[QuantumRoar]

The questions are actually pretty clear. The problem is that you lack a general understanding of mathematical concepts and therefore you don't know what to do with it. But that's fine and that's actually what the exam is for, i.e. only those may pass who understand these things.

>This is probably not a view shared by many here, but if math problems were to be communicated in more natural ways, far more people would be interested in the sciences.

I would argue the opposite. If more problems could be as well posed as mathematical problems, we wouldn't have people bullshitting their way through arguments that are in dire need of some scientifical rigor (see climate science, psychology, and other disciplines that are too complex to isolate phenomena completely). You can't handwave your way through a math exam and you shouldn't be able to do it in other fields of science.

[demonshalo]

> I would argue the opposite. If more problems could be as well posed as mathematical problems, we wouldn't have people bullshitting their way through arguments that are in dire need of some scientifical rigor (see climate science, psychology, and other disciplines that are too complex to isolate phenomena completely). You can't handwave your way through a math exam and you shouldn't be able to do it in other fields of science.

Amen. I have been saying that for years. But I think you misunderstood my original post.

I am all for 100% scientific rigidity and less bullshit in society. But what you seem to classify as "clear" is not-so-clear to others. It's actually about how condensed the information is in each question. In order to unpack those questions, you need years of experience within that field in order to get anywhere.

I bet you anything that each one of these questions could be posed in a different, yet still mathematical, manner that would make most non-mathy people (such as myself) at least understand the gist of what is being asked. But that is not something mathematicians are interested in. Which is what I was trying to say.

[tankenmate]

The issue is that each provable discovery in mathematics is named; it has to have a unique name. These discoveries are exact with at least one proof for their validity and for their limitations and assumptions; all that information is tied up in a name, say for example eigenvalues. These proofs are built on top of previous proofs (which of course are named as well), names and phrases built upon each other.

So this ever growing collection of proofs and names is an accretion (or in our moments of grander hubris a pyramid). What you are asking for is the tip of the pyramid (with its wonderful view) without the stones below, in effect what you are asking for is magic, a stone floating in the air with nothing to support it.

[demonshalo]

>in effect what you are asking for is magic, a stone floating in the air with nothing to support it.

Isn't that how we all learn math? in fact, isn't that how we all learn anything really?

When you are in 2nd grade, you don't start by learning about Riemann hypothesis. You start at the tip of the pyramid and drill downwards into complexity.

I am not asking for something magical here. I just wish that more math was communicated in a simplified manner that would help bring in people from all walks of life into the world of science.

[tankenmate]

The simple way is to follow the steps, start at the bottom and work your way up. Eventually you will get to the point where it makes sense. The terminology and the understanding is opaque to a neophyte because ideas are non-trivial.

Any sufficiently advanced technology is indistinguishable from magic -- Clarke

[bmuon]

> You can't handwave your way through a math exam

This reminds me of a calculus exam a long time ago. One of the problems was "given the ellipsoid define by formula ______ and a certain line, find the point in the line closest to the ellipsoid". The goal for this problem was for us to use Lagrangian multipliers and I hadn't studied that one particular subject. However... They made a mistake writing the exam. The ellipsoid was symmetrical, its intersection with the xy plane was a circle and the line was also in the xy plane. I only needed high school math to successfully handwave it. Lots of facepalms from my TAs.

[tonyarkles]

You've just described the vast majority of my experiences in my EE E&M class. Very hard multi-variate calculus problems, but as soon as you can find the symmetry they get dramatically easier.