What do grad students in math do all day?

In any case, I imagine there's more glory in digging further into intellectual stuff than spending time making it palatable for newbies. :)

Yes, true, but I think that amounts to the same thing. Our inability to prove the thesis casts in doubt our right to assert it at all. That's certainly true for any other mathematical idea. No one was willing to say that Fermat's Last Theorem, or the Four-Color Map Theorem, were proven, until they were.

Nevertheless, I shouldn't have said that the Theorems "falsify" the logical consistency of mathematics. They prevent the notion from being demonstrated, but doesn't invalidate its existence as a hypothesis.

> They also don't remove the possibility that there is some metamathematical justification for ...

Yes, but that's not a positive claim, it's the assertion that it can't be ruled out. And such an effort might fall afoul of the "sufficiently complex" criterion of Godel's Theorems, which brings us full circle.

Listening to a coworker of mine:

Marketing, obviously. This is how industry wide 99% of SUVs will never leave suburban blacktop but most SUV commercials have the vehicle speeding up and down dirt trails in a national park. Sometimes similar things in business come from random convergent individual evolution, but more often from the outside. Somebody released a paper on the topic of Americans being germophobes about 5-10 years ago, predictably we had to sit thru a product cycle where anything that can theoretically include triclosan, had to include triclosan (and other anti-bacterials, etc). You may remember a similar fad a decade earlier for citrus oils.

Generalized, generic version of what they'll do on an individual case basis with numerical metrics in private sector. Talk to buddies in the field to get raw randomized data and turn the data into a report from a business perspective if you pay $x bounty for finding a security bug that results in a supply demand curve shaped exactly as such, with this effect on product development times, and this effect on total cost of production / ownership, sales figures, etc, all theoretically "industry wide" or at least "subindustry wide"

We don't have a free market system, more of a centrally controlled system. So there's a basically infinite collection of govt laws, rules, regs, where you can gather the raw data for game theoretic analysis of what the central controllers have decided for us. Is it better, purely economically, to hire illegals to staff fast food restaurants? Identifying all the economic costs is actually pretty hard. Someone out there is probably researching every law/rule/reg out there... costs of obeying vs disobeying, cost to purchase alternative legislation via election funds / lobbying, and repeat each along the short term / long term axis.

For accounting the rules are often "what rule can you purchase" or "what you can get away with" but there's also real world accounting. You need to keep two sets of books, one with how fast does the IRS allow you to depreciate "XYZ" for tax purposes, and another set of books for how fast "XYZ" actually depreciates in the real world. Then you have to live off the real world books or else you can get in a horrible cash crunch if your cashflow depends on selling a used "XYZ" to make payroll this month or as a downpayment on a new "XYZ".

Finally criminals spend a lot of time inventing new crimes. New forms of control fraud, etc. Basically, classic social engineering without computer involvement.