J

dont take my X super seriously unless you can actually handle it 😉

physicist and gambler

[J @jetbundle]

the contact geometry is a fucking bitch in this lol

[The Scientific Lens @LensScientific]

Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

— Nikola Tesla

[J @jetbundle]

neuralink me up elon im trying to be superhuman at this point

[J @jetbundle]

the fuck

[Asymmetric Insight @billheckler1]

@ericweinstein Tks. for flagging.

I call it "American Stupidity."

We do not know, what we do not know.

[Scott Manley @DJSnM]

Sound synchronized from @NASASpaceflight footage

[J @jetbundle]

@mirkovicdev hahha bro you are the mathematician everyone is scared of 😦😦😦 crazy bookshelf

[Antonije Mirkovic @mirkovicdev]

I use AI every single day so I'm definitely not against AI. I think it's one of the most powerful tools humans have ever created but I do think there's a big difference between using AI to help you think better and using AI so you don't have to think at all.

Especially with mathematics I don't think the point is only to get the answer as fast as possible. A big part of the value is what happens to your mind while trying to understand something. When you struggle with a problem, make mistakes, fix your reasoning, and slowly build intuition, you're not wasting time, you're training your brain.

[J @jetbundle]

@iamspi_ its a specific quantum potential in the option surface of a quantum computing companys option market chain lmfao

[J @jetbundle]

i genuinely believe this was one of the greatest moments in financial history

and i hope no one figures out which team was responsible for it

[J @jetbundle]

it just doesnt feel like a mortal wrote it

[J @jetbundle]

i cant believe someone like shilov could write an entire universe in a linear algebra book... genuinely i cannot stop going back to it

genuinely, especially since it was translated too its a perturbed version of the original Russian text

[J @jetbundle]

i cannot get myself to rush through it. i read , work all of the problems but then just keep going back and dont want to move on from a chapter... simply because it just is one of the greatest books of all time

it should be printed as much as charles dickens or the bible lmao

[Elon Musk @elonmusk]

The SpaceX team is incredible!

[J @jetbundle]

@his4Everz its going to be okay :)

[J @jetbundle]

i should solve time dependent density functional theory when i get the chance lol

its been solved before prob but you all know how discovery is

its censored

[J @jetbundle]

we need a grand society/order of mathphys,,, economists/financiers need to be at the table as well. econo/financial phys. financial physics one of fields that i fortunately had a part of inventing...

[J @jetbundle]

algebraic geometry, algebriac topology,
differential geometry, differential topology

in what representation would you like your isomorphisms? 🌹

[Elon Musk @elonmusk]

First Starship V3 launch later this week!

[Antonije Mirkovic @mirkovicdev]

draw any loop on a circle. that loop is secretly an integer.

take a circle, pick a point, and draw a loop that starts and ends there. you can describe the whole loop by how many times it wraps around on its way back. once clockwise is +1. twice is +2. counterclockwise gives negatives. no wrap is 0.

here's the move. in topology, two loops are "the same" if you can smoothly deform one into the other. and once you allow that, everything about the loop washes out except the winding number. how wiggly it is, where it bunches up, none of it survives. only the wrap count.
so the set of essentially different loops on a circle is just the integers. an infinite topological universe collapses to ℤ.

this is the fundamental group of the circle. π_1(S¹) ≅ ℤ. one of the cleanest theorems in topology, because it takes a continuous question (which loops can deform into which) and gives a purely discrete answer (count the wraps).

[J @jetbundle]

@mirkovicdev i haven't done this but it might be interesting to see Liouvilles density equation and how radon nikodym bridges the gap. i would need to check Souraius book on dynamical systems

[J @jetbundle]

radon nikodym is a goated result in measure theory

[Antonije Mirkovic @mirkovicdev]

spent today proving radon-nikodym.

if one measure is absolutely continuous with respect to another, there's a function h that links them. integrating against h recovers the first from the second. it's the formal way to say "this measure is just that one, reweighted".

without this, conditional expectation isn't a real mathematical object. probability collapses.

the beautiful part is the move you don't expect. you don't construct h directly. you combine both measures into a sum, work in the hilbert space L^2 over that sum, and define a linear functional that integrates against the first measure. riesz representation hands you a function g. a few indicator tricks show 0 <= g < 1 almost everywhere. and the h you wanted falls out as g/(1-g).
you never build it. the hilbert space geometry summons it.

probability rests on a riesz argument applied to the right space.

[J @jetbundle]

@mirkovicdev adding onto this, abstractly i see it as a true correspondence between geometric/set based objects to pointwise objects like functions. it is what allows relating probability mass to the infinitesimal density...