I was in class a couple of nights ago, and we were presenting some linear programming models.
Once one of the groups was done, the professor threw them a curve ball and asked them why their model was correct.
Upon explaining their methodology - they end with '[microsoft excel] solver told us'.
The professor did not like the answer and questioned the validity of the software itself - the group had no argument for his argument (they appeared blind-sighted by the whole discourse.) One classmate suggested that they could argue that their model is correct because you can experiment with other figures and you will not find a better answer - try as you might. The professor agreed that that was a good answer, and solicited others. Someone said that linear programming models have a finite number of possibilities and solver goes through all of them and determines the best one (brute force attack in other words). The professor liked this answer better - so it seemed.

I questioned him on it because 'solver told me so' is the condensed version of 'linear programming models have a finite number of possibilities and solver goes through all of them and determines the best one.' You could STILL argue that the software itself is flawed. Then the professor argued that you could buy a software package that is accepted to be of high quality, run the numbers and if solver has the same answer - then solver is just as good. (paraphrasing of course) Then the professor went back to the 'try other numbers as much as you want, but you wont get anything better than what I tell you' argument - and here I had a flashback to my undergraduate mathematics days.

I was younger, and more naïve, and I was trying to prove that my answers to something were absolutely correct by using the 'try other numbers as much as you want, but you wont get anything better than what I tell you' argument. The professor did not buy it, and rightfully so, and went on to teach me how to prove my argument mathematically.

So what is the difference between math and business? In math you don't beat around the bush in an attempt to tire your opponents - you provide a full mathematical proof - even if it is beyond the comprehension of you audience, whereas in business you tango (figuratively speaking) and try to tire out your opponents. At least that is what I got from those presentations - in solver we trust and if you don't, feel free to plug in numbers and test it out yourself ;-)