Is it normal for a society to no longer require proof? Of anything? Is elimating the maths next on the list?

Australian syllabus for arithmetic - preparation required before highschool.
There are slight variations between the States, but the following applies for all publicly-funded (free) and private schools.

Kindergarten
preschool: Counting objects, fewer and more, names of colours, inside and outside, longer and shorter and more.
foundation: Comparing numbers, counting by tens, names of shapes, above and below, classify and sort and more.

Primary school
age 5, year 1: Counting, sequences, number patterns, adding and subtracting, comparing, fractions, measurement, telling time, money.
year 2: Place-values, fractions, data and graphs, probability, 2 & 3-dimensional shapes, geometric measurement, mixed operations, estimation, multiplication & division

The subsequent years build more detail and complexity into the basic operations until by year six, just before high school, a kid is also learning percentages, exponents, number theory, fractions and mixed numbers, calculating & plotting co-ordinates on planes, basic statistics (mean, median, mode & range), calculating probability and more.

Actual levels of outcomes for this syllabus vary greatly, with the most striking difference in results being socio-economic area and parental attitude and support for school.

When the American Naplan testing system was brought in, standards began to drop dramatically. Most teachers agree that the problem is that too much time is spent preparing for the tests, and not enough time in teaching the syllabus itself. There is a huge amount of anger and controversy about it in four-way disputes between parents, teachers, department of education, and government. This post was edited by Benedict Arnold at October 4, 2016 10:01 PM MDT

I like proof.
Unless something is reliable and sound via facts or logic, there is forever a shadow of doubt and skepticism in me about whether something is real.
It's one reason why I am 99% atheist: something that requires faith just can't be real for me.
As a dilettante amateur, I love science, philosophy, psychology, anthropology, comparative religion, the arts, literature, polemics...
but even when people are sharing intangible abstract ideas or the depth of their feelings and experiences - facts and proof make all the difference. This post was edited by Benedict Arnold at October 4, 2016 10:16 PM MDT

Thank you Hartfire for explaining the Australian system.

It goes into far more advanced topics at an early age than anything I experienced in the UK system in the 1950s-60s; I don't know how maths is taught now as I've no children of my own.

In that system, it was Arithmetic, not Mathematics, right up to the last year of primary school (aged 10-12). Once in either Grammar School ("public", i.e. private) or state, or in the more vocationally-minded Secondary Modern Schools, the syllabus expanded rapidly, and reached the General Certificate of Education O[rdinary]-Level exams at age 15-16. Mathematics at this level included Calculus and Classical Geometry. Those who stayed on in the Sixth Form specialised in 3, sometimes 4, subjects only for 2 years to the GCE A[dvanced]-Level. The A-Level course in any subject, followed its corresponding O-Level in advancement, and the A-Levels were intended as foundation courses for Degree or similarly higher-level education.

This was all swept away in the 1970s in favour of the "Comprehensive System" which thought every child should be taught to equal, hence lower, level, standard irrespective of actual ability. This was to suit Labour Party dogma, with its heavy insistence on theoretical "equality" more than actual education, and one effect is that the A-Levels were retained but the smooth advancement through school was broken. As I found when I took first the standard school Maths then A-Level, on part-time adult-education courses, about 20 years ago. It did however remove a mistaken but very common perception of "failure" by those who could attain "only"  Secondary Modern education - the name could not have helped, with its unfortunate double meaning.

You mention the problems of tests. This is a big problem in the UK too, although I do not think they are based on US practice. It has put teachers under enormous strain, leaving them feeling they are there to satisfy Department of Education "targets", with teaching children being a means to artificial tests and targets set by non-teachers, rather than to the children's futures.

UK education has also been through assorted, pointless experiments; but UK Governments love to tinker with public services they don't really understand, so we think they are Doing Something Useful! My brother tells of being unable to help his children understand long-multiplication because he had been taught the direct way, whereas the schools had adopted a very odd, indirect method. I think they'd done similar to ordinary "adding sums", teaching a clumsy left-to-right alternative to the simple R-to-L , units-tens-and-upwards route. 

I found the Maths syllabus very different: the school-level maths course had no theorems, no calculus, only rudimentary trig, and a subject totally new to me, matrices.

I failed utterly to understand matrices because they are taught as purely-abstract sets of simple sums with no definitions for the various terms, and no obvious purpose or even any link to any other branch of mathematics. I still fail to understand why matrices are even taught in schools because they are an arithmetical tools for professional mathematicians carrying out very advanced, very large-scale scientific calculations or certain computer programming applications - but I did discover one of their 19C developers was Prof. Charles Dodgson, aka the children's author Lewis Carroll!  

Sadly, now there is a lot of public concern over low average attainment by British school-children, with many leaving school barely literate or numerate. There are probably many reasons, but I wonder how much all these experiments and initiatives have to do with it...

Eliminating mathematics? Intriguing idea - surely the maths would still exist, even if no-one knew that. For example, a circle of diameter 1 metre would still have a circumference of 3.142 metres, even if no-one knew how to prove that. More philosophically, when Isaac Newton laid down the foundations of Mechanics, he did not "invent" the acceleration due to gravity of a body falling to the surface of the Earth. It has existed on Earth ever since the planet formed, but had to wait until Newton analysed it for anyone to know its value. 

Even more intriguing is the quote Sharonna gives. I'm not sure on whom it reflects the worse though: the <49% of students who can't recognise a set of numbers and symbols as mathematics, or the Undersecretary of Education! And if you can't look at a map of the Earth and recognise it as the World, there's no hope!  It does though, reinforce my suspicion that the US education system breaks mathematics into separate curriculum fields, rather than treating it as a single syllabus within the curriculum, with various, often inter-related, topics within that syllabus. For example, you cannot split Algebra from Trigonometry and Calculus, because you need algebra to express and manipulate problems in those other areas, and the trigonometrical equations themselves have their own calculus functions. I have asked about this but no-one seemed sure.   

I use Answers.com sometimes, and among the many questions obviously from schoolchildren trying to use its Mathematics section to cheat in their homework, was one question, "What would the world be like without trigonometry?" Some ignoramus had answered with the one word "Awesome", to which I pointed out that "awesome" is lazy slang that might mean 'awe-inspiring' but there meant 'awful', before explaining why: for one thing, without Trigonometry we would not be able to talk about it on-line - we would not have mains electrical supplies let alone electronics!

Yet even if you knew no trigonometry, provided you have a rule and protractor you can still prove the three basic ratios. They'd still exist!

And yes - we all live in a world that still needs proof in most areas of life - whether mathematical or not.