Let us imagine a mad tailor who makes all sorts of clothes. He does not know anything about people, birds, or plants. He is not interested in the world; he does not examine it. He makes clothes but does not know for whom. ….

Mathematics works in the same way. It builds structures but it is not clear of what. These are perfect models (i.e., perfectly accurate), but a mathematician does not know what they are model of. He is not interested. He does what he does because such an action has turned out to be possible. ….

The space of his constructions is not our space, as it can have an infinite number of dimensions.

Stanisław Lem, Summa Technologiae (via amoratumbeneficus)

And the scientists are rushing, desperately trying to clothe their naked data, rummaging through the mathematicians’ sale rack for something good.

Interview with Maryam Mirzakhani, the brilliant Iranian mathematician who was the first woman to win the Fields Medal

  • Interviewer: What advice would you give lay persons who would
  • like to know more about mathematics—what it is,
  • what its role in our society has been and so on?
  • What should they read? How should they proceed?
  • Dr. Mirzakhani: This is a difficult question. I don’t think that everyone
  • should become a mathematician, but I do believe that
  • many students don’t give mathematics a real chance.
  • I did poorly in math for a couple of years in middle
  • school; I was just not interested in thinking about it.
  • I can see that without being excited mathematics can
  • look pointless and cold. The beauty of mathematics
  • only shows itself to more patient followers.
She knew there must be a way to tap into what students already understood and then build on it. In her classroom, she replaced “I, We, You” with a structure you might call “You, Y’all, We.” Rather than starting each lesson by introducing the main idea to be learned that day, she assigned a single “problem of the day,” designed to let students struggle toward it — first on their own (You), then in peer groups (Y’all) and finally as a whole class (We). The result was a process that replaced answer-getting with what Lampert called sense-making. By pushing students to talk about math, she invited them to share the misunderstandings most American students keep quiet until the test. In the process, she gave them an opportunity to realize, on their own, why their answers were wrong.
Inquiry-based approaches seem very good for this, and it’s something I’ll be thinking about a lot as we go into this school year. 

vipernugget asked:

Also I initially wrote "Mewton's Method" which I have to assume is how cats find roots, though what they would need roots for I do not know as they don't eat vegetables?

It’s actually a little known fact that cats are in complete control of the mice who run everything, and they do all the math behind the simulation themselves. Mewton’s Method comes in very handy, but more than that, my feline overlords won’t let me tell you.