[FOM] Convincing math-blind people that math is different

[Frank Waaldijk]

Dear all,

having read some of the responses to Tim Chow's question, let me respond
also with a somewhat ironical counterquestion:

Is it possible to convince an art-blind person that artistic knowledge is
qualitatively different from other kinds of knowledge?
By an art-blind person, I mean someone who lacks the internal experience of
artistic beauty and the feeling of wonder and spirituality that art
(usually) confers.

Tim wrote:

>
> Roughly speaking, the question is whether it is possible to convince a
> math-blind person that mathematical knowledge is qualitatively different
> from other kinds of knowledge.
> By a math-blind person, I mean someone who lacks the internal experience
> of mathematical proof and the feeling of certainty and objectivity that
> mathematical proof (usually) confers.


Personally, I would agree that math is different from other kinds of
knowledge, that is precisely why it is called math. But the same holds for
physics, history, music, discourse analysis, philosophy, zoology, art, etc.

I do not see that history resembles zoology more than mathematics resembles
physics.

But now for the details of Tim's question: is it really true that we are
all so agreed as mathematicians? I don't think so (self-fulfilling my own
view here :-) ).

In fact there are very important disagreements on the nature of
mathematics. For now I think I could summarize these disagreements thus: we
are quite divided on the nature of infinity (if it exists at all).

In my experience, mathematics is not objective at all. This can be seen
retrospectively in history as well. The irrationality of sqrt(2) comes to
mind, and the existence of non-euclidean geometries. But these have been
resolved. The current fundamental debate (in my eyes) is on infinity, and
sides in this debate are not taken objectively (whatever that word may
actually mean) - at least not in my subjective opinion.

`No one shall expel us from the paradise that Cantor created for us.'

These are hardly the words of an objective scientist (if such a person
could even exist). And the feeling behind these words is still very alive
today, accounting for much of why classical mathematics is taught so
predominantly - over constructive mathematics or finitism.

The feeling of certainty that Tim mentions to me is just that: a feeling.
Art and music also provoke feelings,  and as has been pointed out, so does
religion. `No one shall expel us from the paradise that Cantor created for
us' is a phrase which to me exemplifies that mathematics is governed by
social dynamics just like any other discipline.

To me, there is a special beauty in mathematics, which is why I like it so
much.

Hoping to have contributed something, best wishes,

Frank Waaldijk

-- 
frank waaldijk
visual artist and mathematician
www.fwaaldijk.nl/mathematics.html
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