“A Mathematician’s Apology” by G.H. Hardy (1940) – the beginning of a 2014 dialogue

I read Hardy’s short essay and was inspired on several points – first, his observations on what drives a young man or woman in their early years (in short, curiosity, ambition, and pride); second, his observations on how many men or women are really GOOD at what they do (in short, 5 – 10% of all humanity); third, his observations on what it’s like to be “past one’s prime” (in short, after age 50 for mathematicians) and how might one continue to live after that.

Personally, I “buy into” about a third of his points BUT I think his thoughts provide extremely rich material for discussion. Particularly, what is the role of, let’s say “generationally challenged” humans (in short, 60 years or older).

A friend of mine has asked that I post this kickoff dialogue online (via WordPress, Twitter, FaceBook et.al.) so that he and I (and you) might have and participate in a 2014 dialogue, beginning now, on these and related topics.

I acquiesced (“accepted somewhat reluctantly but without protest”) because he’d already ordered a copy of “A Mathematician’s Apology” with a Forward by Dr. C.P. Snow. Who am I to argue with someone willing to spend 14 bucks?


7 Responses to ““A Mathematician’s Apology” by G.H. Hardy (1940) – the beginning of a 2014 dialogue”

  1. Michael Delaney Says:

    First I must set the record straight – it was $19.47 bucks. I don’t get free shipping. So, given that, I appreciate your efforts to overcome your reluctance. According to my dictionary, you “accepted, agreed, or allowed something to happen by staying silent or by not arguing”. I’ve never known you to argue and silence is not one of your strong points. Let’s not quibble with words, let the fun begin.

    I read the book on a four hour flight from Houston to Calgary and set a record for the most sticky notes/page of any book I’ve read. Where to begin? I would like to first consider Mr. Hardy’s state of mind at the time he wrote this book. From Mr. Snow’s forward, p.49, when Hardy arrived at the University cricket match – “:In those the last of his happy years, everything he did was light with grace, order, a sense of style.” p. 50 – “his creative powers as a mathematician at last, in his sixties, left him.” For the next few pages it’s downhill from there. I can’t help being reminded of my hero Winston Churchill who hit his stride in his 50’s, went on to win the Nobel Prize in Literature in 1953, at the age of 79. Is there something about mathematics, and being a pure mathematician, that makes getting old so difficult?

  2. sitearm Says:

    Michael: Best wishes there in Calgary!

    I am still trying to figure out if our dialogue here in WordPress can be successfully echoed in Twitter/Facebook. Rest assured I shall pursue this!

    MOVING ON – I love your explicit data including your quotes of Snow.

    WHERE I’M AT – I’ve already said what I admired in Hardy’s essay. Since then, and what I want to add to our dialogue, is the concept of “deconstruction” https://en.wikipedia.org/wiki/Deconstruction, which says (the way I look at it), that whatever the heck we think the author meant, it is comPLETEly a matter of our own projection of meaning(s) onto the the author’s works. If this were accurate, it would mean, for example, that Snow projected his own concerns of losing creative power on something that Hardy may, or may not have, meant to express in his essay.

    In this spirit, I project my own thoughts on Hardy’s essay as follows: I dinna care how old ye may be – ye may contribute from now until ye die and maybe even beyond, to the world (and ye’re children and mentees, do ye ken?). I project that he realized that once he got beyond his “early” years, which were about “curiousity, ambition, pride” and “who was really good at something,” he may have approached a philosophical regard, which my favorite local Baptist church has espoused as, “Love God, Love People, Equip Future Generations.”

  3. Michael Delaney Says:

    OK, so I’ll answer my own question. Apparently so. By Hardy’s own count, p. 71, of the four mathematicians he mentions, the oldest died at the age of forty. Would of been nice to know the causes of death to see if there might be any similarities. Hardy would have like the Billy Joel song, “Only the Good Die Young”.

    At the risk of starting to sound like a Freud wanna-be, I can’t help but be intrigued with what Hardy considered, in his early years, important in how one lives his life (as a mathematician I suppose):
    “A man’s first duty, a young man’s at any rate, is to be ambitious”, p.77
    ” ….intellectual curiosity, professional pride, and ambition are the dominant incentives…….”, p.80

    Seems reasonable to me, although we might question the pride thing. So, what happened to him?

