
Lessons I Wish I Had Been Taught (1996) [pdf] - samasblack
http://www.math.tamu.edu/~cyan/Rota/tenlesses.pdf
======
cholmon
1) Lecturing \- Every lecture should make only one main point \- Never run
overtime \- Relate to your audience \- Give them something to take home

2) Blackboard Technique \- Make sure the blackboard is spotless. \- Start
writing on the top left-hand corner

3) Publish the Same Result Several Times

4) You Are More Likely to Be Remembered by Your Expository Work

5) Every Mathematician Has Only a Few Tricks

6) Do Not Worry about Your Mistakes

7) Use the Feynman Method

8) Give Lavish Acknowledgments

9) Write Informative Introductions

10) Be Prepared for Old Age

~~~
joe_the_user
A good portion of these points involve "integrate into the mathematical
exposition methods of your time" and become useless as exposition methods
change. If blackboards are supplanted by digital whiteboard that autoerase or
autoscroll, exposition may different - slide techniques would be useful to
include.

Another portion involve the "exposition culture" \- that the greatest of a
given mathematician still has to interface with mathematics proper (or at the
limit, a mathematician who is "outre", "out-there", may publish a theorem and
have mathematics simply throws up it's hands as happened with ABC theorem - at
least so far). Essentially, have a strategy that lets you keep working on the
hard stuff but without getting entirely lost on it.

But I think the really cool parts involve rules of thumb for going through
life and solving a few hard, important problems. This reminds me of Andrew
Wiles talking about the problem that really, really smart math grad students
have when confronted with problems that they can't solve in 24 hours.

Edit: and naturally, it's worth noting that exposition method and culture are
important for anyone also working on hard problems since knowing the "smell"
of good or bad proofs is crucial if one is going forward towards a really big
proof - see the point that most good proofs can survive a little bit of error.

~~~
jacobolus
Blackboards are much better as lecture tools than digital whiteboards with
autoscroll, or most uses of powerpoint, or whatever else people try, in my
experience.

I wish that more lecturers would consider returning to blackboards, instead of
the lazy slides they currently do. It would both improve their talks and waste
less of their prep time.

The nice thing about blackboards is that lecturers don’t try to write every
word on a screen, but just talk as normal, only putting up explicitly
technical content like diagrams and formulas. They can add or remove things
from the board in response to audience feedback, and can improvise new ideas.
Maybe most importantly, (sufficiently large) blackboards keep a large amount
of context in view at any given time.

Blackboards are especially good as classroom tools because they are a
fundamentally improvisational and accessible medium. You can’t prepare all the
drawings in advance, which means that anything a lecturer can do on the board
a student can in principle also do, and the form of the teacher’s lecture is a
direct part of the pedagogy: the student can learn to imitate the same mode of
thought with access to the same tools. There can be a drawing- and formula-
based dialog between teacher and students in which they are all operating as
equal peers, unlike powerpoint where one participant spent hours making a
bunch of pretty graphs or typing up formulas in a cryptic markup language, and
the other participant gets no insight whatsoever into how.

Making _good_ use of computers would mean handing out interactive
demonstrations with their full code available [code might be implemented in
some drawing-based environment, not necessarily just lines of ASCII] at every
lecture, and then showing how the code works and showing how to twiddle the
parameters as part of the lecture, alongside the traditional writing-and-
drawing-on-a-blackboard part of the lecture. Ideally students would have some
way of also interacting with the same medium during class.

But making good interactive diagrams or writing code whose primary purpose is
exposition takes 2 orders of magnitude more prep time than just throwing words
and static diagrams up, and is just not feasible for individual lectures in a
current education setup. Ideally we would have much better improvisational
computer demonstration/diagram tools, but in practice the drawing tools we
have are not really designed for a computer medium, and all pretty much suck.
(If Bret Victor’s ideas from “Inventing on Principle” and “Stop Drawing Dead
Fish” and “Drawing Dynamic Visualizations” were turned into polished,
production-ready, mainstream tools, we might have a chance.)

