Is being awake unnecessary for a mathematician?

Less than 2 hours of sleep, and I have developed my idea further. I may have a method for topologizing small abelian subcategories. Could it really be that sleep deprivation turns off the idea blockers?

(OP)#
You need to be awake to eat, which is necessary for survival. So unless you would be fed by an I.V. drip, you would need to be awake to survive, let alone do mathematics.

Why do I have to be new to Veeky Forums.
Kill me.

...

D-don't mind me, I'm just trying to refind the proof of Riemann's series convergeance

Why would I mind you doing that? Refinding forgotten stuff is good to do occasionally.

Because it seems rather [math]trivial[/math] tb'h

If I remember correctly, in the book I read about lucid dreaming there were some examples on how lucid dreaming can be used to make your waking life better. One of the examples explained how you can use the lucid dream to better understand abstract mathematical concepts.
So I would say yes.

That kind of thinking is pretty toxic, imo. Even if some result would follow trivially from something, it is good to know how and understand the proposition. Feeling inferior because you check such "trivial" things can make you skip such results and eventually you will find yourself crying yourself to sleep because you don't understand what the author did, as he uses this "trivial" result you skipped every now and then. Or, this is how I see it.

No inferiority, no hierarchy. Math makes us all equal as long as we use the same axioms.

>Math makes us all equal as long as we use the same axioms.

That's... that's actually pretty inspiring. Thanks for that and good luck in your research (even though I don't have the slightest clue what it is about)

Thanks! I can give you a brief explanation, a bit vague because the details are technical and not that interesting.

I borrowed some ideas from topology to define nice subcategories for my categories with already a nice structure. I then used an equivalence relation to make them small enough to be used properly. I then used this en.wikipedia.org/wiki/Mitchell's_embedding_theorem to connect my categories to rings, which I then reduced to their isomorphism classes. Using these isomorphism classes, I was able to define a semigroup, and then the Grothendieck group of this semigroup I used to get a topological space for these categories. The details were a bit hazy, but i refined them so that it was close enough to work, but then I found out the same thing was already done with a slightly different way, this thing en.wikipedia.org/wiki/Q-construction by Quillen.

I then returned to the very beginning, and started following another path I could follow. I have so far been able to construct these topological spaces out of the categories with a lot easier method, and my current project is to show I can induce a topology in my small abelian subcategories using this space. Since I defined my subcategory so that its properties are independent of its objects, I could then make a local topological/topology-like structure over this category using these categorical deformation retracts I have, and, with luck, this may even give me something analogous to a manifold. I just need to find a way to formalize my ideas properly.

Sorry if my text is hard to follow, I've slept about 11 hours this week.

Which field are you in ? This sounds like abstract algebra.

>suggesting someone something because you read it is a '''''possible''''' scenario...

This is just like suggesting an algorithmn with no proof.

Kill yourself my man. This is Veeky Forums not fucking /x/

My main field is algebraic topology, but this is a mixture of algebra, category theory, topology and (if you want to include them) homotopy theory and K-theory. The two ultimate reasons for me to do this are to try build another bridge between certain categories and topological spaces, and out of interest. The accidental Q-construction analogue of mine makes me believe this idea can lead to something, and thus I am going to see how far I can get along this path.

What this may lead to is sort of an opposite version of algebraic topology, as you often would transfer the topological problems into algebraic categories to deal with their easier versions, but here I would transfer category theoretical problems into topological categories, and use those spaces to bypass hard stuff. I could then possibly classify these "medium sized" abelian categories using their spaces like I could classify small abelian categories using the Mitchell embedding, modules and rings.

How about you, monsieur?

These examples were taken from what people achieved after utilizing lucid dreaming and I consider LaBerge's book as a reputable source.
Fuck you.

>How about you, monsieur?
Electrical/Network Engineering. Favourite math topic is Analysis and infinitesimal calculus.

That's like the total opposite to what I've been doing. Nevertheless, good luck!

I like it because it's very visual and somewhat intuitive, plus it has a board range of applications.

I find if I focus intensely on math for several hours, then when I go to lie down, I can get into that hypnagogic state, and mathematically creative "Eureka" ideas will flood my brain. They are easy to forget, and can be ephemeral, however.

Yes, the amount of applications is gigantic. It is good to find stuff intuitive, as that makes things a lot easier to handle. And, also, it is a good thing that you find analysis intuitive, considering that you are going to be an engineer.

That is why you should record your ideas somehow. I usually write them down, and my home looks like I was some schizophrenic as I have my little reminder papers taped all over the place.