Once upon a time, I decided I would be vulnerable on Twitter. As part of that, when someone posted a puzzle that I was interested in, I decided that I would not wait until I had a complete answer to a problem before I responded, but instead I would tweet out my partial thinking. If there were mistakes I would leave them there and respond with how I resolved them, rather than deleting them and removing the evidence that I had made a mistake. I wanted the whole process of solving problems to be out there in plain sight for everyone to see.
One reason I wanted to do this was because too often we give the impression that maths is all so slick and easy, when really it is actually messy and hard. This issue is exacerbated by the nature of puzzles, which often have clever simple solutions, and when people share only that, we give this impression that maths is done by some sort of divine inspiration of the clever trick. I wanted my responses to problems to show the honest process of muddling through things, and getting them wrong, and only seeing the clever idea after I’ve done it the unclever way, and even if a clever way did occur to me, what it was that made me think of it.
Over time, this has grown into me doing epically long tweet threads where I live-tweet my whole solution process, including all the extra bits I ask myself that are sideways from or beyond the original goal of the problem. I have to say I really really love doing this. I love puzzles and learning new things, and it’s nice to do it and count it as part of my job. I also get to have a record of the whole process for posterity to look back on. Even in the moment, it’s very interesting to have to force myself to really slow down and be aware of my own thought processes enough to tweet them as I go. In my daily work I have to help other people to think, so the sort of self-awareness that this livetweeting of my thought process brings is very useful to me, not to mention fascinating.
In the beginning, I had some trouble with people seeing my rhetorical questions as cries for help and jumping in to try to tell me what to do. I also had people tell me off for not presenting the most elegant solution, saying “Wouldn’t this be easier?” Every so often I still get that happening, but it’s rarer now that I have started to become known for this sort of thing. I am extremely grateful that a few people seem to really love it when I do this, especially John Rowe, who by rights could be really annoyed at me filling up his notifications with hundreds of tweets with a high frequency of “hmm”.
I plan to continue to do this, and so if you want to keep an eye out for it, then I’ll happily let you come watch. From this point forward I will use the hashtag #trymathslive when I first begin one of these live problem-solving sessions, so I can find them later and you can see when I’m about to do it. (I had a lot of trouble looking for these tweet threads, until I remembered that a word I use often when I am doing this is “try” and I searched for my own handle and “try”. In fact, that’s the inspiration for the hashtag I plan to use.)
Note that I am actually happy for people to join in with me — it doesn’t have to be a solitary activity. I would prefer it if you also didn’t know the solution to the problem at the point when you joined in, but were also being authentic in your sharing of your actual half-formed thoughts. I definitely don’t want people telling me their pre-existing answers or trying to push me in certain directions. If you feel like you must “help” then, asking me why I did something, or what things I am noticing about some aspect of the problem or my own solution are useful ways to help me push my own thinking along whatever path it is going rather than making my thinking conform to someone else’s. I will attempt to do the same for you.
To finish off, here are a LOT of these live trying maths sessions. (If you click on the tweet, you’ll go to the thread without having to log into twitter. You’ll have to scroll up a tweet or two to get to the original problem and scroll down, often a long long way, to find what happened.) I hope you enjoy reading them as much as I enjoyed doing them.
4th July 2019
Do you mind if I give this a go?
— David Butler (@DavidKButlerUoA) July 4, 2019
28th June 2019
— David Butler (@DavidKButlerUoA) June 28, 2019
23rd June 2019
— David Butler (@DavidKButlerUoA) June 23, 2019
12th June 2019
I am going to live-tweet my solution process for this. Look away if you don’t want to know… https://t.co/av1yPL98R8
— David Butler (@DavidKButlerUoA) June 11, 2019
May 28 2019
OK let’s try it!
(1+9^(-4^(7-6)))^(3^2… hmm. That stack of powers I’m a bit confused about. Is it 3^(2^5) or (3^2)^5? I may have to come back to that later.
— David Butler (@DavidKButlerUoA) May 27, 2019
May 17 2019
I wonder: at what height is the volume of a cone above that height equal to the volume below? What about the surface area? Are there any cones where it’s the same height?
— David Butler (@DavidKButlerUoA) May 17, 2019
17th April 2019
Ooh! I’ve done this before but I can’t remember. So let me try again now…
— David Butler (@DavidKButlerUoA) April 17, 2019
20th March 2019
The 72 makes it more accurate but when I do it for a class I tend to use 70 as well and stress the fact it's an approximation but very useful without having to use logs
— Gavin Scales (@ScalesGavin) March 19, 2019
24th February 2019
I don’t know how to solve it in my head yet (or at all) — and I don’t want any hints — but I do notice I can put a circle here: pic.twitter.com/QTjRqlKln1
— David Butler (@DavidKButlerUoA) February 24, 2019
21st February 2019
Ooh! Let me try!
— David Butler (@DavidKButlerUoA) February 21, 2019
28th November 2018
Hmm. If assuming that top edge is divided exactly in half. I hope that’s ok. I’ll figure out it it’s necessary later.
— David Butler (@DavidKButlerUoA) November 29, 2018
5th November 2018
Ok. Not sure where to start but I do see a halved triangle up the top there. pic.twitter.com/a0bPMVkR2R
— David Butler (@DavidKButlerUoA) November 5, 2018
14th October 2018
All right. I will live tweet my process. Be aware I will go to bed very shortly, so there will be a several-hour gap.
— David Butler (@DavidKButlerUoA) October 14, 2018
4th October 2018
Ok, I don’t know how to do this already so here are some live thoughts about it…
— David Butler (@DavidKButlerUoA) October 3, 2018
11th March 2018
My first thought is: how would I even start thinking about that?!
(This is not a request for help, just being honest about my thought process.)
— David Butler (@DavidKButlerUoA) March 11, 2018
21st Janurary 2018
— David Butler (@DavidKButlerUoA) January 20, 2018
5th December 2017
— David Butler (@DavidKButlerUoA) December 14, 2017