Settingsitting
I would like to ask eg mathanxiety and others whether studing maths at a good uni abroad means that WE is not necessary?
There is no such thing as unnecessary WE imo.
As a pp who is involved in university admissions also pointed out however, having some work experience (no capitals) that you found for yourself and kept at is possibly even more valuable. Or a commitment to volunteering (e.g. several years doing a regular and frequent stint at a homeless shelter).
My own DCs found plenty of opportunities for volunteering through our parish, which sponsors many volunteering groups that are always looking for hands. Examples are church decorating and gardening, home and garden maintenance for elderly parishioners, participating in the Appalachia Service Project, participating in a service project in Detroit, tutoring disadvantaged children in an after school programme, participation in a food pantry in an inner city twin parish, participation in a local homeless care organisation that shelters and feeds the homeless and manages transition to permanent housing, lots and lots of fundraising committee work, planning and execution of fundraisers there is lots more.. They start the teens on compulsory volunteering 
as part of prep for Confirmation, which happens at age 13/14. The hope is that teens will continue to volunteer even if the only reason to do so is to get brownie points for university applications. Nobody cares as long as what is needed gets done.
The objection (Hakluyt?) that some valuable experiences are beyond the reach of underprivileged students is an interesting one -- the Appalachia Service Project that two of my DCs so far have participated in required finding $350 each to cover their food, basic shelter and transport, and on top of that each student was expected to generate a few hundred dollars more for overheads. They had babysitting money and they also wrote to local offices, restaurants, and businesses of many different kinds asking for any amount of sponsorship. This was a 15 letters sent, 1 reply received proposition. Upon figuring out that her letters had not borne fruit, DD2 dressed herself up, armed herself with brochures and her sponsorship talk, took her spiel to the businesses themselves and spoke personally to managers and in some cases owners, with much better results. The group also ran car washes and bake sales and other fundraisers. Every element of all of this was a valuable experience. I did not contribute financially to any of the DCs' Appalachian Service experience.
If a prospective student of maths is applying to American universities he or she would find plenty of space on application forms to fill in experience outside of school or school-sponsored activities. American universities do not rely on academic results alone when choosing students, even those from overseas iirc.
And as asked many times upthread, what happens when the maths grad tries to enter the workplace but has no way of showing prospective employers how well he or she can work with others and not just on school projects?
Belloc
This thread is about work experience for school kids and pre university. Not the same thing.
They absolutely are the same thing.
Ability to work well with others is a really important element when it comes to discriminating among applicants, all of whom will be very well-qualified, academically speaking. Ability to be consistent and disciplined is another. You can only demonstrate these traits to a prospective employer by having a CV and references.
I know I would be inclined to pick DD1 who had both excellent results and a six-year unbroken work history under her belt upon graduation over someone who had 'merely' excellent results. On her CV by the time she graduated were three summers in a law office at 16, 17 and 18 followed by three years in a medium-sized museum (part time during term and full time during all breaks, in various roles including serving in and managing the little museum restaurant, plus admin and exhibit design) during her undergrad years, as well as Spring Break trips to Habitat for Humanity sites and contributing to building homes for the disadvantaged.
It would have been clear to any prospective employer that DD1 had basically spent 18 hours a day sleeping, going to class and the library (her degree result would have shown that she put her time there to good use) and working at her job, 362 days a year for four years running. She had three rounds of interviews to battle through to get her great job offer, even with an excellent result in economics from a very well regarded university and her excellent CV. The pool her employer recruited from consisted of graduates of excellent universities with results above a certain benchmark.
Belloc
He doesn't need a job for work experience nor for a CV. And he already earns sufficient money to cover his small costs. So he isn't looking for a job. You are really quite maddening.
I beg to differ. Your DS needs teen and student work experience for the CV he will be sending to prospective employers upon graduation, be it ever so humble. So he needs a job or preferably two. The money is immaterial. The sort of work is also immaterial. What is important is that he has a decent CV upon graduation, not merely a parchment, and people willing to provide excellent references.
Otherwise, with the best will in the world, when he hits the recruitment pool, the best he will be capable of is looking like an entry-level graduate who has nothing against the principal of working.
I wish him luck with that. He will be going up against people like my DD1, DS and DD2 for his big break.