    BTW – totally unrelated to the book, sort of: What is the difference between mathematics and arithmetic?

    Deconstruction??? I’m looking for a book on that, get back to ya shortly.

  4. sitearm Says:

    1. For our reference, one definition (and, by definition, it’s one of multiple possible, and contradictory, definitions!)

    “Deconstruction generally tries to demonstrate that any text is not a discrete whole but contains several irreconcilable and contradictory meanings; that any text therefore has more than one interpretation; that the text itself links these interpretations inextricably; that the incompatibility of these interpretations is irreducible; and thus that an interpretative reading cannot go beyond a certain point.”

    2. Hardy practiced atheism

  5. Michael Delaney Says:

    Once again, I’ll answer my own question, what happened to Mr. Hardy? Simply put, he failed to live by the key precepts required for a full, happy and productive life, which I maintain are:
    1. Remain ambitious and motivated to continue to learn and grow, which is driven by,
    2. Your unending curiosity.
    3. Maintain a strong sense of intellectual integrity (RE; Peter Drucker, “Adventures of a Bystander)
    In short, see the world as it is and not the way you’d like it to be. Absolutely critical for those in position of
    4. Hang with young people.
    5. Watch the movie “Heartbreak Ridge”, starring Clint Eastwood as an old-fart Marine drill instructor who teaches his
    newbies how to “improvise, adapt and overcome” every time life presents you with yet another cluster-fuck.
    6. Maintain a healthy and vigorous sex life right up to the very end. (see #4)

    It doesn’t have to be complicated but what about Mr. Hardy? Well, it’s quite simple and Mr.Hardy said it himself. On p. 67-68, he says, “..most people can do nothing at all well.” “…perhaps five or even ten percent of men can do something rather well. It is a tiny minority who can do anything really well,..” How many people do you know that “lived a life well done”? So, Mr. Hardy turned out to be just another ordinary Joe, of the overwhelming majority who come and go and don’t leave much behind. No need to apologize for being ordinary!

    So, on to deconstruction!

  6. sitearm Says:

    So far, trying to converse on one topic by social media for me, using ways I already know, seems so slow – it’s bandwidth-limited compared to live conversation. It’s like watching a movie of your favorite novel instead of reading it – it leaves so much out! Yet shall I persevere in the interest of learning and adapting new ways to keep a discussion alive even if there are days between replies.

    Re Hardy – I will say that one of the praises of his Apology that I agree with is that it showed that mathematicians are creative people (artists) too – and I will add that Hardy’s comments about being proud of how “useless” maths are, do ring true with me re Snow’s interpretation that Hardy was bitterly disappointed in how readily humans stupidly go to war. Hardy lived through WWI and the beginnings of WWII. In these, our own times, the increasing likelihood of WWIII makes me heartily sympathetic with Hardy – but not necessarily feeling despair on my own part. As always we are going to have to work this out, and war has ever been a part of recoverable, recorded history-to-date over the last 13,000 years.

    One of my mother’s favorite mystery authors was Dorothy Sayers, who was a scholar (as was my mother), whose detective lead Lord Peter Wimsey suffered and survived WWI though it changed him immeasurably.

  7. Michael Delaney Says:

    Good morning,

    I prefer to view this exercise as a throwback to the days when people “conversed” by writing letters to each other. I find writing to be great way to focus my thoughts and avoid the temptation to pontificate on a topic. I hate people who pontificate, especially those who do it for a living on cable TV! On the topic of bandwidth, like inertia, bandwidth is good – bandwidth is bad. Just depends on your state of mind at any particular time.

    Another way to look at it is: Let’s treat this the way people did in the days of the Victorian Internet – the telegraph. BTW – people were known to misbehave using that technology just as we do today. Like I said – bandwidth is good – bandwidth is bad. When it comes to human behavior, turns out it’s all the same.

    More comments on Hardy coming soon.


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