Wow, that conclusion is crap. Mathematics is one of the most open fields of science. There are excellent free resources for learning math, even cutting edge research is usually easily found for free, the scientists are very open to sharing ideas. Anyone who has the necessary talent can learn any part of Mathematics they fancy.

Large portions of the worlds children grow up with barely primary school level education and an economic reality that requires them to go into work as soon as possible.

When would they have the time and money to set aside to get deep into a subject that most of them do not have the academic background to see the value of?

Yes, everyone could learn mathematics. Just like everyone could get rich and go into space. It's just that for a huge proportion of people the pre-requisites are not there.

> Yes, everyone could learn mathematics. Just like everyone could get rich and go into space.

Ah the false analogy[1], we meet again. You don't really believe this do you? I mean you could make the same argument about gardening. Literally anyone can learn at least basic math, most people just don't have the inclination.

1) http://onegoodmove.org/fallacy/falsean.htm

While not denying that access to academic math is a privilege, we should also notice and be clear that math is used by many people without formal training. People manage their money, for instance, and often learn sophisticated methods for accounting and calculation via apprenticeship. People build physical objects using measurements and geometry and, again, understandings of mechanics gained through apprenticeship. The formal language of math as written down in books is available to only a fraction of the world's population, but many people do use economic and maker math in their everyday lives.

Right and many proofs math textbooks are so old that anyone can print them, so they're actually much more available than say a chemistry textbook.

Indeed. I've learned more mathematics from free online resources (IRC, Math.SE, nLab, papers available online) than anywhere else. In most other fields, when you pester experts to share their knowledge, the very first thing they first ask you is how much you're going to pay them. In mathematics, the only real bottleneck for the transmission of knowledge is my own ability to assimilate it.

I feel particularly deceived about this state of affairs because my parents paid a lot of money for my formal education (school, university), and I got significantly less value from it than from people simply willing to share their knowledge for free.

Formal education is like eating a steak with an eyedropper.

Those whom I get help from often have a formal education in mathematics, so formal education can be good. But most of the time it isn't.

I've thought extensively about this and one of the conclusions I've reached is for example:

Imagine me or someone else that was never part of the math research establishment came up with the exact same proof Perelman came up with. Ipsis verbis.

You can rest assured that at least the slack that they cut him on sketchy details would not be extended to an outsider. (In a way the Yau debacle was a manifestation of this)

There are a few examples of this already in somewhat obscure fields.

That's assuming anyone would even give the proof the time of day.

the evidence given in the article doesn't directly support this, but the author may have tried to get at the "[those that have] the necessary talent can learn any part of maths" statement you made. Without exposure to and engagement with a comprehensive education in mathematics (even just basic numeracy and arithmetic), it's incredibly difficult to teach oneself any given mathematical concept. Access to maths educational resources is ostensibly unrestricted, as (at least in the US) library cards are free of charge and the internet is readily accessible there; however, one can easily point at the many banes of lower-income households as immediate barriers to receiving any sort of education, either autodidactic in nature (i.e. sitting in a library with an geometry textbook) or through public schools.

It might be worth thinking in this "math for and from the elites" mindset when describing public aversion to the subject. Seeing it as beyond oneself or not relevant to one's life lends little towards anyone's desire to learn anything about it.

It's easy to say "why don't they just do it," with some diffuse definition of "they" in mind, but even the most basic things can be hard to get for the poor. A proper maths education is one of them, I think.

He's not comparing math to other academic fields, he's comparing it to the most realistic alternative for most people, which is working a garbage McJob in which math isn't relevant to their lives at all. There's a lot of privilege involved in burying your head in books, no matter what the field, barring a few obsessive prodigies who live in public libraries and have extremely supportive parents.

Then why point out Math? Everything is inaccessible to people who work all day to get by. Art, Sports, DIY, whatever, not just STEM.