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If math is more than proof, we need to better celebrate the rest of it

433 points · 285 comments · num42

ForgotMyUUID · 1789802300 · focus · HN ↗
I’m reminded of that famous debate between Poincaré and Hilbert at the International Congress of Mathematicians in Paris in 1900. It was then that everyone decided to follow Hilbert’s path, and proof came to be valued more than intuition. I think modern math at school and at applied university kind of lost this intuitive part.
I try to teach my students that mathematics is, first and foremost, a very precise language of communication. It’s sometimes amusing to ask those who don’t like math to do without it entirely, just to see how much harder it becomes to describe the things around them.
Second thing I tell them, formulas are the essence of mechanisms in their purest form. And in this form, they’re much easier to grasp and mentally manipulate. It always amused me, after taking a mechanics course, to imagine that for any formula, you could visualize a mechanism or process that implements it.
And third thing, I suppose, the ability to verify one’s own statements as proof. Although, of course, mathematicians would probably tear me apart here for my heresy:sorry, I’m not a mathematician, but an engineer. You can make mistakes by using incorrect assumptions, but at some point, analysis itself will show you that you were mistaken. There’s a wonderful book, How to Prove It by Daniel Velleman, which provides an introduction to proof for the uninitiated like me. I really enjoyed it.
1. Geof25 · 1789804528 · focus · HN ↗
  People often hate math because it was not explained to them correctly, usually by people who are good mathematicians but know close to nothing about teaching.
  It was so infuriating to see everyone in the class absolutely fail on a specific subject and the "teacher" assumed that everyone must be stupid then. No self reflection, no questioning himself why he is not getting gaussian distribution in marks, just straight Fs.
  1. krisoft · 1789807927 · focus · HN ↗
    > usually by people who are good mathematicians but know close to nothing about teaching.
    I higly doubt that. Maybe in university level courses. Most people’s only experience with mathematics is an elementary or high school teacher who were probably themselves at best mediocre at the subject. Simply because of selection factors. Those who are good at math are encouraged to go into STEM. There will be of course exceptions everywhere, but that is not what “usually” happens.
    And thats just about being good at maths the school subject, which is distinct from being “ good mathematicians” the science / research topic. Mathematicians are few and far between, simply because it is a specialist subject. There just aren’t enough of them to go around for them to be the formative experience around math for most people.
    graemep · 1789814775 · focus · HN ↗
    I think the problem is partly circular. Most people do not like maths. This includes most primary school teachers - in places I know primary school teachers are not subject specialists so just reflect the population of those with the required level of education in terms of their attitude to maths.
    If you do not enjoy a subject, any subject, you cannot make it fun for those you teach. In the case of maths specifically its pretty bad: <a href="https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician%27s_Lament.pdf" rel="nofollow">https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician%...
    My daughter hated maths when I took her out of school at the age of nine. A few years later she was very good at it and enjoying maths and STEM subjects. When she went to a sixth form college[1] she liked it well enough to pick it as one of her A levels[2].
    [1] <a href="https://en.wikipedia.org/wiki/Sixth_form_college" rel="nofollow">https://en.wikipedia.org/wiki/Sixth_form_college
    [2] <a href="https://en.wikipedia.org/wiki/A-level" rel="nofollow">https://en.wikipedia.org/wiki/A-level

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