Why have I never seen this before?

[ALine]

So I am taking my first proofs class this semester along with an application of it in mathematical statistics and I got to say. This is pretty awesome. Why have I never seen this stuff before in my lower level mathematics courses. Like it provides general reasoning and evidence for each mathematical equation. 

I am currently reading over "Journey into mathematics-an introduction to proofs" by Joseph J. Rotman and it answer ssooooo many questions. Like a proof for that cosine equation that was just given to me. I thought it involved like some super human levels of mathematics. It turns out it just uses the pythagean theorem and some geometry identification and relationship forming. 

Also I am reading "The Elements" by Euclid for class as well, picked it up because it looked kind of cool when I was younger and it turns out I needed it later on, nice coincidence. Turns out it is now my favorite book. Like a book that you do not want to pick up because you know you will not be able to put it down.

Like my biggest issue in my math classes was that I did not understand how the conclusion was reached.

Like omg, this is the most I have learned in a long time.

(source: Family guy)

(reason for use: for dramatic comedic appeal )

Is this what math is? finding patterns and relationships in order to develop unique structures in order to better understand the interworks of different behaviors being observed?

[Strange]

It is great when a whole new area of understanding is opened up to you (it doesn't happen often, so enjoy it while it lasts!)

And it is surprising that so many proofs are incredibly simple. Not all though: proving Fermat's Last Theorem took a long time and is pretty complex. 

[uncool]

4 hours ago, ALine said:

Is this what math is? finding patterns and relationships in order to develop unique structures in order to better understand the interworks of different behaviors being observed?

Formally, no.

Informally, spot the fuck on. 

And of course, with the new structures, you get new patterns and relationships, which need new structures, which ...

[ALine]

4 hours ago, Strange said:

It is great when a whole new area of understanding is opened up to you (it doesn't happen often, so enjoy it while it lasts!)

And it is surprising that so many proofs are incredibly simple. Not all though: proving Fermat's Last Theorem took a long time and is pretty complex. 

Thank man, I never thought that math could be so exciting. I only assumed it was just rate relationships. 

Ye

3 hours ago, uncool said:

Formally, no.

Informally, spot the fuck on. 

And of course, with the new structures, you get new patterns and relationships, which need new structures, which …

Continue the cycle of increasing complexity until brain equals explosion.

[ALine]

ok so right now I my understanding of mathematics is " A structural formation thing that overlays on top of reality in order to form unique structures from the observed structures." Like an wireframing of reality and the use of imagination to create and develop new wireframes. Does this sound close to what mathematics as a field accomplishes? 

[Strange]

Just now, ALine said:

ok so right now I my understanding of mathematics is " A structural formation thing that overlays on top of reality in order to form unique structures from the observed structures." Like an wireframing of reality and the use of imagination to create and develop new wireframes. Does this sound close to what mathematics as a field accomplishes? 

I would say that is quite a good description of what physics attempts to do.

Mathematics can be completely abstracted and independent of reality.

[ALine]

3 minutes ago, Strange said:

I would say that is quite a good description of what physics attempts to do.

Mathematics can be completely abstracted and independent of reality

ahhh, ok. This makes a lot of sense to me.

So would mathematics be like a wire framing for any "reality"?

Like say for example you are in another universe that does not have the same laws as we do "here." Would mathematics still be able to describe those laws in order to form understandable theories?