Not A Spectator Sport

Recent changes
Table of contents
Links to this page


My latest posts can be found here:
Previous blog posts:
Additionally, some earlier writings:
One of my university lecturers gave what we all thought were dreadful lectures. Muddled, unclear, chaotic, with no discernible thread. It took ages to reconstruct and rework the material to a point where we could attack the problems and old exam questions.

I got nearly full marks on that exam.

Other lecturers were brilliant. Clear, lucid, entertaining. But I didn't get full marks on their exams, because I found it hard to do the problems, even though I thought I'd understood the material from the lectures.

I hadn't.

Maths is not a spectator sport. You need to get involved, otherwise you're in the situation of someone who has watched a lot of tennis, but never played.

I used to mock the "it is clear that" phrase when it would then take two or three pages to show the result. But I learned that having done the work to show it, I was then equipped to handle the next stage of the work. Having the explanation given to me as to why it was "clear" would not have done that, my understanding would have been meagre and unsatisfactory, and I would have gradually fallen behind and not been able to understand what was missing.

So when used properly, when used well, when used constructively, the phrase "it is clear that" and its friends are not there because:

  • that's how the game is played (tradition);
  • it excludes the uninitiated/untalented;
  • it's neater to leave out the truth of discovery;
  • it makes the author seem superhuman;
  • there's satisfaction for the reader in understanding the puzzle.

When done properly it's genuinely for more effective communication.

I'm not saying it's always done well - after all, not everyone writes equally well - and I'm not saying that everyone always has the best of motives. But working on what you see as gaps in the presentation really is the best way to understand the material.

There was an occasion when I said all this, and someone replied:

Someone, somewhere will have to work out the combination - I'm suggesting it is more efficient for it to be the one writer than the many readers.

If your purpose is simply to have it written down, then yes. However, if your purpose is to communicate effectively to the readers, then no. The "doing" is an essential part of the eventual "understanding".

This was prompted by a discussion of "How to Read Mathematics" by Shai Simonson and Fernando Gouvea. The article is here:

This has been submitted multiple times to Hacker News, and at the time of writing, the most recent discussion is here:

The comments there repeat similar sentiments time and time again:

  • Mathematics writing should be
    more like computer programs:
    Complete, and unambiguous.

So much misunderstanding, so many misconceptions.

Another rant, another time.

<<<< Prev <<<<
Left Truncatable Prime
>>>> Next >>>>
Just Teach My Child The Maths ... You can follow me on Mathstodon.

Of course, you can also
follow me on twitter:


Send us a comment ...

You can send us a message here. It doesn't get published, it just sends us an email, and is an easy way to ask any questions, or make any comments, without having to send a separate email. So just fill in the boxes and then

Your name :
Email :
Message :



Links on this page

Site hosted by Colin and Rachel Wright:
  • Maths, Design, Juggling, Computing,
  • Embroidery, Proof-reading,
  • and other clever stuff.

Suggest a change ( <-- What does this mean?) / Send me email
Front Page / All pages by date / Site overview / Top of page

Universally Browser Friendly     Quotation from
Tim Berners-Lee
    Valid HTML 3.2!