I’ve seen some pretty effective lectures that were done live-coding style,
e.g. in some notebook-based tool, but it depends on having the right topic for
the lecture.

~~~
joe_the_user
_Blackboards are much better as lecture tools than digital whiteboards with
autoscroll, or most uses of powerpoint, or whatever else people try, in my
experience._

If you're down voting me for mentioning these, I have no dog in the fight. I
only said that the advice was "learn your tools" \- IF the tools HAPPENED to
change, the advice would change. If not, sure, use a blackboard well.

~~~
jacobolus
No idea why people are downvoting you. My comment about blackboards is kind of
a tangent.

------
manmal
„Every mathematician has only a few tricks“

I think the same is true for programmers. My trick (in mobile dev) is to use
state machines everywhere. State management has become my mantra, and it’s
helped me tremendously in making sure my apps don’t end up in an undefined
state. Swift is especially great at this because it can store values in enum
cases. Now, most of my bugs stem from overlooking potential substates and not
propagating state changes correctly to other parts of the app; the 2nd of
which can be fixed by having proper boilerplate code.

Other tricks I‘ve encountered so far, partly from other programmers:

\- Make it work, then make it better (awesome for very rapid prototypes that
evolve into mature products over time)

\- Go as low level (eg C or C++ for iOS; examine OS internals with Hopper) as
possible (superior performance and awe-inspiring source code, leading to wider
community recognition)

\- Ask other people first if working on an unfamiliar problem (only works if
your network is strong; can speed you up x100 though vs googling and digesting
yourself)

\- Use Reactive style deliberately (if done properly, only semantical bugs are
left; bonus: streams are very natural abstractions of app IO)

Those are in part orthogonal to each other, but I feel that you (or just I)
can’t use more than 1 or 2 tricks at once.

~~~
scotty79
My trick for fixing software is "If you can't fix it, break it more and use
effects of your damage to learn about the system and see what you can affect."

~~~
tonyarkles
That’s often my approach to diving into performance problems too. When a
client says “it starts to slow down a bit at 2 requests/sec”, my first thought
it “what happens at 20req/sec?”

I call it “turn it up to 11 and see what breaks”

------
trentnix
This appears to have been linked to Dr. Catherine Yan's faculty page. She is a
faculty member for the math department at Texas A&M. I was fortunate to take
Discrete Math from her and I learned a lot. I also worked with her husband,
Hua, and learned a lot from him as well. Very nice people.

This may seem a bit off-topic, so I apologize if I'm stealing bits from
anyone.

Reading the blackboard technique item gave me a good laugh. Dr. Yan is, on her
tiptoes, maybe 5' tall. And that's generous. She used the whiteboard
prolifically while she lectured, and the bottom half would be covered as she
provided examples for her lesson.

The top half, the half she couldn't reach, was utterly spotless.

------
AnimalMuppet
It's not obvious from the title, but it's lessons about giving mathematics
lectures and about doing mathematics. Most of the lessons are applicable to
any technical subject, though.

Worth reading.

------
dang
Discussion from 2016:
[https://news.ycombinator.com/item?id=11747598](https://news.ycombinator.com/item?id=11747598)

From 2011:
[https://news.ycombinator.com/item?id=3220746](https://news.ycombinator.com/item?id=3220746)

------
perl4ever
I always thought the Feynman method was "Write down the problem. Think very
hard. Write down the solution."

~~~
nicwilson
That's the Feynman Algorithm.

------
stablemap
A small thing: I think it makes sense to link to the AMS’s copy. The _Notices_
are all free.

[http://www.ams.org/notices/199701/comm-
rota.pdf](http://www.ams.org/notices/199701/comm-rota.pdf)

------
mighty_bander
I think this is satire. If it is, it's damned good. If not, it's at worst
practical.

------
yesenadam
(1996)

~~~
mighty_bander
> 2017

> Arguing flippantly

