/sci/ - Science & Math

>>8973220

I mean seriously, how do people not go insane by deriving and proving such equations? I want to understand what makes people love doing this?

>>8973220
There's a lot of information in these symbols. I'll admit right now that I have nfc what this is actually saying. I know what the individual symbols mean but they're all crammed together without explanation so it's hard to get the whole picture.

In short:
On one hand when you say something like "the hessian is the jacobian of a gradient" you need to understand what the jacobian and gradient are. On the other hand, if you define the hessian without bringing up what these other terms are, using the definition of a limit or something even more elementary, you'll end up with a ridiculously unwieldy definition that reinvents the wheel at least three times.

>>8973220
>that the universe just "clicks" into place
It never just clicks, the moment when it clicks always comes after years of hard work. I remember watching Horizon interview Wiles about his proof, and he said that (after a decade of work) he a sudden moment of clarity and it all just fell into place.

All I know is that doing it by hand just for H2+ was fucking cancer how long it takes, but was extremely satisfying. thank god for computers being good at matrices

>>8973229
>how do people not go insane by deriving and proving such equations?
/sci/entists are insane by default.

You can succeed in math & /sci/ence only if you are a mad /sci/entist Spergerlord.

actual mathematician here
>>8973220
this is really just a simple hamiltonian which gives you an expectancy value for the inner product number operator for the wave function psi and the electrical shielding of the nucleus in spherical coordinates. It's honestly not that complicated.

>>8973229
this is the complete Lagrangian for the known forces including standard electro-weak theory. It is needlessly complicated in this formulation but it shows that the Noetherian currents of the semi-classical theory can be shown to be linear operators in some Hilbert space. You can clearly see the Dirac matrices.

Anyway, I do this shit for a living and it is actually pretty easy if you have the right brain wiring
>inb4 INTP robot

still me btw..
>>8973645
worth noting that all solutions to the Schrödinger equation are of some variation of the form EΨ = iħ (d/dt)Ψ which basically just tells you that the energy varies linearly with time (SE is a second order equation, as opposed to the Dirac/Klein formulation which is a first order DE).

>>8973654

EΨ = -iħ (d/dt)Ψ
forgot the negative sign, but you can just take the absolute value as:

|EΨ| = |iħ (d/dt)Ψ|

>>8973641
maybe, but I am also really good at music, languages, games, and abstract thought in general. Perhaps I am a Sperglord but at least I am a pretty well-rounded genius.

>>8973641
This is true, I was very happy to finally have a reason to explain my uncanny genius.

>>8973252
Totally this. I'm not yet a mathematician, but I understand this from from doing my undergrad thesis. My advisor explained a lot of shit to me almost in passing and at the end, handed me a paper to use its proof for my proof. I had a vague idea of all these theorems and seemingly disjoint ideas.

I reached a point where I had to patch up all of the wholes in the logic from the proof down to the theorems and math that made it work. One night, while thinking furiously before falling asleep about my whole daunting project, everything just fell into place. Just suddenly I saw the whole picture; the theorems all fit together and made sense and I saw my whole work in my mind completed. I got so excited I got out of bed and read the the theorems in my references just to be sure I was right.

>>8973229
>>8973220
they're written in a manner that makes them appear complicated, but they're actually not that bad

the second one just has a ton of routine computational steps

>>8974029
Yeah, I went in to talk to my advisor once about feeling discouraged when I tried to read some mathematical paper and there was so much shit going on but everything was so clean. She showed me her notes from what she was working on at the time and it was full of scribbles, statements that got crossed out, and ideas that never went anywhere. It was a nice reminder to me that tons of hard work goes into proving pretty much anything, and for the most part we only see it once it's cleaned up enough and all the trash is thrown out.

>>8973242
i thought the hessian was the outer product of the gradient operator with itself.

i guess it can be the Jacobian depending on your coordinate representation.

t. math grad in numerical analysis