
A quest for beauty and clear thinking: interviewing John Baez - mathgenius
http://www.mathisintheair.com/eng/2018/12/30/a-quest-for-beauty-and-clear-thinking-interviewing-john-baez/
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hyperpallium
> In math everything has a reason and you can understand it, so you don't
> really need to remember much.

I used to hope for this, but the more I go into mathematics, the more complex
it becomes, the explanations more complex than the explained. I suspect
"mathematical maturity" is the absorption of all this information. It takes
years and years.

Of course once you know it it's easy - like fluency in a natural language, you
aren't aware of all you've learnt.

Probably, if I had John Baez's experience, I wouldn't feel this way...

> everything has a reason

Proofs show _that_ it is true, not _why_ it is true.

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alienfromalphaC
> Proofs show that it is true, not why it is true.

Proofs tell you exactly why something is true as they are nothing more than a
water-tight explanation of why you think your claim is true. Oftentimes proofs
actually precede the claims they are a proof of. For example, you can start
with a set of axioms A from which you derive a packet of theorems and
definitions B. In turn, combining (or separately) you derive more statements
from A, B which we call, say, C. You can continue this process for however far
and long you want. Suppose, at some point you end up at a statement W. Then
you can do this:

Theorem: W.

Proof: Starting at A (or later down the chain/network of theory you built up),
you can just retrace your way back to W. This perfectly explains why W is
true.

Where I agree with you is that the role of memorization is downplayed.
Sometimes, it's helpful to memorize some algorithms and definitions. It clears
up your mind for actual thinking. Partly why they make you memorize a lot of
elementary algebra rules (without proof) in high school so that when doing
Calculus you don't have to think about "lower level stuff". Often, if I
produce a proof that's different from that in my book or someone else, I try
to memorize their proof because likely this way of thinking will recur down
the road in the book and someone else's ideas might produce insight that would
be unavailable to me had I decided to stick to what I know.

edit: I'd add induction proofs usually won't tell you something you didn't
know beforehand. I never read induction proofs unless the author alludes to
some clever trick that's worth remembering.

~~~
hyperpallium
> Proof: Starting at A (or later down the chain/network of theory you built
> up), you can just retrace your way back to W. This perfectly explains why W
> is true.

How does that differ from "showing _that_ it is true?"

> why you think your claim is true

"Why you think your claim is true" is not the same as "why it is true".

I contrasted "showing _that_ it is true" versus "showing _why_ it is true" as
a shortcut to show the distinction; since "why" something is true can also be
interpreted as showing something is true, i.e. how we know it is true. Let me
try to elaborate what I mean by "showing _why_ it is true":

You can trace through a sequence of proof steps, and confirm each one is true
and therefore the conclusion is true, without understanding the whole. For
example, even an automated prover can do this, but, like a Searle's Chinese
room, it ia without understanding.

In the natural sciences, the distinction is clearer, because you show _that_
something is true by empirical observation and experiment: what is the colour
of starlight? what is the trajectory of the moon?

But there are also theories to explain these facts: the life-cycle of stars;
red-shifting due to acceleration; inverse square law of gravity. Though we do
bottom out to "it just is".

\---

Even for highschool elementary aithmetic algebraic, that seem general, there
are (sort of runtime) exceptions: divide by zero (and multiply by zero).

You must learn notation, variations amd abuses of notation.

You have to learn definitions, but I think that's fair enough. They are the
rules of the game, and with even slightly different definitions, you're simply
playing a different game.

But I think elementary geometry doesn't suffer from this: even though it's not
taught rigorously these days (from Eulcid), it still makes sense from first
principles/axioms, and you can see it is true.

It may simply be that modern mathematics has become so divorced from the
directly graspable (and yet so powerful and useful), that you just have to
teach it without understanding.

"Young man, in mathematics you don't understand things. You just get used to
them." \- John Von Neumann (criticism here:
[https://math.stackexchange.com/questions/11267/what-are-
some...](https://math.stackexchange.com/questions/11267/what-are-some-
interpretations-of-von-neumanns-quote))

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yantrams
If I had to choose just one blog or a twitter account for that hypothetical
deserted island question(what is the one x-item you'd choose if stranded on a
deserted island?), it would be that of John Baez without a second thought. His
personal blog and tweets are absolute treasure troves for anyone interested in
Math.

[https://johncarlosbaez.wordpress.com](https://johncarlosbaez.wordpress.com)
[https://twitter.com/johncarlosbaez](https://twitter.com/johncarlosbaez)

The recent breakthrough in finding the smallest Lebesgue cover [1] was
triggered by one of his blog posts about it a few years back.

1 -- [https://www.quantamagazine.org/amateur-mathematician-
finds-s...](https://www.quantamagazine.org/amateur-mathematician-finds-
smallest-universal-cover-20181115/)

~~~
intuitionist
real heads will remember his proto-blog, “This Week’s Finds in Mathematical
Physics,” which goes all the way back to 1995:
[http://math.ucr.edu/home/baez/TWF.html](http://math.ucr.edu/home/baez/TWF.html)

------
S_A_P
I read the title of the article as Joan Baez at least half a dozen times
today. I really thought this was about her.

~~~
anybodyoutthere
This is about her brother (I'm not joking).

~~~
mlevental
cousin

------
Ericson2314
> Mathematics seems to attract people who enjoy patterns, who enjoy precision,
> and who don't want to remember lists of arbitrary facts, like the names of
> all 206 bones in the human body.

I do love that dig at the insane US medical education system.

~~~
throwawaymath
Why is that a dig? It doesn't seem strange to me that someone in medical
school has to learn all 206 bones in the human body.

~~~
hyperpallium
The quote is not about learning the bones, but their _names_.

TBF there is some regularity to the names e.g. the finger bones (phalanges)
are named in a 2D grid of thumb..litte X inner..tip:

    
    
        I..V x proximal,middle,distal - Imiddle
    

Toes are same named!

~~~
kryptiskt
If a doctor didn't know the names, what would he put in the patient's journal
pre-surgery so the surgeon knew where to operate? Would he draw a hand with an
arrow to the correct bone or write a paragraph describing where it is?

~~~
hopler
A diagram seems less likely to be incorrect.

