Common ideas

Common ideas

First of all, thanks to my friend Josh who offered his thoughts on grading. I already started to make solutions promtly, and changed the maximum score of the exercises. Let's see if that is going to make students distracted from grading and focused to learning. Also, he just wrote his thoughts on math books, math problems and the quality of thought that goes into the mathematical education of middle and high school students (see Oct.13). I totally agree with him. Our high-school math textbooks, were not bad, but just not enough. I remember ho everyone was trying to find in the beginning of each academic year books new, old, even from our parents, to complement the understanding and do more exercise for the exams. But, the problem is that none of these were REAL math books. I think my first real math book was not even considered a real math book (E.T.Bell, 'The Mathematicians') it was short biographies along with the major work of a lot of prominent mathematicians. Then, I read Gleick's 'Fractals' and then by Van der Waerden a book on Egyptian, Babylonian and Greek math. Not a real math book either (it falls into the category of history of science). The point is that doing trigonometry is school is OK, it's necesary, but I understand why it cannot be fun. Not even the so-called real examples will make math more understood (not to mentions how underdeveloped is the 3D thinking in a lot of students and how painfully they discover once taking vector analysis in college, while so easily they could have been introduced to the concept of geometry and stereometry) But, the joy of math comes from understanding concepts, mainly abstract, mind games, even making with ruler and compass a hard construction.

And off to what made my past week hard. Last May when studying for my quals I cme up with a beautiful idea relating proteins and microfluidics. I ahd no idea how to find my material, or how to observe it, but I somehow knew that the experiemnt would be cool, not that hard to actually do, and could open up the field for new questions.
Later this summer, in Germany I came up with a nice way to make networks of "vessel-like" micron-scale pipes in natural extracellular matrix proteins. This I knew how to do, but it was not the right time to do, since I was in Germany to learn sth completely different.
Last week I was at a lecture at which a professor was asked about his latest reearch project. I couldn't believe it. It was exactly my May idea. An they had preliminary data.
The week before, I had gone to another talk where I found out that my little netwrok system has been done, with a few problems, but has been done.

You know how sometime is the history of Science you come up with equations, proofs and ideas that two people published independently the same time? I always wondered: first: how could they not know that another person in their field was working on the same exact problem, and second: how probable is that two people come up independently with the same idea at about the same time?
Apparently, neither shoud be surprising to me. I didn't know that someone in the same university had done sth I was thiking of doing. And I didn't know (there was no way I could have) about the fact that someone this past spring came up wit hteh same idea as I did. Maybe because we all are interested in similar problems, and because the needs of the medical community and the techniques we use are the same, we will with probability = 1 end up working in (partially) overlapping problems. The question is to come up with a lot of ideas. One of them will be innovative. Remember my (Microsoft) T-shirt? "Think" " Impact"