We are only visiting the shore of mathematics

I like Doron Zeilberger’s 66th Opinion:

all what human mathematics does is apply implicit exponential-time algorithms, called “heuristics” to find some trivial pebbles on the shore of the (even decidable part!) of the mathematical ocean.

In short, a mathematician solves trivial problems, a mathematician with a computer solves semi-trivial problems, but we are only visiting the shore of mathematics.

It is very insightful. One could look at the current state of higher mathematics, observe that progress is slowing and conclude that we have pretty much covered the realm of useful mathematics. In truth, we have maybe covered the realm of mathematics we could handle with a human brain. And current computers probably can’t help us too much.

Leave a Reply

Your email address will not be published. Required fields are marked *

To create code blocks or other preformatted text, indent by four spaces:

    This will be displayed in a monospaced font. The first four 
    spaces will be stripped off, but all other whitespace
    will be preserved.
    Markdown is turned off in code blocks:
     [This is not a link](http://example.com)

To create not a block, but an inline code span, use backticks:

Here is some inline `code`.

For more help see http://daringfireball.net/projects/markdown/syntax