathematical and scientific modelling and problem-solving," he writes.

One of the best-known and most controversial of many special advisers working in government, Cummings is due to leave Gove at the end of the year. He worked in the department for two years, having previously advised Gove before the election, although his appointment within the department was initially blocked by David Cameron's then director of communications, Andy Coulson, who regarded Cummings as untrustworthy.

Labour's Sure Start programme, aimed at pre-school age children, is sharply criticised by Cummings, who says there is little evidence for its practical impact.

He writes: "There is great political pressure to spend money on things like Sure Start, but little scientific testing, refinement and changing budgets to reinforce demonstrated success. Therefore billions have been spent with no real gains."

General government spending amounting to half a trillion pounds a year is of dubious value "of which vast amounts are wasted and it could easily divert a few billion pounds if it could prioritise to strengthen world-class humanities, maths and science departments". He questions the relevance of many degree courses, writing: "In many third-rate higher education institutions there is a large amount of 'social science' work in economics, anthropology, sociology, literary theory and so on of questionable value both from an intellectual perspective and from the perspective of students, jobs prospects."

Students, too, are criticised for not having enough work to do: "Undergraduates should be required to spend more of their time studying," he says. "The days of an essay or two per term should end."

In one of the most controversial passages of the thesis, Cummings maintains that individual child performance is mainly based on genetics and a child's IQ rather than the quality of teaching.

He says: "There is strong resistance across the political spectrum to accepting scientific evidence on genetics. Most of those that now dominate discussions on issues such as social mobility entirely ignore genetics and therefore their arguments are at best misleading and often worthless." He claims research shows that as much as 70% of a child's performance is genetically derived.

He denies his views are embarrassing for either Gove or the government, but says he wants to see an attempt to build in a more scientific way to develop a more ambitious education and training system.

But his views on genetics, government inefficiency, the examination system and the quality of teaching will confirm the worst fears of some in the education system about the underlying direction of Gove's reforms.

Cummings is highly critical of the quality of teaching, writing: "While some children will always be blessed by a brilliant teacher, by definition that is not a scaleable solution to our problems: real talent is rare and mediocrity is ubiquitous."

He argues that chains of schools with better management may represent the best way to improve teaching, as well as abandonment of responsibility for teacher training by the department.

Cummings sets out what appears to be an end point to the first wave of Gove's reforms, saying: "Hopefully, it will push the English system towards one in which the state provides a generous amount of funding per pupil, which parents can spend in any school they wish, breaking down the barrier between private-state school, while the Department for Education does little more than some regulatory accountancy, and due diligence functions."

• This article was amended on 11 October. The original referred to half a trillion pounds being spent on higher education instead of "general government spending". This has been corrected