Series 1: Mathematics, King of the World: Casual Remarks on Foundational Issues in Modern Mathematics!
2006/3/4 16:26:18
This ID rarely discusses mathematics online. Most people have very little understanding of mathematics. The vast majority, even with an undergraduate degree, have grasped mathematics only at roughly the seventeenth-century level. Even with a PhD, what they have learned is still just the surface of mathematics. There is nothing to discuss with them. And even mathematics majors don't really understand the whole of mathematics—the system is simply too vast; any tiny sub-field is enough to occupy a person's entire life.
Mathematics is artistic in essence—this is absolutely not nonsense. The materials of mathematics and art differ, but fundamentally, the creative processes are isomorphic. Mathematics harbors the greatest imagination of humanity. Under normal circumstances, mathematics looks down on things like physics. Einstein pilfered a bit of the surface of what Riemann had developed years earlier and became the most celebrated physicist of the last century. Today's theoretical physics is essentially a minor branch of mathematics. Of course, physicists will never admit this—they will trot out a pile of excuses about experiments, physical interpretations, and so on to protect their titles. These people strut around every day using the creations of mathematics. Look at Einstein: after swiping bits from Riemann and from his first wife, he never did anything serious again. This tells you that the problem of "82 and 28" is no longer a major issue among physicists.
People who do mathematics generally look down on everyone else intellectually. Someone in ancient Greece said "all things are numbers," but really, all things don't amount to anything—mathematics is vaster than the world itself. The world is merely one of infinitely many possible mathematical forms. In other words, the world we can now exist in and face is just one of infinitely many mathematical possibilities. The imagination of mathematics transcends the world; in mathematics, the world is not even a speck of dust.
Ordinary people, including many so-called philosophers, constantly play various theoretical tricks, which, in the eyes of mathematics, are just leftovers that mathematics finished playing with long ago. The most laughable nowadays are the so-called economists, who boast of such incredibly sophisticated mathematical tools—aside from fooling people outside mathematics, they merely continue to flaunt the despicable shamelessness typical of economists. The so-called logic frequently deployed in everyday arguments is nothing more than a special case of one particular mathematical structure called a "lattice." Watching them treat this worn-out mathematical toy as a treasure is truly hilarious. As for all those garbage pursuits—computers, operating systems, economics, astronomy, finance, insurance, and so on—without mathematics, they are nothing. Recently, high-tech, finance, insurance, military, and intelligence industries in the US and Europe have been poaching top mathematical talent at annual salaries of several million US dollars. In truth, a bit of mathematical surface knowledge is enough to handle all of that, while the true grand players of mathematics would never deign to engage in such trivial affairs.
(To be continued)