ℝolliℵg M∀th Thr∑a∂

i know, right

Students who will make significant progress towards the solution of any open problem on the list posted here will get the grade of A+ regardless of their numerical score.

This is kind of old news, but I enjoyed this article. I never tire of these kinds of stories about unknown mathematicians toiling on hard problems in obscurity for years and then reaching a breakthrough, plus it does a good job of explaining the topic in layman's terms:

https://www.simonsfoundation.org/quanta/20130519-unheralded-mathematician-bridges-the-prime-gap/

yeah that one's great

there was a great slate article where they explained why twin primes conjecture is an obvious conjecture (because primes behave *as if* they are randomly distributed, even though they're not)

this interview with the guy is awesome http://nautil.us/issue/5/fame/the-twin-prime-hero

I am working on a problem related to the Goldbach conjecture.

TIL

flopson: what courses did you end up registering for? Real Analysis 4, I hope. :-)

i have until third week of the semester, probably gonna feel it out. not sure if ana will work out though, it's a pretty heavy workload

you like analysis?

One of the songs on Fade I don't care for, but the math is very good:

https://www.youtube.com/watch?v=4IwA9IimYSc

http://www.cut-the-knot.org/

Reminds me I need to change my screenname.

HI DERE

merry xmas math nerds

^ let xmas be any holiday

man this thread needs some actual words in its title

i cracked open a graph theory book, been doing some problems to relax

i realized that when i tried to 'write math', i automatically write a symbol (kind of a backward epsilon, though it was never quite that before when i used it) for 'such that'—which i/we NEVER do now when writing logic.

what is wrong with logicians?! why don't they write it? ('logically unnecessary', prob.)

do you mean existential quantification? as in ∃ x. x > 5 ?

You need it in higher order logic obv, but it tends to be implicit in first order logics.

yes, i mean after the quantifier and before the statement of the condition involving the bound variable

ah, as opposed to just the dot?

yeah; we certainly never used dots in any of the informal math style/notation i learned. backwards 'epsilons' or words.

maybe it's because logicians tend to be writing formulas after quantifiers which they just intend to be satisfied by values for the relevant quantified variables,

whereas a mathematician writing down an existential quantifier usually intends the subsequent conditions to say something meaningful about the 'x' (etc.) whose existence is being asserted (usually in terms of some conditions stated initially, or a principle or theorem etc.), so that he reaches for a piece of notation that emphasizes the subordination of the condition to the existential quantifier.

(i find that when i'm writing math, i will even put in a comma after a universal quantifier, for somewhat analogous reasons maybe)

do you mean '∍' ? I think that it might have to do with set theoretic roots there. You can read it as there exists an x drawn from the set of 'x > 5' for example. But if you're working without a set-theoretic model in mind then its terribly confusing. or if you have exists x ∍ R, then that's more like giving a 'type' than a condition -- x drawn from the reals.

i do mean that, but in concert with a membership epsilon, and w/in the general background of a naive set theory (the 'jargon of mathematicians' kind)

so it may be e.g. there exists x epsilon R backwards-epsilon x > 5

I wasn’t familiar with ∋ in a set-theoretic context. Nonetheless, Wikipedia’s article on Elements: http://en.wikipedia.org/wiki/Element_(mathematics) mentions it:

Another possible notation for [x ∈ A] is:

A ∋ x

meaning “A contains x”, though it is used less often.

I assumed you were talking about the traditional notation for “such that.” Most contemporary mathematicians, however, use a semicolon.

The relevant Unicode code point: http://www.fileformat.info/info/unicode/char/220b/index.htm

contemporary my ass

contemporary my ass

http://thuginpastels.files.wordpress.com/2012/09/grandpa-simpson.jpg

so they made you chair and you think that means you know about math huh well sonny let me tell you in my department chair was merely an administrative position

giving a talk at a conference on saturday

undergrad conference, and it's just exposition. but im still pretty psyched

http://www.slate.com/blogs/bad_astronomy/2014/01/17/infinite_series_when_the_sum_of_all_positive_integers_is_a_small_negative.html

i didn't realize that the clickbait function was unbounded on some intervals, but this seems to be fairly strong proof

blegh

oh btw this is the best thing ever: http://sciencevsmagic.net/geo/

^ ruler & compass constructions game

wow what a shitty slate article.

anyone have any good suggestions in philosophy of math btw? i'm tempted to get Corfield's Towards a Philosophy of Real Mathematics, but I doubt I'll really get to reading it carefully.

never really understood the point of that stuff tbh, aside from like water cooler chat

He notes that much of the philosophical depth and richness of contemporary philosophy of physics comes from that field’s engagement with cutting-edge topics in physics—gauge theory, string theory, quantum gravity, etc.—and he suggests that philosophical investigation of, e.g., category theory or algebraic topology might prove equally fruitful.

hard to think of something more pretentious than philosophers talking about category theory

Mathematicians are—as Corfield emphasizes in an interesting series of examples and case studies—pretty good at plausible reasoning. They evaluate the plausibility of conjectures; they argue about whether certain proof-strategies are likely to “pan out”; they discuss the likelihood that specific analogies will turn out to be fruitful. Unfortunately, it’s hard to see how they do all this.

lol

reading thurston's geometry & topology of 3-manifolds notes right now, so so good

sterl, the last thing i was read to read/look at in grad school was stewart shapiro's 2006.

by the time i had stopped caring about phil. of math, though, i was really floored by a talk by ken manders about knot theory as a source of examples for philosophy of mathematics. a lot of his older work is on diagrams in geometry, but unfortunately he is apparently a slow one so he hasn't published an inordinate amount - and the book his bio says he's writing is the same one he's been writing for years. still, his stuff seemed so insightful and mathematically realistic, from what i saw.

if you're thinking about reading Corfield, try reading a few reviews of the book first (I have some, er, acquaintance with these).

how gar are you in greek constructions, flopson?

i am stuck on circle packing.

just did the first two on my friend's ipad yesterday. will continue after i finish my analysis assignment

Euler did u write the review i was linking excerpts from above?

that one's not mine, but I know the author very well

corfield took the one you quoted pretty hard though

he was cooler with mine though I think mine's deeper

hard to think of something more pretentious than philosophers talking about category theory

spoken like a person who has never heard category theorists talking about philosophy

thanks for the pointers to the reviews, but they made me want to read corfield more, since i get the sense i'm more sympathetic to the sort of approach he advocates. i've definitely read some mclarty i really like, and have been v. taken by his historical exposition.

any thoughts of/knowledge of john bell btw? i enjoyed his primer on infinitesimal analysis.