ℝolliℵg M∀th Thr∑a∂

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i know there are at least a couple mathematicians in the building. do mathematicians have anything cool to talk about? would be fun to hear about what research ppl are doing, or did in past lives, what courses people are taking or teaching, books we're reading, problems we're stuck on etc

i'm in my last year of undergrad program in pure math right now, currently taking general & alebraic topology (with a total madman who looks like this http://upload.wikimedia.org/wikipedia/commons/thumb/2/25/Daniel_Wise.jpg/220px-Daniel_Wise.jpg), real/functional analysis, and probability. kind of toying with the idea of pursuing grad school. i've taken a couple grad courses so far & they've gone down pretty smoothly, and there are a lot of opportunities to teach math at CEGEP (2 year mandatory pre-university program) and a masters degree is the only requirement. buuuut idk. currently applying for funding to do some research in geometry & topology with a postdoc this upcoming summer. will be spending this weekend trying to understand automorphism groups of covering spaces ^_^

flopson, Friday, 8 November 2013 18:39 (eight years ago) link

We could discuss whether there is a satisfying proof for the Nilsson Conjecture.

Aimless, Friday, 8 November 2013 18:43 (eight years ago) link

my own contribution: why does well-being look like this?

durianlychee (imago), Friday, 8 November 2013 18:44 (eight years ago) link

xp never heard of it!

flopson, Friday, 8 November 2013 18:44 (eight years ago) link

viz 1 is the loneliest number

Aimless, Friday, 8 November 2013 18:46 (eight years ago) link

oh lol -_-

flopson, Friday, 8 November 2013 18:47 (eight years ago) link

exactly

Aimless, Friday, 8 November 2013 18:50 (eight years ago) link

i am a dormant mathematician

ciderpress, Friday, 8 November 2013 18:54 (eight years ago) link

xp now you have ammunition for chatting up a mathematrix at your next conference

Aimless, Friday, 8 November 2013 18:54 (eight years ago) link

i teach math

the late great, Friday, 8 November 2013 20:42 (eight years ago) link

cool! how is it?

flopson, Friday, 8 November 2013 20:43 (eight years ago) link

high school?

flopson, Friday, 8 November 2013 20:44 (eight years ago) link

yes. prealgebra through AP calculus. it never fails to surprise me how much easier it is to teach "hard math" than it is to teach "easy math"

the late great, Friday, 8 November 2013 20:55 (eight years ago) link

i'm teaching logic right now, to the least academically prepared students i've ever taught (it's not a huge difference, but it's significant), and that seems to be otm.

the extra complement of math that people generally take to get into a university, even if it stops right at or just before calculus, does seem to make a huge difference in terms of experience, comfort, confidence, mastery of working with forms and symbols.

j., Friday, 8 November 2013 20:58 (eight years ago) link

How are we supposed to search for this thread title?

Somebody pointed out recently that the Notices of the AMS are online and free which is great for people like me who are not in academia anymore and don't get a paper copy. Been meaning to read through the article on Beethoven's Metronome: http://www.ams.org/notices/201309/rnoti-p1146.pdf

Also recently bought a copy of Best Writing on Mathematics 2012 which is very nice and pitched at a similar level, the article on Math and Music was very interesting, written by a guy who is both a practicing musician and research mathematician.

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 21:07 (eight years ago) link

mathematical dorks should be able to remember 98225

Nilmar (Nilmar Honorato da Silva), Saturday, 9 November 2013 21:08 (eight years ago) link

thats an elegant number

Nilmar (Nilmar Honorato da Silva), Saturday, 9 November 2013 21:09 (eight years ago) link

Yes!
225 is square of 15. (Which you can remember as fact in itself or as exemplar of (10 + x)^2 = 100 + 20x + x^2.
98 is multiple of 7 and figures in the decimal expansion of 1/7 if you think about it.

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 21:13 (eight years ago) link

you are ridic

bored of Canada (Stevie D(eux)), Saturday, 9 November 2013 21:15 (eight years ago) link

Let's see if I can do this:
100 = 2 mod 7 so 100^3 = 8 mod 7, 100^3 =10^6 = 1 mod 7 so 7 should repeat with 6 digits
1/7 = 7/49 = 14/98 = .14 * 100/98 = .14 * 1 /(1.0 - 0.02) = .14 * ( 1.0 + .02 + .0004 + ...) = .14285(6+1)..

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 21:23 (eight years ago) link

currently participating in a seminar on homotopy type theory and learning the rudiments of algebraic topology. been spending time with v/a Theory and Applications of Categories reprints.

lollercoaster of rove (s.clover), Saturday, 9 November 2013 21:27 (eight years ago) link

Really? Where?

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 21:28 (eight years ago) link

the seminar? at the cuny grad center http://nylogic.org/homotopy-type-theory-reading-group

didn't realize that someone else on the board would have an interest in this!

lollercoaster of rove (s.clover), Saturday, 9 November 2013 21:30 (eight years ago) link

Are you enrolled in any kind of graduate program at CUNY or elsewhere? What about the other people in the seminar?

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 21:34 (eight years ago) link

the seminar is open to the public, like lots of cuny things actually. i'd say its only about 30% people with any current relation to NYU, grad students included. v/a former students/phds, as well as just a cross-section of ppl currently just employed but with a math background, as well as maybe students at other campuses.

lollercoaster of rove (s.clover), Saturday, 9 November 2013 21:37 (eight years ago) link

we're meeting in the eves biweekly to make it feasible for people who work

lollercoaster of rove (s.clover), Saturday, 9 November 2013 21:37 (eight years ago) link

Thanks. By NYU I assume you mean CUNY or CCNY, although there are probably people from NYU there too.

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 21:39 (eight years ago) link

Also how long does it go for: two hours,

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 21:41 (eight years ago) link

oh yes by nyu i meant cuny. goes about 1.5 hrs and then some people go off to the pub afterwards for however long. there's a google group too https://groups.google.com/forum/#!forum/hott-nyc

whats yr maths background and how does it bring you to HoTT?

lollercoaster of rove (s.clover), Saturday, 9 November 2013 22:12 (eight years ago) link

'how did you first know christ?'

j., Saturday, 9 November 2013 22:20 (eight years ago) link

pretty much

lollercoaster of rove (s.clover), Saturday, 9 November 2013 22:26 (eight years ago) link

constructivism had that flavor

lollercoaster of rove (s.clover), Saturday, 9 November 2013 22:26 (eight years ago) link

How are we supposed to search for this thread title?

yeah sorry, had that thought while making the thread but couldnt resist lol. bookmark it, i guess?

s clover we should def homotope it up itt, stoked. what books are you reading? my course is based on munkres (<3) but prof is doing some additional topics, so far i've only looked at hatcher... it's all very intense, though. i slayed point-set but algebraic topo makes me feel v dumb

flopson, Saturday, 9 November 2013 22:31 (eight years ago) link

had some halfbaked thoughts while hi the other day about some group theoryish intepretation of (basic) music theory. trying to figure out how to make like, arpeggios/chords subgroups of keys/scales?? i don't know enough group theory tho

flopson, Saturday, 9 November 2013 22:37 (eight years ago) link

Don't have much background in this area per se, but have some background in math in general, was on the math team in junior high and then at the Bronx High School of Science, undergrad degree in math at Yale and graduate degree from NYU. First professor I had Freshman year was topologist William S. Massey, at graduate school I took the topology course from Sylvain C, but it was kind of easy and I didn't really learnd too much and most of NYU is about applied math anyway. Actually guy who wrote that music and math paper did a post-doc in topology at NYU, now he is at Lehman College. Sort of curious about this topic but more importantly like the idea that it is free and of being on an equal footing with the other students, other people not currently in academia but presumably mathematically literate - have toyed with idea of going back to finish (start?) thesis and get PhD now that my advisor is the chair but don't really want to deal with have to crank out research-level material, plus I didn't always like the Eloi vs. Morlocks setup of formal grad school, as I recently discussed with former ilxor Casuistry.

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 22:45 (eight years ago) link

I don't know how much higher math you really use to understand music or music theory, the article I was talking about basically says that he thinks a lot of mathematical research on music is sort of bogus, drawing a picture or creating blinking lights that sort of looks like what music is doing. To him the most interesting thing seemed to be the way the similar processes of collaboration jazz improvisation and mathematical research.

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 22:47 (eight years ago) link

i teach high school math but im an econ undergraduate and yall are simply adding fuel to the fire that rages inside me that i shd not be teaching math

shiny trippy people holding bandz (m bison), Saturday, 9 November 2013 22:50 (eight years ago) link

plus I didn't always like the Eloi vs. Morlocks setup of formal grad school,

what does this mean?

flopson, Saturday, 9 November 2013 22:52 (eight years ago) link

xp would u rather be teaching econ? my first major was in econ, then i was like ah fuck it and turned my math minor into a full major

flopson, Saturday, 9 November 2013 22:53 (eight years ago) link

The few mathematical ideas I use to think about music are:
*Thinking about the twelve semitones as the Abelian group Z12. (supposed to be a subscript)
*Looking for least common multiples when counting out polyrhythms
*Realizing that the names of the intervals are Ordinal Numbers and
*Realizing that sometimes there are Fencepost Problems in either counting out beats or even in that the octave is the same as the one, which is why some people talk about a heptatonic scale

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 22:55 (eight years ago) link

*Thinking about the twelve semitones as the Abelian group Z12. (supposed to be a subscript)

yeah this was basically the extent of my ruminations lol

flopson, Saturday, 9 November 2013 22:56 (eight years ago) link

well hey you know

http://en.wikipedia.org/wiki/Set_theory_%28music%29

j., Saturday, 9 November 2013 22:58 (eight years ago) link

Fully funded PhD student with good background (perhaps trained abroad) and famous advisor, who can sail through qualifyings, has good chance of helping advisor push out papers and securing post-doc and just generally burnishing his legacy = Eloi
Rest = Morlocks

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 22:58 (eight years ago) link

hmm, in the humanities the 'fully funded' part of the distinction doesn't really apply anymore at lots of places, programs looking to trim, improve graduation rates/times etc. figured maybe they should only admit those who they could fund

the other part, though…

j., Saturday, 9 November 2013 23:00 (eight years ago) link

Someone told me Hindemith was into group or set theory as it applies to music but I couldn't find a reference. Maybe that Wiki page will have.

Telling you, that Fencepost thing saved me some headaches.

Oh yeah, one more thing
*Thinking about musical entities as partitions- triads as partitioning into three (with the fourth being a "generalized, augmented third*), seventh chords as partitioned into four (with the second between the seventh and the octave as a *generalized, diminished third*)

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 23:02 (eight years ago) link

homotopy type theory isn't exactly homotopy theory bear in mind -- its this wild new realization that homotopy theory is precisely isomorphic to that branch of logic known as martin-lof type theory, and this all works only in a constructivist setting. so you have math/logics ppl without much topology background (hi!) and topology people trying to understand type theoretic notation all sort of in the mix together. i have a coworker with some topology so he's good at explaining things like fibrations and fundamental groups etc. oh right and the other part of the hott project is now you have a setting in which the claim is you can do the foundation of _all maths_ as an alternative to set theory, so eventually (tho it may be 6 mos before we get there, if we can keep up the momentum) we'll stop just building up the theory and do applications and use it to do classic results in e.g. actual homotopy theory, set theory, category theory, analysis etc.

lollercoaster of rove (s.clover), Saturday, 9 November 2013 23:07 (eight years ago) link

the hatcher book is very approachable but it does sort of require someone with a bit of background to explain what he means by certain things, since the geometrical intuitions aren't totally obvious without someone drawing things or waving their hands or etc. to illustrate movement.

lollercoaster of rove (s.clover), Saturday, 9 November 2013 23:08 (eight years ago) link

sounds cool xp

flopson, Saturday, 9 November 2013 23:16 (eight years ago) link

xp would u rather be teaching econ? my first major was in econ, then i was like ah fuck it and turned my math minor into a full major

― flopson, Saturday, November 9, 2013 4:53 PM (17 minutes ago) Bookmark Flag Post Permalink

there are many things for which i am better qualified to teach. don't get me wrong, i know the hs curricula v well, i just didnt take much advanced math and sometimes feel like i am training my kids for a sport ive never seen or played before. being the good economist, tho, i know my comparative advantage is in the high-need HS math field rather than the social studies or journalism positions i'd have an absolute advantage in.

shiny trippy people holding bandz (m bison), Saturday, 9 November 2013 23:19 (eight years ago) link

Now I remember the problem with math, you have to beef up all this apparatus, before you can really understand or prove anything- except for trivial variations on the proofs in the book with slightly different initial conditions- let alone do a calculation, for what seems like an eternity.

I Wanna Be Blecch (James Redd and the Blecchs), Saturday, 9 November 2013 23:22 (eight years ago) link

I wasn't really cut out to be an academic- I went back to grad school later in life and wasn't really in quite the right subject. Upon reflection many of my cohort of mathletes didn't go on to become research mathematicians - with some notable exceptions of course! My advisor was a nice guy but didn't really push, although he did get most other people through to the PhD but not to any big jobs that I know of. Sometimes I slightly regret I didn't try to work with the one guy whose father won a Nobel Prize or the other guy with an Erdős number of one.

Time Will Show Leo Weiser (James Redd and the Blecchs), Wednesday, 29 July 2020 15:01 (one year ago) link

That's how it is for most people. I chose my grad institution knowing that it was really only good in the one area I wanted to study, so it's a good pedigree even if I'd studied, like, number theory it would have been a trash place to be. (Or any other discipline except philo & theology, it's not a very good place to do grad work in general, but it's a wealthy place so it worked out.) The big advantage of my well-established advisors was that they taught me, from my 2nd year on, how to talk to big shots, the senior faculty at other universities that I'd meet at conferences. I.e. networking, still the most important skill I learned aside from first-order "here's how you solve a problem" etc.

Joey Corona (Euler), Wednesday, 29 July 2020 15:06 (one year ago) link

ILX - COVID-77

Time Will Show Leo Weiser (James Redd and the Blecchs), Sunday, 2 August 2020 02:29 (one year ago) link

two weeks pass...

Woke up in the middle of the night and thought about R. L. Moore for a second. Ugh.

Isinglass Ponys (James Redd and the Blecchs), Sunday, 16 August 2020 08:37 (one year ago) link

Now thinking about Paul Garabedian, a more pleasant memory.

Isinglass Ponys (James Redd and the Blecchs), Sunday, 16 August 2020 09:01 (one year ago) link

what's wrong with Moore?

I had at least one undergrad prof who'd been a doctoral student of his. He told us a story of how, when Moore taught courses to engineers, he'd bring a loaded gun to class, and told the engineers that if any of them asked a question in class, he'd shoot them.

Joey Corona (Euler), Sunday, 16 August 2020 11:52 (one year ago) link

Heard a similar story from that son of a Nobelist I mentioned. Applied mathematician is hired at UT Austin. Shows up for first semester of work, is greeted by R. L. Moore sitting there with a shotgun his lap. “What are you doing here, son?”
“I came to teach <insert applied math subject here>.”
“Oh no you aren’t.”

Isinglass Ponys (James Redd and the Blecchs), Sunday, 16 August 2020 14:06 (one year ago) link

haha

Joey Corona (Euler), Sunday, 16 August 2020 14:09 (one year ago) link

what's wrong with Moore?

I had at least one undergrad prof who'd been a doctoral student of his. He told us a story of how, when Moore taught courses to engineers, he'd bring a loaded gun to class, and told the engineers that if any of them asked a question in class, he'd shoot them.

Posts Whose Second Paragraph Answers The Question Raised In Their First Paragraph

Guayaquil (eephus!), Sunday, 16 August 2020 15:10 (one year ago) link

;)

Joey Corona (Euler), Sunday, 16 August 2020 15:25 (one year ago) link

two weeks pass...

RFI: best way to express a half open range in a non-or-quasi-mathematical setting.

Two Little Hit Parades (James Redd and the Blecchs), Monday, 31 August 2020 16:09 (one year ago) link

maybe...

integers: "x, x+1 ... y-1"
reals: "from x up to but not including y"

but if "quasi-mathematical" is like programmers or physicists then [x, y) is understood or quickly understandable for both integers and reals, and certainly a <= x < b is fine.

𝔠𝔞𝔢𝔨 (caek), Monday, 31 August 2020 16:31 (one year ago) link

not exactly what you're looking for but maybe useful

https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html

𝔠𝔞𝔢𝔨 (caek), Monday, 31 August 2020 16:31 (one year ago) link

Thanks, already went with your last suggestion.

Two Little Hit Parades (James Redd and the Blecchs), Monday, 31 August 2020 18:07 (one year ago) link

three weeks pass...

HI DERE!

Erdős-szám 69 (James Redd and the Blecchs), Saturday, 26 September 2020 22:55 (one year ago) link

three weeks pass...

Does anyone read the Cantor’s Paradise section of Medium?

Here Comes a Slightly Irregular (James Redd and the Blecchs), Saturday, 17 October 2020 12:57 (one year ago) link

never heard of it before, but just read this nice post on concentration bounds https://medium.com/cantors-paradise/concentration-of-measure-the-glorious-chernoff-bound-1e96777cc29d

flopson, Sunday, 18 October 2020 01:16 (one year ago) link

The few things I’ve read have been pretty good so far.

Here Comes a Slightly Irregular (James Redd and the Blecchs), Sunday, 18 October 2020 01:21 (one year ago) link

seven months pass...

Twitter programming language enthusiasts are the absolute worst promoters of category theory applicability.

Allen (etaeoe), Sunday, 30 May 2021 21:10 (eleven months ago) link

Who's the picture at the top of this thread a picture of?

Guayaquil (eephus!), Sunday, 30 May 2021 21:16 (eleven months ago) link

https://www.youtube.com/watch?v=sdlWiDgvjAY

flopson, Sunday, 30 May 2021 21:21 (eleven months ago) link

two months pass...

sometimes things work out well:

I taught a course in computational algebraic geometry this summer.

To high school students.

Here's how it went.https://t.co/fCASlEoExx

— Bill Shillito (@solidangles) August 3, 2021

mark s, Wednesday, 4 August 2021 12:57 (nine months ago) link

Good stuff, especially leading up to this:

In short, we need to stop conflating logical foundation with pedagogical foundation.

Two Severins Clash (James Redd and the Blecchs), Wednesday, 4 August 2021 14:16 (nine months ago) link

I think this is good but I also think it is super unclear to me that "pedagogical strategies that work well in a small group of student selected specifically as self-motivated high math achievers" has THAT much to say about what K-12 should be doing generally. And of course the idea that school math should involve playing around, discovery, "why do we do it this way? what if we did it this other way? if that doesn't work, what went wrong?" rather than "follow these rules to get the answer" is exactly the aspect of Common Core that was hated by legislators and parents and to be frank lots of kids (though I still can't help feeling there has to be a way to do it right.)

Guayaquil (eephus!), Wednesday, 4 August 2021 14:35 (nine months ago) link

Fair enough.

I want to look at his divide by zero thing later.

Two Severins Clash (James Redd and the Blecchs), Wednesday, 4 August 2021 14:40 (nine months ago) link

never divide by zero, it always ends badly

mark s, Wednesday, 4 August 2021 14:55 (nine months ago) link

and yes, it absolutely depends on this being a schoolroom of the self-selectedly curious in a territory where the outcome stakes aren't especially high yet (in a bridge-will-fall-down car-will-catch-fire sense)

mark s, Wednesday, 4 August 2021 14:58 (nine months ago) link

never divide by zero, it always ends badly

Eh, not quite

Two Severins Clash (James Redd and the Blecchs), Wednesday, 4 August 2021 15:00 (nine months ago) link

trying to vibe at the pole of a reimann sphere, just not happening man

mark s, Wednesday, 4 August 2021 15:50 (nine months ago) link

four weeks pass...

I was trying to work out myself how to prove that pi is a constant, that all circles have the same ratio between diameter and circumference. I got stuck -- I couldn't figure out a way to prove that if there exists the same angle-side-angle values for two triangles, they are congruent. I looked it up in Euclid's Elements, but Euclid's proof only works when that applies for ANY given side. Is there a simple proof of this without going into the law of sines?

adam t. (abanana), Friday, 3 September 2021 23:11 (eight months ago) link

Found it, Book I Proposition 26 in Elements.

adam t. (abanana), Saturday, 4 September 2021 00:27 (eight months ago) link

To me the definition of a circle implies that all circles are similar to each other so pi has to be constant.

Gwar ina Babyon (James Redd and the Blecchs), Saturday, 4 September 2021 20:14 (eight months ago) link

I suppose using Euclidean methods you could use dilation and then superposition.

adam t. (abanana), Saturday, 4 September 2021 21:17 (eight months ago) link

here’s one way to prove it using integral calculus

take any circle x^2 + y^2 = r^2

circumference is the arc length of the curve, which is equal to 2r times an integral not involving t (as here https://math.stackexchange.com/a/1049390)

flopson, Saturday, 4 September 2021 21:21 (eight months ago) link

not involving r*

flopson, Saturday, 4 September 2021 21:21 (eight months ago) link

four months pass...

Okay, someone take the Terence Tao masterclass and tell me what he says.

Tapioca Tumbril (James Redd and the Blecchs), Monday, 31 January 2022 16:29 (three months ago) link

I never heard the term The Martians before.

Ferryboat Bill Jr. (James Redd and the Blecchs), Wednesday, 9 February 2022 12:20 (three months ago) link

three weeks pass...

I'm laughing so hard at this slide a friend sent me from one of Geoff Hinton's courses;

"To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it." pic.twitter.com/nTakZArbsD

— Robbie Barrat (@videodrome) June 10, 2018

𝔠𝔞𝔢𝔨 (caek), Tuesday, 8 March 2022 22:02 (two months ago) link

Lol

Mardi Gras Mambo Sun (James Redd and the Blecchs), Tuesday, 8 March 2022 23:03 (two months ago) link

Old enough to remember when the thing was to watch Tom Banchoff rotate a tesseract to help see the fourth dimension.

Mardi Gras Mambo Sun (James Redd and the Blecchs), Tuesday, 8 March 2022 23:06 (two months ago) link

Hinton's a real one

Guayaquil (eephus!), Tuesday, 8 March 2022 23:33 (two months ago) link

who knows how to visualize a complex or even quaternionic one

Guayaquil (eephus!), Tuesday, 8 March 2022 23:33 (two months ago) link

Anyway I see what he is saying.

Mardi Gras Mambo Sun (James Redd and the Blecchs), Wednesday, 9 March 2022 00:33 (two months ago) link

one month passes...

Category theorists are always wilding out on my timeline

Allen (etaeoe), Monday, 11 April 2022 13:14 (one month ago) link

I have just learned that it may not be related to category theory and is likely a byproduct of Twitter’s new recommendation features (I assume it’s inferring an interest based on following math people and following computer science people).

Allen (etaeoe), Monday, 11 April 2022 17:13 (one month ago) link

pic.twitter.com/maySTJd1wA

— depths of wikipedia (@depthsofwiki) April 18, 2022

mark s, Monday, 18 April 2022 14:22 (one month ago) link

What does Snopes have to say?

jmm, Monday, 18 April 2022 15:10 (one month ago) link

Surely there is a Medium article or two addressing this. I believe I may have gotten an email alert about one this morning iirc.

Ramones Leave the Capitol (James Redd and the Blecchs), Monday, 18 April 2022 15:15 (one month ago) link

three weeks pass...

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