

Terence Tao: Evidence for mathematical conjectures short of proof - _delirium
http://rjlipton.wordpress.com/2010/06/19/guessing-the-truth/#comment-3711

======
cma
"The Mathematical Experience" goes into this in pretty good depth.

[http://www.amazon.com/Mathematical-Experience-Phillip-J-
Davi...](http://www.amazon.com/Mathematical-Experience-Phillip-J-
Davis/dp/0395929687)

~~~
btilly
Upvoted for bringing up _The Mathematical Experience_ in a relevant way.

If I could get everyone to read just one book about mathematics, that book
would be _The Mathematical Experience_. More than any other book, it gives the
actual experience of what mathematics is like.

Much of it is accessible to someone who is still in high-school. And yet it
has valuable lessons for people who have PhDs in the subject. I know a number
of mathematicians who say that it explains why they went into math. And I can
say that in its pages I can find explanations of both what caused me to love
math, and eventually to leave it.

~~~
calibraxis
For anyone interested, a new book by Reuben Hersh is scheduled for this
Christmas: "Loving and Hating Mathematics: Challenging the Myths of
Mathematical Life".

[http://www.amazon.com/Loving-Hating-Mathematics-
Challenging-...](http://www.amazon.com/Loving-Hating-Mathematics-Challenging-
Mathematical/dp/0691142475)

[Edit: I asked why you left math, out of curiosity, but then I realized you
might have a blog...]

~~~
btilly
I take it you found <http://bentilly.blogspot.com/2009/11/why-i-left-
math.html> then? :-)

~~~
calibraxis
Yes, exactly. :-)

------
ced
This discussion is even more interesting in the context of natural sciences,
since no scientific law is ever proven. What were the odds, in 1850, that
Newton's laws would be "disproved"?

From Jaynes' _The Logic of Science_

 _It depends entirely on this: Against which specific alternatives are we
testing Newton's theory?

For example, if you ask a scientist, "How well did the Zilch experiment
support the Wilson theory?" you may get an answer like this: "Well, if you had
asked me last week I would have said that it supports the Wilson theory very
handsomely; Zilch's experimental points lie much closer to Wilson's
predictions than to Watson's. But just yesterday I learned that this fellow
Wolfson has a new theory based on more plausible assumptions, and his curve
goes right through the experimental points. So now I'm afraid I have to say
that the Zilch experiment pretty well demolishes the Wilson theory."_

I think that the first ~6 chapters of the book should be required reading for
anyone in the natural sciences. An early drafts can be found here:
<http://www-biba.inrialpes.fr/Jaynes/prob.html>

------
gjm11
The whole discussion of which Tao's comment is a part is well worth reading
for those who enjoy such things: lots of interesting ideas there.

------
teuobk
On a related topic, what are some examples of well-known conjectures,
generally believed to be true, that were later proven to be false?

~~~
myffical
The Kelvin problem: what is the optimum way to partition 3D space into
identical cells, such that the surface area between them is minimized? Lord
Kelvin conjectured that the Kelvin cell gave this optimum partitioning. This
conjecture stood for 100 years until Denis Weaire and Robert Phelan found a
better cell in 1993.

<http://en.wikipedia.org/wiki/Weaire%E2%80%93Phelan_structure>

