The PM's senior adviser has called for changes to how government works, saying there are "profound problems" with how decisions are made.
In a blog post, Dominic Cummings said the civil service lacked people with "deep expertise in specific fields".
He said he wanted "weirdos and misfits with odd skills" to work in government.
But a civil servants' union said currently staff were recruited on merit and "because of what you can do, not what you believe".
The union also said recruiting world-class experts is hampered by the "government's failure to pay a market rate".
In an unusual move, Mr Cummings also called for people keen to work in Downing Street to get in touch with him via a private Gmail address.
The former Vote Leave campaign director said he wanted to hear from "an unusual set of people with different skills and backgrounds", some to work as special advisers and "perhaps some as officials".
He said No 10 was keen to recruit data scientists, software developers and economists to improve the performance of government.
In his blog, Mr Cummings added:
- The aim of the new recruits is to improve performance but also make Mr Cummings himself "much less important — and within a year largely redundant"
- A junior applicant will become his personal assistant for a year - a role which will involve "very interesting work and lots of uninteresting trivia that makes my life easier which you won't enjoy". The job will be so exhausting that "frankly it will be hard having a boy/girlfriend at all"
- He also urged against applications from "confident public school bluffers" and added anyone who plays office politics "will be discovered and immediately binned"
- He wants to hire "some true wild cards, artists, people who never went to university and fought their way out of an appalling hell hole"
Mr Cummings added that the Conservatives' 80-seat majority meant ministers would try to solve political problems without worrying about "short-term unpopularity".
"The point of this government is to do things differently and better and this always looks messy," he wrote.
"We do not care about trying to 'control the narrative' and all that New Labour junk."
He added that officials should be encouraged to stay in their roles for longer so that they are able to build up expertise in particular policy areas.
"Shuffling some people who are expected to be general managers is a natural thing but it is clear Whitehall does this too much," he said.
"There are not enough people with deep expertise in specific fields."
'Pay restraint' criticised
Responding to the blog, the FDA union, which represents senior civil servants, said Mr Cummings had not clarified how new recruits would be selected or what their role within government would be.
Dave Penman, the union's general secretary, told BBC Radio 4's Today programme: "The civil service is recruited on merit, it's a really fundamental principle.
"You are employed in the civil service because of what you can do, not what you believe."
"If you surround yourself with people who are recruited simply because they believe the same as you believe, and whose employment is at your behest, is that the best way for the civil service or advisers to speak truth unto power?
"I don't think it is, and I think some of those approaches are quite dangerous as well."
In a statement, he added: "It would be ironic if, in an attempt to bring in radical new thinking, Cummings was to surround himself with like-minded individuals - recruited for what they believe, not what they can do - and less able to provide the robust advice a minister may need, rather than simply the advice they want."
Mr Penman also said senior officials moved between different jobs in an effort to boost their pay after a "decade of pay restraint" within the civil service.
Mr Cummings's desire to recruit experts might prove difficult because of pay rates, he added, which he said were "typically half of those paid elsewhere".
"All senior civil service roles are already open to external competition, yet time and again, government's failure to pay a market rate restricts the pool," he added.
"There's no word on this in his blog, or on addressing the longer term pay restraint that has created these issues."
It comes after Rachel Wolf, who co-wrote the Conservatives' election manifesto, said "seismic" changes to the civil service were being planned by No 10.
Writing in the Daily Telegraph, Ms Wolf said Mr Cummings believed changing how government works was a "prerequisite" to delivering on promises made to the voters by the Conservatives during last month's election campaign.
She said officials should get more training in science-related skills, and "reorient" policy decisions towards the public rather than "special interests".
She also added that regularly moving civil servants between different departments "kills institutional memory and expertise".