Talk:Andrew M. Gleason

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Good article Andrew M. Gleason has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
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April 13, 2016 Good article nominee Listed
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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)
  • So, David Eppstein, what do you think about going for FA? No rush, of course, but perhaps we can start talking about it. I've never done it before. What would we do first -- one of those peer review thingees? Or is there cleanup/extension we still need? EEng 07:43, 22 September 2016 (UTC)
    • I've worked on a featured-article review before (for Euclidean algorithm) but not an actual new FA, so I also don't have a lot of idea about what is involved. —David Eppstein (talk) 15:41, 22 September 2016 (UTC)
I mean, I'd like to see this TFA someday, for his sake, but everything I've heard about GA, and what little I've seen, is unpleasant. Let's keep the idea in the back of our minds and someday the spirit will move us. Thanks for being willing to stand up earlier -- this mophead has pulled this with me before. EEng 17:02, 22 September 2016 (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)

GA Review[edit]

This review is transcluded from Talk:Andrew M. Gleason/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: MPJ-DK (talk · contribs) 01:50, 8 April 2016 (UTC)

I will be picking up the review of this one - both for the Wiki Cup and the GA cup as well. I will be making my review comments over the next couple of days.

Side note, I would love some input on a couple of Featured List candidates, Mexican National Light Heavyweight Championship and NWA World Historic Welterweight Championship. I am not asking for Quid pro Quo, but all help is appreciated.  MPJ-US  01:50, 8 April 2016 (UTC)

GA Toolbox[edit]

I like to get this checked out first, I have found issues using this that has led to quick fails so it's important this passes muster.

Peer review tool
  • The quote on proofs from the lead is not in the article? Why not?
    • Because repeating the same exact text twice is stupid, there's nothing to elaborate, and the lead seemed like a better place than the rest of the article to include a quote such as this one on his general philosophy. Note that this quote was the one used for the DYK. —David Eppstein (talk) 17:53, 10 April 2016 (UTC)
Copyright violations Tool
  • The quotes seem to be the main thing the tool hits on, I checked through it and I don't think anything else is directly lifted from anywhere Green tickY
Disambiguation links
  • No issues Green tickY
External links
  • The reference titled "Andrew Gleason, 4 November 1921 - 17 October, 2008" is dead and has been since November 30, 2015

Well Written[edit]

  • One of the notes refers to the subject as "Andy" outside of a quote, that is too informal a phrase for Wikipedia
    • Are you sure? There's a note with "Andy" inside a quote, but I didn't see one outside a quote. —David Eppstein (talk) 17:53, 10 April 2016 (UTC)
      • You are right, I did not pick up on the fact that it was a quote in the note. MPJ-US  18:10, 10 April 2016 (UTC)
  • "mechanics normally for juniors." should be "mechanics normally intended for juniors."
 Done EEng
  • ", including graduate real analysis in his sophomore year." it seems like this is not really a logical follow up on the quote?
 Done It was okay as it was, but reworded. EEng
  • "and on graduation should be "and upon graduation"?
Not done Upon is fussy, on is better. EEng
  • The sentence that starts with "(Others on" does not really need the parenthesis
Not done An aside like this should be set off. EEng
  • "published the most important in his series" - is that missing a word after "important"?
 Done Reworded. EEng
  • Staring a new paragraph with "But" seems wrong.
Not done That's something rulebound 7th-grade English teachers say. Perfectly appropriate here. EEng
That's just hurtful man, not cool. Pistols at dawn!!  MPJ-US  20:47, 12 April 2016 (UTC)
You say when and where! That old Miss Snodgrass couldn't hit the broad side of a barn! EEng 23:34, 12 April 2016 (UTC)
  • "(This work also involved deeper math­e­mat­ics related to permutation groups and the graph isomorphism problem.)" does not need the parenthesis IMO.
Not done As before, it's an aside which should be set off to avoid disrupting the main flow. EEng
  • "a Lieutenant Commander in its Nebraska Avenue Complex" should that be "the Nebraska Avenue Complex?"
 Done EEng
  • "this period remains secret" I think the word "classified" is probably more appropriate here, other people know about it, it's probably documented but not made public.
Not done Classified is just a fancy way of saying secret. Of course other people know about it (he didn't work in an isolation booth) but those who know are forbidden to tell, and that's what secret means. EEng A little story... Once in a while he'd say, "My boy, I'll be gone next week -- down to Washington for some NAS meetings." NAS = National Academy of Sciences. Years later I realized -- ha, ha! his little joke. Not NAS, but NSA.
Secret means "he did not tell anyone about it", classified means "he was not allowed to tell anyone about it", there is the intend behind it. MPJ-US  20:47, 12 April 2016 (UTC)
Secret means secret. Classified means officially designated secret or confidential or something else, the actual meaning of which is defined in some complicated way. One is a plain word and the other is a popularized technicality. Not to get all OR or anything but the man himself used the word secret in our (very short) conversations about it. And the section of the source on this point is entitled, "The secret life of Andy Gleason". EEng 23:34, 12 April 2016 (UTC)
OK, well, that source does say, "Most of Gleason’s applied work during this period remains classified", so having displayed my inside knowledge and erudition, I guess I'll capitulate. But only on this one point! And I'll be back! You'll pay for this! EEng 23:37, 12 April 2016 (UTC)
  • First time NSA is used it should be spelled out.
 Done EEng 16:00, 12 April 2016 (UTC)


