The House of Mathematics

he overall subject of mathematics can be compared to a house with multiple rooms occupied by various "characters" ... perhaps even a hotel ... Let's take a tour and see why it's not the kind of place you would like to visit (or live in).

The Entry

Ww notice immediately that the door is not locked. Anyone can get in. No human being is barred from entry. All it takes is the desire to open the door ... and ...

Wait a minute! The door is stuck!

Push harder. HARDER ... HARDER! Slowly, and with excruciating difficulty the door gradually opens. As we enter, we see the reason for the difficulty. The dead bodies of Gauss, Euler, Newton, Hilbert ... hundreds of bodies were blocking our path. You need to push them aside to get in.

That is the price of entering the unbarred door ... you must learn a great deal which has already been discovered ... and ... all that information has never been integrated into a consistent "whole" for the purpose of your education. Hence, you must learn it piecemeal ... disconnected ... just as it was discovered.

The Foyer

Here you come to the realization that this place is a dump. It looks like an Ozark-hillbilly-tarpaper covered shack ... no maid service here. There are papers, coats and hats, garbage on the floor and the phone is off the hook (nobody here accepts telephone calls - there tooooo busy making the latest cutting edge discovery).

Climb over the piles and make your way to ...

The "Living" Room

You'll find various mathematicians busily, singlehandedly and singlemindedly engaged in the process of "mathematics". There are papers all over the floor, books, calculators, computers. No one talks ... they are mesmerized ... at the "beauty" of their equations ... the ones they've made ... not the ones someone else has made ... unless the beautiful equation is from one of the corpses over by the door. To have your equation recognized as beautiful by other mathematicians before you are dead is very rare. In fact, if your equation is recognized early ... it's probably an omen of early demise (Ramanujin - spelled wrong no doubt).

What they are really looking for is not truth or beauty ... They are looking for recognition ... from their peers. They never get it. The only ones who get recognition from their peers are the ones seeking truth as an end in itself ... they get recognized ... by their peers ... after they're piled over by the door.

Unless you're in on a "scam" with multiple joiners. These elect one of their own (by consensus) to receive pre-mortem recognition ... as the defacto-dejure leader of the scam ... by those involved in the scam ... e.g. Edward Witten.

The trouble with recognition ...

is that it is hard to get recognized for discovering something trivial. I mean "trivial" in relation to the body of mathematical knowledge which has already been discovered. How many times can we invent addition, multiplication, group theory ... ? There is only a finite supply of fundamentals. There is a hierarchical structure to everything. The fact is that the subject of "fundamental" mathematics is undoubtedly exhausted.

Like the subject of "geometric mechanics" (the invention of various machine actions independent of materials ... gears, pulleys, wheels, motion transformers, etc.) which was exhausted in the 19th century, mathematicians need to "mop up" the leftovers. And this is just as hard to do. The only difference between the fundamentals and the leftovers is that the fundamentals get more "press".

The Bedroom

In one bedroom you find several mathematicians gang-banging another. In the next ... more of the same ... and so on ... and on ... and on. What these guys need is a woman. And, come to think of it, the whole damn house needs a woman's touch ... at least a good cleanup. Hmmmmm ... mathematical maid service!

The Bathroom

You don't wanna' go there.

Who will get the next supreme recognition in mathematics?

Who will be the next ... Gauss, Euler, Newton?

It will be him who can perform the service of cleaning up this God-awful mess. What is needed is a Euclid. Someone who can bring order out of the chaos. Not necessarily someone who finds the new idea ... rather someone who can make the "house of mathematics" more accessible to the population at large. After all, mathematics is quite simple ... if ... you take one concept at a time ... in an integrated fashion. Today, this subject is thrown at students as a huge conglomeration to be swallowed seemingly all at once.

"Why won't it go down?"
That's the crux.
That's where real beauty and honest recognition is to be found.

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