29 April 2010

What is mathematics (education) for?

Underwood Dudley, in a critical article in the latest Notices of the AMS, states it accurately:
What mathematics education is for is not for
jobs. It is to teach the race to reason. It does not,
heaven knows, always succeed, but it is the best
method that we have. It is not the only road to
the goal, but there is none better. Furthermore,
it is worth teaching. Were I given to hyperbole I
would say that mathematics is the most glorious
creation of the human intellect, but I am not given
to hyperbole so I will not say that. However, when I
am before a bar of judgment, heavenly or otherwise,
and asked to justify my life, I will draw myself up
proudly and say, “I was one of the stewards of
mathematics, and it came to no harm in my care.”
I will not say, “I helped people get jobs.”

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What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant