Talk:Andrew M. Gleason

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated B+ class, Mid-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
A-BB+ Class
Mid Importance
 Field: Mathematicians

More sources[edit]

  • [1] Talk by AG in 2000 -- OR, unfortunately, but... sponge cake?
  • Faculty Memorial Minute -- excellent
    • This photo would be wonderful -- I'm talking to Harvard about this now to see if it's possible to get it released
  • Harvard Math Dept. history page
    • "His areas of research were Banach spaces and classical geometry"
    • Lists source: AMS President's entry
      • AMS History -- within which...
        • "Presidents": nothing not elsewhere
        • "Index": under Gleason, many entries needing lookup in other pdfs linked off parent page
  • [2] Excerpt from Puzzle Palace mentioning Gleason -- here's search for Gleason in PP [3] (also [4] but this is probably nothing)
  • Harvard death announcement
  • Father's bio of grandfather [5], includes genealogy
  • Finding aid for father's papers at NY Botanical Garden -- includes personal papers and photos [6]
  • Academic Genealogy of Mathematicians pp.395-396: "In 1946 Harvard University appointed him as a Junior Fellow, which is a very prestigious academic position similar to the research fellow of Colleges at Cambridge University. Gleason did not need to get a doctorate. Several Junior fellows won Nobel Prizes."
  • Pollak interview -- mentions AMG as MAA representative to Putnam family
  • In Barret (in AMS) see refs to Science 31 Jul 1964:451-7 "Evolution of an Active Mathematical Theory"; AMG festschrift
  • Gazette death notice
  • Linked from de.wikipedia:

Basis for N-C prize[edit]

[7] says it was 'For "Natural Coordinate Systems," an address before the American Mathematical Society,' while Bolker p.1236 (r col) says it was for H5th. EEng (talk) 19:56, 5 April 2013 (UTC)

Parking place for random article thoughts[edit]

Initial list by EEng (talk) 20:19, 5 April 2013 (UTC).

Others please add to, annotate, object, cross off (using <del></del>, etc. at will:


  • cryptography added to "fields" in infobox -- distinct enough from mathematics to justify?
  • Should the following go in infobox?
    • Presidency/chairmanships:
      • AMS (yes?)
      • Society of Fellows (no?)
    • Memberships/Fellowships: (initial feeling is no)
      • NAS
      • AAAS
      • APS
  • Signature at p222 (pdf p.46) -- usable?

Service to Harvard[edit]

  • Lowell House associate
  • Quantative Reasoning Requirement
  • Science Center building committee
  • other at Harvard, Fellows, societies, elsewhere

His own teaching[edit]

  • Math 55
  • Bamberg/Math 21/22/25 (I forget which)

Reform/innovation in mathematics teaching[edit]


  • Technical term(s) e.g. depth need explaining
  • Review which Enigma article to link to


  • I'm not sure it's appropriate to call Gleason a frog. From all I know he was of Swiss-Irish ancestry.
  • More seriously, I don't see anything explicitly characterizing him as a Dysonian frog. While I completely agree it's the right category for him, I don't see how this can escape being WP:SYNTH.
    • This is a shame, since a great hook would be: DYK, that colleague X called mathematician AG "more of a frog than a bird" in a national publication? (But this does give one a good idea for a new article, on birds/frogs, that's a cinch for DYK...)

EEng (talk) 20:59, 5 April 2013 (UTC)

My feeling is that it's not too much of a leap of deduction to prevent including it in the article, but it isn't solidly enough sourced to use as a DYK hook. Mostly I wanted to say something about his research style; this was just a colorful way of phrasing it. —David Eppstein (talk) 21:34, 5 April 2013 (UTC)
First let me say I appreciate your apparent good grace about my somewhat aggressive copyediting, but do speak up if I go too far. Now then, as to frogs... Having read Dyson in detail now, I have to say I think that, beyond being what I really think is SYNTH, I'm just not sure I agree. Dyson says, "People who solve famous unsolved problems may win big prizes, but people who start new programs are the real pioneers." No doubt AMG falls on the problems side of this, looking strictly at his research, but outside of research proper, was he not very much a bird? Even though your text is within the Research section I think it sells him short. Can we agree to drop it, at least for now? I think there's some other way to express the essential idea but I'm still trying to pull together Teaching. EEng (talk) 23:44, 24 April 2013 (UTC)
But Dyson's classification, and the section of the article here in which we mention it, are both purely about research. I don't necessarily agree with Dyson's opinion about who is most innovative, but I didn't include that part in what I said about Dyson. —David Eppstein (talk) 00:02, 25 April 2013 (UTC)
As I said, I recognize it's in the Research section but nonetheless laymen can easily misinterpret the breadth of the applicability. But more fundamental is that (to me at least) it seems obvious this is synthesis precisely on the order of the plagiarism example at WP:SYNTH. And I don't even see the predicate facts in the sources. Lots of people say Gleason was a terrific problem-solver, liked to come to grips with the fundamentals, but who says he didn't also have attributes we can match to Dyson's birds? Are you and I miscommunicating somehow? -- this seems perfectly plain to me but perhaps I'm just blind to something. EEng (talk) 01:55, 25 April 2013 (UTC) P.S. Thanks for not being upset at my restoration of the giant intro sentence.
The source we're using for this, the "50+ years" piece, says explicitly "Andy was a problem solver more than a theory builder". That's exactly the same as Dyson's dichotomy. —David Eppstein (talk) 02:13, 25 April 2013 (UTC)
But see, this is why synth is a no-no. Dyson says all kinds things about birds, none of which are particularly close to "theory building". You honestly don't see why this is synth? Please take a look at the plagiarism example, if you haven't already. Honestly I'm not trying to make fuss but I'm genuinely intrigued now. EEng (talk) 03:01, 25 April 2013 (UTC)
Dyson says all sorts of things *that we don't repeat in this article* and that don't detract from his classification of mathematicitians into problem solvers vs theory builders, a classification that is repeated by the 50+ years article in the particular case of Gleason. All we are saying in this article is that Dyson called problem solvers "frogs" and theory builders "birds"; there seems nothing problematic to me about that. —David Eppstein (talk) 03:10, 25 April 2013 (UTC)


Need to figure out if his preference for Hollis Professor of Mathematicks was officially adopted. If so, how do we handle that in article, esp. wrt the little "academic chair" box at the bottom? EEng (talk) 23:46, 6 April 2013 (UTC)

Notable students?[edit]

There's a list of his students at [8] p.1262. Ideally each of them who is himself/herself notable should be listed in the infobox (actually, should check WP guidelines on this), or even discussed in the article if appropriate. A good start on this would be to check who on the list has a WP article of his/her own. Any volunteers? EEng (talk) 03:23, 8 April 2013 (UTC)

I think it's simpler to only list bluelinked students in the infobox — that's the usual standard for Wikipedia lists. But it's not hard to make this match up with your looser "each who is notable should be listed" idea, by making a short article for each one who is notable but doesn't yet have one. Judging by number of doctoral students and by citations in Google scholar, Richard Rochberg looks plausible as next in line. —David Eppstein (talk) 02:36, 5 May 2013 (UTC)

Possible DYK hooks[edit]

Coupla us editors plan to nominate this article for WP:DYK soon. Some possible "hooks" (but don't forget sourcing!):

Did you know...

  • ...that mathematician AG, who held the Hollis Chair of Mathematicks and Natural Philosophy at Harvard, asked that the k be restored to the chair's name, in fidelity to the 1727 bequest that paid his salary?
Gleason's request, and the chair's historical name, are for sure -- I'm just guessing about the bequest and the salary and so on (i.e. whether Hollis' original 5 pounds 5 shillings or whatever is still the source of the money).
  • ...that mathematician AG, Harvard's Hollis Professor of Mathematicks and Natural Philosophy, never earned a Ph.D. [or doctorate]?
But actually, faculty without doctorate weren't completely unheard of at that time, and as written implies he's still in the chair
  • ...that mathematician AG, who had helped break the German and Japanese military codes during World War II, continued to advise the US government on cipher security for 50 years, but this work was so sensitive that his Harvard colleagues knew nothing about it?
A bit long, and certainly at least some at Harvard knew, if for no other reason than that at least a few did related work
  • ...that for several years, Harvard mathematician AG spent mornings talking with small children to understand how they learn mathematics, and afternoons advising the US government on military and diplomatic cipher security?
Obviously this is not really true as stated, but you get the idea -- a fun juxtaposition and I really like the idea of showing his range of interests and activities.
  • ...that mathematician AG once said, "Proofs aren't there to convince you that something is true; they're there to show you why it is true." [Misquoted -- see below]
from More Mathematical People, 1990, p.86

EEng (talk) 06:44, 5 April 2013 (UTC)

Well, it does need to be both true and sourced. And at this point, all but the "never earned a Ph.D." one are too long — they need to be under 200 characters. —David Eppstein (talk) 16:41, 5 April 2013 (UTC)
Well, duuuuh! Clarifying: Duuuuh is for the must-be-sourced bit. As to 200 chars, we've got a built-in problem in that Hollis P of M & N P is 836 characters just on its own -- maybe we can get an exception? My idea was to go looking in the sources for appropriate cites. "no PhD" is fine if that's all we have in the end, but it would be so nice if we could come up with something more... I don't know... more something. I've added a few more above -- I'd prefer the Mathematical People quote over the PhD thing. The bios have lots of anecdotes and talk about his way of thinking so I'm sure we'll have plenty to choose from at the end.
How are we coming on 5X? I tried one of the DYK tools but there's something wrong.
EEng (talk) 18:52, 5 April 2013 (UTC)
We're long since past 5x (I'm measuring about 8.6x currently), and at this point there are no maintenance templates, so I think we're ready to nominate for DYK (despite the lack of coverage of some topics such as mathematics pedagogy). I like the MMP quote but it needs to be somewhere in the article to use as a hook; you have any suggestions for where it should go? (Also, the exact quote is "really aren't there", not just "aren't there", but that could be handled by moving the word "proofs" out of the quoted part. I don't think the slight change of punctuation is important.) —David Eppstein (talk) 23:51, 5 April 2013 (UTC)

