

A new way to write mathematics - qubitsam
http://rjlipton.wordpress.com/2013/07/14/surely-you-are-joking/

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zepolud
This is extremely shallow. This guy deliberately focuses on the most tabloid-
style reporting of the HoTT book he could find, a New Scientist piece, and
then uses it to attack the book itself for having unsubstantiated grandiose
claims. Well, guess what -- you're reading a New Scientist article, what did
you expect?

Perhaps it would be more befitting to a person in his position (a CS
professor, it appears) to actually critique the book itself. Judging by his
rant, it's doubtful he even read it. Otherwise he would have known that the
most controversial thing about it is a preference of constructive proof, when
possible, as they are generally both more illuminating and rely on fewer
assumptions.

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tome
Is he really attacking the book, though?

"I feel compelled to say something about not his work, but the New Scientist
article. The article is at best in my opinion misleading."

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strangestchild
Horses for courses. Whilst I'm skeptical that we're at the stage where
mechanical proof-checking is viable, such a technique would be immensely
valuable.

On the other hand, it is of course true that if the proof _itself_ is
mechanistic, most mathematicians would feel that a lot of the important
essence of the result had been lost.

Voevodsky's work is apparently in the former, and the blog author conflates
this with the latter in order to (wrongly) criticise it.

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Tichy
I really disagree. A proof is a proof, doesn't matter if it helps you
understand anything or not.

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phaemon
That can't be right. Otherwise you might as well just churn out billions of
proofs like "Proof that 34634+7684=42318". Surely the _only_ value in a proof
is whether or not it helps you understand something?

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Tichy
The value of a proof is a different matter.

And for example knowing e=mc^2 might be valuable in itself, independent of
understanding relativity theory.

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phaemon
I don't know what you mean. e=mc^2 requires at least _some_ understanding to
make any use of it, lest you suppose burning a single lump of coal will keep
your power station running all week ;-)

And even then, you need to know that "e" stands for "energy"...

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Tichy
It wasn't the best example, but let's take the area of a circle, which is
r^2*PI. I don't even know the proof for that by heart, but I can still make
use of the information. A proof simply tells me that something is true.
Further understanding is just a bonus.

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phaemon
The understanding here is that πr^2 is the area of a circle.

You are saying that this understanding is important/useful _even without the
proof_.

This is in direct contradiction to what you said earlier, where you said the
proof was important/useful _even without the understanding_.

Perhaps we're using the word "understanding" to mean two different things here
and that's where the contradiction lies.

