I'm reading Alfred North Whitehead's "An Introduction to Mathematics". I need help understanding a sentence at the beginning of the book:

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 great 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.

I understand the Shakespearean reference, but I'm having trouble understanding the last phrase.

I believe the author is saying something like this: stuff we see in mathematics (that we lack understanding) cannot be blamed illusive (the ghost can, but not math) and in the end, math is too noble for our gross methods (and that's why we can't understand it).

This sentence looks weird to me. I'd love to hear what other people think about it.

  • 5
    No, he’s saying that you can’t use the “too noble excuse” for math.
    – Jim
    Commented Feb 4, 2019 at 4:48
  • Illusive or elusive?
    – Lawrence
    Commented Feb 4, 2019 at 5:00
  • Ok, I see your point. At the same time, I'd love to know why my post was downvoted. If there is a better Stack Exchange site to post this or if there is something wrong with my post I'd love to know. I'm not a native English speaker, and it would be lovely to find a non-hostile place where I can discuss my doubts. I've been trying to understand this sentence since yesterday, so I don't think merely reading it more times would help.
    – Daniel B.
    Commented Feb 4, 2019 at 5:05
  • The original text says illusive.
    – Daniel B.
    Commented Feb 4, 2019 at 5:06
  • Today we might say "illusoriness" rather than "illusiveness." The root concept in both words is "illusion." Presumably, Hamlet and his friends might dismiss the ghost of Hamlet's father as an illusion, but students of mathematics can't realistically argue that mathematics is a mere illusion. What makes it hard to grasp is its complexity, not its spectral insubstantiality or its refusal to follow the dictates of logic or reason.
    – Sven Yargs
    Commented Feb 4, 2019 at 5:26

1 Answer 1


It targets our feelings when trying to understand mathematics: It is like a ghost, we believe to grasp him, but he escapes in the next second... We know that ghosts are ghosts, and they just disappear, with mathematics it is different. We experience the same feeling of escaping from our minds every time we feel to be close, but in this case, we know for sure this is for our minds not to be finely tuned to it (yet).

This is the way I understand to the above, after some years of math studies and countless sleepless nights...

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