Live hook candidates[edit]

Here's another alternative:

(the MA is from the APS obit). —David Eppstein (talk) 00:02, 6 April 2013 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── Or maybe (giving Gleason himself pride of place):

But as my spaghetti was coming to a boil I realized that MMP re proofs really is the right choice. Here's why: Gleason felt this insight made him a better mathematician and a better teacher, and he would want the visibility of DYK to be used to pass this on, for the benefit of all. I don't have MMP in front of me so I want to check context and punctuation (I'm not sure how I came up with the semicolon instead of dash, and I wonder if "show why" shouldn't be in italics -- it was an oral history, after all) but for the moment how about:

  • ...that Harvard mathematician Andrew Gleason felt that proofs "really aren't there to convince you that something is true—they're there to show you why it is true." [~150 chars incl. spaces]

Or maybe we can get two for one:

  • ...that Harvard mathematician Andrew Gleason (who received an AM and tenure in the same year) felt that proofs "aren't there to convince you that something is true—they're there to show you why it is true." [199 chars -- need to confirm AM not MA]

EEng (talk) 04:55, 6 April 2013 (UTC)

I fixed a small inaccuracy in the quote. I think I prefer the one with just the quote — the longer one feels too cluttered, and your reasoning for using the quote would imply that he would think of the other part as being unimportant trivia. I'm not going to have more time to work on this before I travel, so please go ahead and make the nomination. —David Eppstein (talk) 06:59, 6 April 2013 (UTC)
I guess I wanted to hint at his brilliance too, plus AM-tenure has the "quirkiness" DYK so prizes. But in the end I agree with you, though we can always think it over. I'll make the nomination in the next 24 hrs.
Meanwhile I'll try to do as well on the areas I committed to as you have done on research -- though you've added a lot to the other areas as well, plus got most of the citations in!
Since I know you'll be busy, where I particularly want your eyes (and those of others -- presumably the nomination will attract interest) I'll put other eds in the edit summary, so as you change planes in Vladivostok perhaps just search that exact string in Article history and Talk history. There's likely substantial delay between nomination and appearance on main page so likely no real urgency, but delay may depend on backlog and of course we don't want any gaffes.
I know you won't mind my contacting some friends who were students in Harvard Math to go over the research sections. Sadly most of the Math faculty I knew at all well (I was in another department) can no longer be contacted by email.
EEng (talk) 15:15, 6 April 2013 (UTC)

EEng (talk) 23:46, 6 April 2013 (UTC)

Coding theory[edit]

I added a new subsection on coding theory this evening, inspired by a combination of events: (1) using the same source that I had used here (More Mathematical People) to improve another article, Irving Kaplansky, (2) coming across the article on Vera Pless in very sad shape, as part of a sequence of small edits I've been making to many articles, and (3) while fixing up Pless' article, learning that she had been inspired both by Kaplansky and by Gleason. I think the new section is too jargon-heavy but I don't know those aspects of coding theory well enough to explain them in clearer language, so help making it more accessible would be appreciated. Also, we might consider whether Gleason–Prange theorem should be an article (it's currently just a redirect) and whether we should have an article on Gleason polynomials. —David Eppstein (talk) 05:59, 6 May 2013 (UTC)

Your continued hard work, and the excellent photos contributed by the subject's wife and others, make me think that FA might be in the future, with moderate additional work. EEng (talk) 04:19, 13 May 2013 (UTC)
I think the usual order is GA first, but we may be close to ready to try that one. —David Eppstein (talk) 04:34, 13 May 2013 (UTC)
Just wanted to confirm that you are in it for the long haul -- not that I had any doubts. There's much to add (outside of Research, for sure) before we need to think about reviews. EEng (talk) 05:04, 13 May 2013 (UTC)

Rename Andrew M. Gleason[edit]

I'm inclined to rename the article Andrew M. Gleason -- this is the style he used in his publications and just about all formal circumstances. Thoughts? EEng (talk) 04:15, 13 May 2013 (UTC)

I don't have a strong opinion on this, but using the name he most commonly used on publications seems like a good idea. —David Eppstein (talk) 04:33, 13 May 2013 (UTC)

Gleason's Theorem[edit]

It is stated incorrectly that Gleason's Theorem can be used to repair von Neumann's faulty proof that quantum mechanics cannot support hidden variables. It is further stated that Bell showed this. This is also false. In fact, Bell showed that Gleason's Theorem COULD NOT BE USED TO FIX VON NEUMANN'S PROOF. I refer you Bell's critique of von Neumann's proof. No one familiar with recent work on quantum mechanics would make this mistake. Hidden variable theories appear abundantly in papers published in refereed journals. -- unsigned by

Maybe Paul Chernoff is losing his familiarity with recent work on quantum mechanics, because at [9] p.1257 we have:
Bell’s argument based on Gleason’s theorem avoids the unjustified assumption of additivity of expectation values for noncommuting operators.
-- though this stops short of claiming to "repair von N.'s faulty proof", but that isn't what the article says anyway. If you think the article can express things better, by all means go ahead, but stop sticking in this uncontextualized link you keep adding. EEng (talk) 05:19, 4 July 2013 (UTC)