Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

+how polym@th works here

There are some/other [massively] collaborative👥 domains across the WWW that are geared towards doing mathematics+computation innovation (what has been referred to as 'polym@th') in one (1) or more logs. I'm too lazy🤥 to pinpoint each one for this note, so I'll go ahead and make this portal/webpage (tree-dependence is negotiable) yet another place* for low-technology idea incubation.My aim is to make this the hub for such activity.

I should start by mentioning that just having a messaging💬 system is sufficient, but that can invite trouble when careless.🤢 To that end, please stay on-topic (pure/applied/recreational math-related); portions that are inadmissible face revocation👎🏿. All polym@th sourcings (hints, compiles, proofs, etc.) are tagged📎 under #polym@th (as opposed to #juking or #polymath), so any @replies from me (@Lnq) that are addressed to (specific members from) the community (ie. readers, etc.) will be placed in the post header. Pages are MathML-enabled, but the kicker is that, since I detest LaTeX!😖, such scripting (it might not parse, anyhow) in that syntax (rather, try to avoid Greek/Latin symbols wherever possible unless essential) is muted; points should be illustrated with (annotated) models [I favor 🖌Paint 3D/Builder at the moment, usually in tandem with a spreadsheet - but other 3d modelers should work as long as the file system🗃 is compatible]. Considering that we are iterating, sketches/pictures move the chain along much faster, anyways.😜That's just to say that I don't care for the coding element (MathJax noticeably slows load times); inherent math symbols in word processors are fine as long as they render.
Lastly, pay attention! Since things are organic and move at the speed of thought💭 here, you can expect a very large number of public domain threads. And yes👍🏿, posts may be bounced around between (third-party) forums.

#OpusSolve

Hodge conjecture

Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

Story

Errata

Presented here are wrong/incorrect approaches to tackling the problem. These are offered as case studies of what to avoid.

+The Egglepple Company

The Egglepple Company (or just Egglepple) is the pseudonym given to what is now known as Egglepple (kindergarten). It was an incorporated@ business entity in various states throughout the United States of America prior to its deprecation, reorganization, and later inclusion into LES. Historically, Egglepple was the very first establishment to be a standalone/independent recreational mathematics+ enterprise (+:=contract-based, sometimes ghostwriting for academe from 10/2000 - 02/2001).Reference: Ohio Secretary of State's Office (also of interest The Stewart Ellis Company - Gobotech, #305)

Note (+): pm:=pure mathematics, am:=applied mathematics. (see Funshine/Toonlight)





"Egglepple" is the middle name of Link Egglepple Starbureiy, after whom the company is called, and by whom the entity was created. It spawned from the unincorporated/unorganized Egglepple Portfolio (for toy [puzzle] design, circa 1991).

Note (+): Nowadays, the 'company' portion is assumed to be my roster (of characters/personalities +gallery) and the yots.

Back at The Ohio State University, I put in my time roving the halls of the mathematics, physics/astronomy, and chemistry departments. I was fairly new in that world ("publish or perish") and really wasn't familiar with LaTeX and that publishing scheme back then (the departments certainly didn't make it easy for non-staff to have access to the system), so I did what I did best when it came to visual expression, I drew stuff up/wrote stuff down on napkins (yes, at times with wax crayons🖍️ or colored pencils✏️).

The astronomy department was awesome in the regard that they treated people who came through their doors respectfully. The math department, however, was the total opposite. There was so much ego (mine included) polluting the building that it was almost laughable, yet frustrating. Anyway, there would be these 'challenge' problems/help requests from the community (ie. intra-departmental) often posted on bulletins, offering modest bounties💵 (very short-term contracts) for their solutions. The opportunist in me would peel these from the boards, take them home, and come back shortly thereafter with my answer(s) written on (paperclipped🖇️) napkins. I remember just vagabonding off of those purses (yes, I was a 'bounty hunter') for periods at a time (sometimes in conjunction with all-levels math tutoring/coaching gigs). I guess that - in addition to responding to Michio Kaku's earlier proposition - was me (being the person responsible for) turning math into my version of a sport.

+normed vector space

+vector space

+integration by parts

(see also flageolet pencil)

+Poincaré conjecture

+Yang-Mills existence and mass gap

+P versus NP problem

+Riemann hypothesis

+Navier-Stokes existence and smoothness

+Hodge conjecture

Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

+Birch and Swinnerton-Dyer conjecture

+Starbureiy style

+holograph

(see also sticker, stamp, touch-and-go)

+Codeo

+operator (mathematics)

+identity

+current

+generator (mathematics)