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I strongly agree with this point. See http://bentilly.blogspot.com/2009/11/why-i-left-math.html for how what I saw in math supports your point. Worse yet, we have not just specialized, we have lost knowledge as well. My favorite example of this is a result I rediscovered. Every mathematician knows that, for instance, sqrt(2)+cube_root(3) must be the root of some polynomial of degree 6. (This one turns out to be x^6 - 6x^4 -6x^3 + 12x^2 - 36x + 1.) I came up with a construction for answering questions like this. I showed it to a number of mathematicians, and none had seen it until I showed an older one who said, "That looks like a very old way to do this. Go to the library, pick up an algebra book from the 1800s, and see if you find it." I did, it was there, and it turns out that two of the mathematicians I had talked to were in fields that had gotten their start from the very construction I rediscovered! (One was in number theory, dealing with things like algebraic integers. The other was in combinatorics, and did a lot of stuff with symmetric polynomials.) If you're curious, the observation behind the construction is that any polynomial expression that is symmetric in the roots of a polynomial can be rewritten as a polynomial in the coefficients of that polynomial. So if a1 and a2 are the roots of x^2-2, and b1, b2, b3 are the roots of x^3-3, then (x-a1-b1)(x-a1-b2)(x-a1-b3)(x-a2-b1)(x-a2-b2)(x-a2-b3) is a polynomial in x and the coefficients of x^2-2 and x^3-3, which means that it is an integer polynomial. All that said, this point doesn't support your argument. It is true that if information were better presented, people could learn more about more subjects than they could otherwise. It is true that trying to do this would have tremendous value. But if you want to learn about multiple subjects then you need to deal with how information actually exists out there in the world, rather than how we'd like it to be organized. The disorganization that you point to is a significant barrier to learning. (This problem does not look like it will improve any time soon.) |