"You don't actually need to know a lot of the groundwork and the basics to appreciate the exciting bits of mathematics. The more technical things are still awes

"You don't actually need to know a lot of the groundwork and the basics to appreciate the exciting bits of mathematics. The more technical things are still awesome as tools and are necessary in some places. But luckily I am usually with other people who do know that stuff." How about this not being an either/or? Anything that exposes more people to the beauty and power of the maths, and convinces some of them to more of the "technical things" is goodness, IMHO.