  • Most of the sourcs with links are missing the "accessdate" parameter
    • Most of the sources are print documents with courtesy links, for which the use of |accessdate= is discouraged; see Help:Citation Style 1#Access date: "It is not required for linked documents that do not change." {{Citation}} (the style used here) also provides similar advice. However, I agree that it should be supplied for web-only documents such as references 40 and 42, and will check those. —David Eppstein (talk) 17:47, 10 April 2016 (UTC)
    • On further checking the only other one that this applies to is the Gallian reference, to which I added the accessdate. The MacTutor and MathGenealogy references are also online without accessdates, but those are generated by specialized citation templates that don't include that parameter. —David Eppstein (talk) 18:46, 10 April 2016 (UTC)
  • Sources look reliable from what I am seeing, I will spot check to see if they cover what's referenced as I review the actual content of the article later.
  • Reference 40 is just a name and a link, please provide the appropriate additional information.
  • Same with reference 42.

Broad in coverage[edit]

  • It has enough to cover the GA criteria of "broad" Green tickY


  • Factual and sourced Green tickY


  • Not seeing much of recent issues on the talk page, a few years back there were questions but nothing recent. History does not reveal any recent issues either. Green tickY

Illustrated / Images[edit]

  • No issues Green tickY

Thanks! I'm traveling this week and may not have much time to get to this, but if I don't I'll take a look when I get back. —David Eppstein (talk) 17:47, 10 April 2016 (UTC)

  • @David Eppstein: - I have completed my review, I must admit I don't actually understand all the content but I did cross check with references here and there and it appears to match what is stated from what I can see. I will put the article on hold to give you time to address the issues.
  • @David Eppstein and EEng: - looking at the work done by the two of you (yay teamwork) I believe you have addressed all my concerns... or called me Fussy ;-)... so I believe this deserves the Good Article Stamp.  MPJ-US  07:37, 13 April 2016 (UTC)

Lead image size[edit]

I figured I'd bring the discussion about the lead image size out of the edit summaries and onto the talk page.

The image use policy provides that, "The lead image (appearing at the top of the page) should usually be no wider than upright=1.35 (which is the default equivalent of 300px at preference selection of '220px')." EEng, I'm wondering why you believe this to be an exceptional circumstance. The image is horizontal, but it still seems to be a pretty typical half length portrait. Although you argue that it "looks better", I don't know that I agree when the lead text is squished into less than two thirds of its usual width (estimate). And that certainly doesn't address the non-compliance with the image use policy. Cheers, Graham (talk) 05:15, 3 August 2016 (UTC)

You're right -- I forgot about 1.35 being the normal limit for lead images. I've changed it to 1.35. EEng 06:14, 3 August 2016 (UTC)