Mathematics today has no resemblance to the real world, and never will have again. I sometimes feel there is almost a cartel at work, a massive clan of academics, whose sole purpose is to justify their existence by developing theory after more esoteric theory, none of which actually matters. They need to do this because people need their PhDs, academics need to keep the hundreds of millions of dollars of grants flowing, and they need to keep publishing to go from being assistant processors to associate professors to professors to emeritus.

It’s their livelihood, fellas. Do you really expect them to rock the boat? What if the grants stop, or if the public start questioning the value of keeping up these behemoths that are pure maths departments?

Just like the credit crunch and the financial services industry today, the higher mathematics community just another industry that is not interested in governing itself. it couldn’t care less.

Sometimes I think it’s even worse than that. I almost think mathematicians actually enjoy living in their fairy-tale land, in their make-believe world that they have created because they can’t handle the real world.

Here are some sample topics of recent papers taken from a randomly chosen journal:
· “A Banach space without a basis which has the bounded approximation property”
· “A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy”
· “A class of idempotent measures on compact nilmanifolds”

If you think any of these have any resemblance with the world we live in (or people writing these have the slightest interest about the real world), you are living in the same cloud-cuckoo land.

If I put a nickel (little mass) into a cup (big mass) and then I take the nickel out (cancel out little mass during the acceleration) what’s left? The cup.

If I put a quarter (medium mass) and then take the quarter out (medium mass again) what’s left? The cup.

In both cases it is the cup which determines the acceleration not the coin.

You are correct though that the smaller acceleration of the Earth toward different masses is different. But that is not what Aristotle said. He said it depends on the mass of the object not the mass of the Earth. Aristotle is the grandfather of the big mass faster acceleration theory. This is exactly the theory that people still cling to because they make the same mistake he did.

The only way you could get out of it is to say you meant the Earth.

Mathematicians being human do not represent reality.

Mathematicians talk about math.

Hence we’re playing telephone and calling it reality.

Danger, Will Robinson!

Next, will you demonstrate that the brain is actually a cooling apparatus and not the center of cognition, which is actually the heart?

2) is far too small an effect for Aristotle to have detected – on the scale available to him, his claim was incorrect. Furthermore the claim is not that the more massive object falls faster, but that the Earth falls faster up to it.

So you’re right in a trivial and limited sense, but completely wrong in the broader course of the argument.

1)due to differing air resistance to a heavy or light body (this is actually the reason explicitly mentioned by Aristotle).

2)even in a vacuum, due to the gravitational attraction of the falling body upon the planet.

Did you think I was disagreeing with you? The point was whether or not von Neumann’s forecast about the future was correct or not. I claim it mostly was, and citing the fact that Hardy’s purely theoretical work came to be used practically does not disprove that when Hardy’s work was done prior to von Neumann’s prediction, although the dates of application are also relevant.

Of course, Hardy was certainly one of the most publicly ardent advocates ever of the idea of pure math being justified as its own end, pure math pour pure math, like l’art pour l’art.

If we judged the quality of work by the reputation of the person producing it, we’d still believe that heavier objects fall faster because Aristotle said so.

This attitude of reverence towards ancestral icons is incompatible with scientific inquiry and, more generally, rationality itself.

It doesn’t matter when Hardy’s work was done; the point is that if you posed the question to Hardy, “Do you think mathematics derives its legitimacy from its connection to (physical) reality?”, he would have answered in the negative.