Is it generally true that mathematics professors do not / cannot engage in consulting work external to their universities?
If I'm not mistaken, plenty of business school / law school / economics professors do consulting work, in addition to their academia work (researching + teaching).
I have heard of one reason, from one of our professors in numerical analysis: for example, a company like eBay.com or Amazon.com would never agree to show its proprietary algorithms to a math professor, without the professor (and his / her school) agreeing that the work to be done is then owned by the company and not by the school -- and even the emails would be monitored. In turn, the school would never agree to this sort of arrangement, and so nothing would ever get off the ground. And that it wouldn't be worth the risk to an eBay or an Amazon to pay for the expertise of a math professor.
So, are there instances of academia mathematicians working something out with industry and doing external consulting work?