
Teaching and Learning “What Is Mathematics” [pdf] - jasim
https://www.discretization.de/media/filer_public/2014/09/05/20140413icm-proceedings-ziegler.pdf
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tinalumfoil
I think the problem with defining Mathematics is that everyone interested in
defining Mathematics has a tendency to cast an overtly wide net such that
nearly can be considered some form of Math. Wikipedia's definition of math (in
the article) seems to have the same implications as wikipedia's definition of
philosophy ("Philosophy is the study of general and fundamental problems") in
terms of scope without the confidence to say it in as blunt terms. Philosophy
can get away with it because it is the historical ancestor of most organized
mental endeavors, but the math page can't seem to admit it.

Speaking of Wikipedia, it's well-documented that first link in many pages is
the parent of that subject, and that the great ancestor of nearly all pages is
"Philosophy" [0].For instance, Delaware is a US. State which is a political
entity which is an entity which is something that exists, making it the
subject of Ontology (study of existence) which is a subject of Philosophy.
Mathematics however is partly the study of quantities, which can exist as a
magnitude which is, of course, a subject of math. This means, nearly all of
WikiProject Mathematics is determined to stay detached from the rest of human
knowledge (admittedly based on this one, anecdotal and inconsequential
metric).

[0]
[https://en.wikipedia.org/wiki/Wikipedia:Getting_to_Philosoph...](https://en.wikipedia.org/wiki/Wikipedia:Getting_to_Philosophy)

~~~
voidhorse
But what of the philosophy of mathematics!
[https://en.wikipedia.org/wiki/Philosophy_of_mathematics](https://en.wikipedia.org/wiki/Philosophy_of_mathematics)

 _All_ intellectual roads lead to philosophy.

Joking aside, I think we also run into problems with defining mathematics
because its application and the thing itself are not really separable. One can
have the philosophy of something, e.g. philosophy of mathematics, because
philosophy as a method or type of intellectual excursion is not a single thing
--you can go about philosophizing in many different ways, even if your topic
is the same (e.g. logical positivist handling of philosophy of language vs.
the ordinary language philosophers)--in the case of mathematics it is a field
of study but it is more fixed as a method or tool of thought--there are
several ways to go about philosophizing no matter what branch of philosophy
you tackle, whereas with mathematics, while there are different branches of
study, there is really only one mathematics--i.,e. there's only one way to go
about mathematicizing correctly for a given problem, whereas there's not
really a 'correct' way to philosophize about a given problem.

I would define mathematics as a particular mechanism of human thought/a
particular way we understand the world (the human mechanism of quantification
and manipulation of said quantities)

Of course mathematical realists will disagree with me.

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ivan_ah
good quote: "Why do so many pupils and students fail in mathematics, both at
school and at universities? There are certainly many reasons, but we believe
that motivation is a key factor. Mathematics is hard. It is abstract (that is,
most of it is not directly connected to everyday-life experiences). It is not
considered worth-while. But a lot of the insufficent motivation comes from the
fact that students and their teachers do not know “What is Mathematics.” Thus
a multifacetted image of mathematics as a coherent subject, all of whose many
aspects are well connected, is important for a successful teaching of
mathematics to students with diverse (possible) motivations."

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johnbender
> Thus a multifacetted image of mathematics as a coherent subject, all of
> whose many aspects are well connected, is important for a successful
> teaching of mathematics to students with diverse (possible) motivations.

Somewhat useless personal anecdote to follow on this quote that I also liked:

Prior to my PhD studies I had heard of math and experienced it largely as
computation. Arithmetic, matrix multiplication, integration by parts etc etc.
This is, to my mind, the most terribly boring part of mathematics.

It's not certain, but I suspect that providing at least a few alternate
characterizations of mathematics to students stuck doing computations for
years and years will almost certainly help some of them find their way to
regions of the subject that they find interesting.

~~~
voidhorse
I had a somewhat similar experience. No PhD but I had always hated math as a
kid learning nothing but, as you say, rote computations in school.

By chance I stumbled on Frege's philosophy of mathematics/investigations into
the foundations of mathematics in college and suddenly math was actually
really interesting. I find proofs, set theory, algebras, and other
mathematical domains closely related to logic way more fun than rote
computations. I recall thinking I could have really fell in love with math and
maybe even excelled at it if my schooling had ever given me so much as a hint
that this stuff was also part of mathematics and it wasn't mere repetition of
the same old computations, and that all those formulas build on each other and
actually have very interesting justifications.

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gmcrews
An old saying with a deep truth: A mathematician is a person who will assume
anything except responsibility.

~~~
lanstin
Which is why devops will always have troubles.

