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There are plans to build a Museum of Mathematics in Manhattan and over $20 million has already been raised for the ’cause’. The Math Midway, which already exists as a traveling exhibition, has something of a preview of coming attractions. There is also a discussion about what mathematicians would like to see at the museum taking place on MathOverflow here.

What do you think of this idea? Personally, I am skeptical, though I may just be being snobbish – it is likely that my academic leaning precludes a fair judgement of such a thing as a museum of mathematics because I will always be tempted to say “If you want to learn about maths, then maybe you should study some maths: Read some books, pay attention at school, discuss maths with teachers, discuss it online, join a math club/circle etc.” I’d be worried about the negative effect of people going in and saying “Oh so this is maths? It’s boring”. Which seems to me even less desirable than “I know nothing about maths”, because my response to the latter can be “If you studied it like I do, then you too would love it!”

So, if it can be accepted that not everything is necessarily amenable to ‘museumization’, then I would definitely argue that mathematics falls into this category and would make a poor subject for a traditional-style museum. (I’ve never been a huge fan of Science Museums either, so perhaps I’m just the wrong person to ask – what do ‘proper’ academic scientists think of the Science Museum in London, for example?)

It sounds a bit romanticised by it’s also arguable that one really does need to invest some effort into appreciating mathematics. Every mathematician knows the feeling when, while at the pub, having just defended the beauty and awesomeness of mathematics, a friend says defiantly “Go on, tell me some maths”…  Show me the beauty and awesomeness. But this is impossible. The passivity of this stance immediately places the friend outside of those who are capable of appreciating mathematics on the scale that the mathematician does. You can’t just sit there and be shown. You have to do. You have to show yourself! The mathematician knows that her friend isn’t actually prepared to spend the next hour struggling to appreciate some minute idea which the mathematician seems to assert is worth understanding.

This comment was sort-of inspired by seeing the MathOverflow discussion, but there is a character limit on comments in the forum!

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Higher Dimensions

I want to extend the treatment to we just went through to higher dimensions. In my view, this provides a very nice way of thinking about why the generalisation of the derivative to higher dimensions is what it is.  It has certainly taken me a while to appreciate the definition of the derivative of a a function of many variables and I am attempting to share some of my thoughts.

In the last post we thought about graphs of functions and tangent-lines. Now, the graph of a function is intially something 0ne thinks of a picture of that function. In my opinion, there is a sense in which one ought to continue to do so. It’s just that now, we’ll be thinking about \mathbb{R}^m-valued functions f defined on  an open subset U of \mathbb{R}^n. Recall that the graph of f is the set of points (x, y) in U \times \mathbb{R}^m such that f(x) = y.

What might we mean by the derivative of f ?

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