G.H. Hardy (Cambridge math.)
from hodges:
Hardy's sharpest reproof was to utilitarian — in his time marxist-influenced — talk of mathematics for planning and order. (It reads oddly now. Today's emphasis would be on short-term profit, which never entered into Hardy's dialectic.) It is now a commonplace remark that Hardy was wrong about relativity and quantum mechanics having no military use, as was soon to be shown. Hardy would have been surprised, I think, that advanced number theory is now of great significance for commercial cryptography. Though allowing the possibility of such an application, Hardy still ended ringingly 'I have done nothing useful.' Turing made no such predictions of purity and issued no soul-searching apology.
But Hardy's point was essentially a moral one about utility being irrelevant to value: the aesthetics of Wilde. He denied the justification by utility because it was untrue: not the real motivation for real mathematical thought. In this awkward truth-telling, Turing also shared Hardy's integrity of integers. 'Phoney' was one of his favourite words of opprobrium, along with 'Politicians, Charlatans, Salesmen.' Turing's motivations, even his practical work, were as unrelated to public or private profit as Hardy's.
G.H. Hardy (Cambridge math.)
from hodges:
Hardy's sharpest reproof was to utilitarian — in his time marxist-influenced — talk of mathematics for planning and order. (It reads oddly now. Today's emphasis would be on short-term profit, which never entered into Hardy's dialectic.) It is now a commonplace remark that Hardy was wrong about relativity and quantum mechanics having no military use, as was soon to be shown. Hardy would have been surprised, I think, that advanced number theory is now of great significance for commercial cryptography. Though allowing the possibility of such an application, Hardy still ended ringingly 'I have done nothing useful.' Turing made no such predictions of purity and issued no soul-searching apology.
But Hardy's point was essentially a moral one about utility being irrelevant to value: the aesthetics of Wilde. He denied the justification by utility because it was untrue: not the real motivation for real mathematical thought. In this awkward truth-telling, Turing also shared Hardy's integrity of integers. 'Phoney' was one of his favourite words of opprobrium, along with 'Politicians, Charlatans, Salesmen.' Turing's motivations, even his practical work, were as unrelated to public or private profit as Hardy's.
G.H. Hardy (Cambridge math.)
from hodges:
Hardy's sharpest reproof was to utilitarian — in his time marxist-influenced — talk of mathematics for planning and order. (It reads oddly now. Today's emphasis would be on short-term profit, which never entered into Hardy's dialectic.) It is now a commonplace remark that Hardy was wrong about relativity and quantum mechanics having no military use, as was soon to be shown. Hardy would have been surprised, I think, that advanced number theory is now of great significance for commercial cryptography. Though allowing the possibility of such an application, Hardy still ended ringingly 'I have done nothing useful.' Turing made no such predictions of purity and issued no soul-searching apology.
But Hardy's point was essentially a moral one about utility being irrelevant to value: the aesthetics of Wilde. He denied the justification by utility because it was untrue: not the real motivation for real mathematical thought. In this awkward truth-telling, Turing also shared Hardy's integrity of integers. 'Phoney' was one of his favourite words of opprobrium, along with 'Politicians, Charlatans, Salesmen.' Turing's motivations, even his practical work, were as unrelated to public or private profit as Hardy's.
G.H. Hardy (Cambridge math.)
from hodges:
Hardy's sharpest reproof was to utilitarian — in his time marxist-influenced — talk of mathematics for planning and order. (It reads oddly now. Today's emphasis would be on short-term profit, which never entered into Hardy's dialectic.) It is now a commonplace remark that Hardy was wrong about relativity and quantum mechanics having no military use, as was soon to be shown. Hardy would have been surprised, I think, that advanced number theory is now of great significance for commercial cryptography. Though allowing the possibility of such an application, Hardy still ended ringingly 'I have done nothing useful.' Turing made no such predictions of purity and issued no soul-searching apology.
But Hardy's point was essentially a moral one about utility being irrelevant to value: the aesthetics of Wilde. He denied the justification by utility because it was untrue: not the real motivation for real mathematical thought. In this awkward truth-telling, Turing also shared Hardy's integrity of integers. 'Phoney' was one of his favourite words of opprobrium, along with 'Politicians, Charlatans, Salesmen.' Turing's motivations, even his practical work, were as unrelated to public or private profit as Hardy's.
...
That application required the war. And war means loss, for mathematics as for everything else. Hardy's 'useless' relativity and quantum mechanics left a Cold War legacy of escalating arsenals; so did Turing's logic.