Behind the Door: End of the Quest?

Question

Once again, the door opens and reveals a medium-sized dark room. "What? No more doors?" you soliloquize. Maybe you are near the end of your quest for the secrets of the universe and ultimate power......

As look around, an ornate box catches your eyes. Immediately you try to reach for the lock... but there is none. Instead there are two button, labelled $\boxed{{``\textbf{This Is True''}}}$ and $\boxed{``\textbf{This Is False''}}$ in golden letters. On the side of the box, you find an inscription:

Welcome, human!

Inside this chest lies the ultimate secret behind universe, that only the worthy shall ever see. Solve the riddle below and hit the right key to open the treasure-trove. But remember, press the wrong key and the universe shall come to an end!

                  A Valuable Question

This is a question. A question about the wild endless Aztec map.
Well, let me be exact. Say the map is worth nothing, and ignore what is obvious. 
Must it be so that the argument you gave is only half-real?
Confusion here, as in hypnotism. Nobody is sure.
No idea? OK, I'll name a few of its relatives; I may be mistaken though:
Her Inner Armband; Third Bad Evil; A Null, Hero Deer; Brainy Crone.
So, can you solve this now?

What should you do?

---

Hint:

There is an anagram tag.

Answer 1

(Much of the hard work was done by other answerers, but they didn't quite get there. Anyone inclined to give this an upvote or checkmark should read Doniel's and Kirex's answers first.)

This is about

the Riemann Hypothesis.

A Valuable Question

It's arguably the most important unsolved problem in mathematics. Also, the Clay Institute will give you a million dollars if you resolve it.

This is a question. A question about the wild endless Aztec map.

wild endless Aztec = wild Azte = zeta. Map = function.

Well, let me be exact. Say the map is worth nothing, and ignore what is obvious.

Say the value of zeta is zero, and ignore the so-called "trivial zeros" at negative integers.

Must it be so that the argument you gave is only half-real?

Does the argument to the function have to have real part 1/2?

Confusion here, as in hypnotism. Nobody is sure.

Anagram of "here as in hypnotism" is "Riemann hypothesis". And indeed nobody is sure whether it's true or false. "Confusion" is an anagram indicator.

No idea? OK, I'll name a few of its relatives; I may be mistaken though:

I think this just means that the following anagrams yield (as found by Doniel and Kirex) names of notable mathematicians who have worked on RH or related material. I guess "I may be mistaken" is indicating the anagrams.

Her Inner Armband; Third Bad Evil; A Null, Hero Deer; Brainy Crone.

Bernhard Riemann (who introduced the zeta function); David Hilbert (who was one of the first other people to do important work on it); Leonhard Euler (whose "product formula" is one of the key reasons why the zeta function is important in number theory); Brian Conrey (important living mathematician, works on the zeta function and the closely related L-functions).

So, can you solve this now?

If only...

Personally I would be very tempted to

press the "This is True" button ... but it would be a bit of a risk.

Answer 2

The riddle refers to:

Mathematics, a "true" science.

This is a question about the wild endless Aztec map. / Say the map is worth nothing, and ignore what is obvious.

This is a reference to the Aztecs' calculations of area, among the earliest civilizations to do so. But for us, the map is worth nothing, as we don't really care how they divided up land now that the Spanish took over.

Argument you gave is half-real:

Complez numbers are part real and part imaginary.

Confusion here, as in hypnotism. Nobody is sure.

...Until somebody finally solves that old math equation nobody's been able to solve yet.

A few of its relatives. I may be mistaken, though.

Thanks a ton for the anagram tag. Solving these was how I figured out the math reference; all of the anagrams are famous mathematicians.

Her inner armband:

Bernhard Riemann.

Third Bad Evil:

David Hilbert.

A null hero deer:

Leonhard Euler.

Brainy Crone:

Brian Conrey.

Can you solve this now?

I'll leave that as an exercise to the reader. I'll leave you with one last equation, as the secret to the Universe: 9*6=42.

Answer 3

This question is referring to something about the

Euler-Riemann-Zeta function

as

All the mathematicians in the anagrams have done research in regards to it.

Another thing pointing at this is "Argument you gave is half-real":

The argument for the function can be a complex number

Confusion here, as in hypnotism. Nobody is sure.:

Maybe this question is about the yet unsolved Riemann Hypothesis

And if it is, you shouldn't press any button? Since you stated the question "What should you do?" so explicitely, this seems like a case where pressing neither button could be the right answer.

On the other hand, I have no idea how to connect this to Aztec maps. Maybe another

anagram? "Aztec" contains "Zeta", after all.

Answer 4

Here's my try at it. EDIT: confirmed false. (Ha.)

"This" is false refers to the map mentioned throughout the riddle, which it says is worth nothing.

After all, the inscription is labeled "welcome human,"

and homo sapiens are considered (by homo sapiens) to be the smartest creatures around. Only such a clever creature could be so deceptive.

Along those lines, the "wild endless Aztec map" is

a reference to the folk legend regarding a cache of Aztec treasure. Note also that the buttons are written in gold letters.

It's "half-real" because

the Aztecs, indeed, did have a lot of treasure in their heyday.

Confusion...hypnotism...nobody is sure...no idea

That's what happens to someone presented with a bunch of lies. They're confused.

Its "relatives" thus refer to

various types of deceit, including liez.

The narrator may be mistaken because

he, too, may have been deceived.

"Her inner armband"

Inner, as in hidden from view, and armband, as in something twisted.

"Third bad evil"

Third, like a third wheel, is something extra nobody pays attention to; this trivial thing is "bad" and "evil."

"Null, Hero Deer"

Null, meaning worthless, is something also ignored. A hero could be a garden path, which at first makes you think it refers to an adventurer such as the person reading this riddle, but it could also refer to an ordinary sandwich (also called a hoagie or sub) that nobody pays attention to. The deer is left to be the prey for the deception, as it's a common hunting target that many hunters lay traps for.

"Brainy Crone"

Brainy, as in smart, and crone, as in an old woman, who most wouldn't suspect of being a mastermind behind a deception.

Can you solve this now?

Well, I'm hoping I didn't explode the Universe. This would be really disappointing if the only thing in the box is a big number 42.

---

TLDR, he should push

This is false, an apt conclusion to a riddle of deception.