There are numerous essays and newspaper blurbs lamenting the poor state of mathematical education in the US. Here is a typical example: Presidential panel bemoans state of math education.

What I see as the problem is that advanced mathematics is introduced in language that is unfit to inspire any but the few that were genetically destined to be mathematicians (or physicists).

Ask a recent college grad what an Eigen value or Eigen vector is. I give you 100:1 odds you’ll get a blank stare. Okay now ask them to read this explanation from a popular Math web site. I bet their face will be even blanker. Now ask them to read this wonderful little explanation. Chances are the lights came on.

This is not to say that the later explanation will allow a person to do the math. But this is certainly where Math education, even at the highest levels, should begin. Illustrate why the problem is important, give a sensory picture to go along with the abstractions. Some might believe that this is how most Mathematicians teach but that is simply not the case. Mathematics is a very macho profession and many mathematicians believe its beneath them to offer intuition prior to rigor. The sad truth is many of them could not come up with compelling intuitive explanations even if they wanted to. It was not the way they were taught either.