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The introductory paragraph of the book An Introduction to Mathematics, written for general audience by the great British mathematician Alfred North Whitehead goes like this:

Chapter 1: THE ABSTRACT NATURE OP MATHEMATICS

The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods, all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this science eludes the efforts of our mental weapons to grasp it - "'Tis here, 'tis there, 'tis gone" - and what we do see does not suggest the same excuse for illusiveness as sufficed for the ghost, that it is too noble for our gross methods. "A show of violence," if ever excusable, may surely be "offered" to the trivial results which occupy the pages of some elementary mathematical treatises.

I am completely at sea trying to understand the last line, starting with "A show of violence"..

Is he referring to The Tragedy of Hamlet (which I haven't read or know much about) or is a "show of violence" used as an expression or a metaphor?

  • Try Googling "show of violence" + Hamlet. 'A display of violence' would be a more common expression nowadays, but Whitehead may be paraphrased 'Most modern maths textbooks are so unspired, you could be excused for slinging them in the bin.' – Edwin Ashworth Dec 17 '14 at 8:05
  • Thanks! It is an expression from Hamlet then. And from what I understand of the scene, your interpretation seems valid. – Lavya Dec 17 '14 at 8:40
  • @Lavya: Edwin means "uninspired" (unmotivated); there's no such thing as "unspired". – user21820 Jan 4 '15 at 12:52
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By way of making explicit the citation that Edwin Ashworth alludes to in his comment above, here is the relevant quotation from Hamlet (Act 1, scene 1), beginning with Horatio's attempt to detain and speak to the ghost of Hamlet's father:

Horatio. But soft; behold! lo, where it comes again!/ I'll cross it, though it blast me.—Stay, illusion!/ If thou has any sound, or use of voice, Speak to me:/ ... Or if thou hast uphoarded in thy life/ Extorted treasure in the womb of earth,/ For which, they say, you spirits oft walk in death, [The Cock crows.]/ Speak of it: stay, and speak.—Stop it, Marcellus.

Marcellus. Shall I strike at it with my partizan?

Horatio. Do, if it will not stand.

Bernardo. 'Tis here!

Horatio. 'Tis here!

Marcellus. 'Tis gone! [Exit Ghost.]/ We do it wrong, being so majestical,/ To offer it the show of violence;/ For it is, as the air, invulnerable,/ And our vain blows malicious mockery.

Whitehead's references to this scene from Hamlet begin with his equating of mathematics to the ghost of Hamlet's father in its illusiveness (that is, its illusoriness, which also makes it elusive when one attempts to grasp it). In Hamlet, Marcellus condemns the efforts of himself, Horatio, and Bernardo to detain the ghost by "offer[ing] it the show of violence" on grounds that the apparition is both "majestical" (that is, noble) and "invulnerable." For his part, Whitehead considers that a show of violence toward some elementary mathematical treatises is appropriate, given the trivial results that fill their pages.

Whitehead's opening paragraph is thus largely devoted to an extended fancy about the difficulty of getting from elementary-level mathematics to what he calls "processes of interest"—a difficulty that he describes by analogy to the difficulty of detaining the ghost of Hamlet's father.

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