This question assumes that pre-calculus, probability & statistics ought still be taught in high school, and involves only those who won't need university-level math. Can studying Logic also teach you the non-quantitative benefits cited below (e.g. thinking, pattern searching, problem solving)? If not, why are they exclusive to studying math?
Mathematics should be a tool for increasing one’s thinking power but for many children it is just a set of rather pointless rules for manipulating symbols.
It is therefore good for the health of a country if its population has high standards of mathematical literacy: without it, people are swayed by incorrect arguments, make bad decisions and are happy to vote for politicians who make bad decisions on their behalf.
But why should maths be privileged above learning a foreign language or history? Does everyone need to know what a cosine is if the UK is to have a brighter future? Does the success of our economy depend on every citizen feeling confident factorising a quadratic equation? It may come as a surprise to you that I don’t think so, but I’m still a big believer in teaching maths to 18. What will be important is making sure that the maths we expose students to is both relevant to their future and the future of our country.
What many are not aware of is that maths is so much more than the technical cogs that currently form the backbone of the curriculum. It is about pattern searching, extended analytical and logical thinking, problem solving. I am just embarking on making a new programme for the BBC about the beauty of algorithms. Many of the best algorithms contain no numbers or equations at all, but are full of mathematical thinking. And it is those algorithms that are creating efficient approaches to a whole range of business solutions, from the distribution of goods from supermarket warehouses to decisions about flight schedules at Heathrow airport.
What about those humanities students or creative artists or vocational students who might argue that they will never need more maths? I believe that even these students, if exposed to the right curriculum, will recognise the benefits of more maths. I am doing an event with the Booker-winning novelist Ben Okri at the Hay festival next month about the connections between mathematical proof and literary narrative. As a novelist, Okri is the first to recognise the importance of a logically consistent narrative to the success of a novel – but also the wonderful benefit that a mathematical sensitivity to pattern and structure can give novelists as they create a narrative arch. From musical composition to carpentry, from street art to journalism, a mathematical mindset potentially gives one an edge.
This Reddit comment affirms that math is logic:
And mathematics is philosophy, it's just a lot less "wordy" and rather brought to the meta level. I mean just look how complicated you have to explain a valid and a sound argument and how nicely you can calculate with them in the boolean framework.