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Yes they do, you too apparently. Please spare me the fact of your degree, it means nothing to me. Argument from authority - a logical fallacy.
If a degree meant anything Prof. Jones, who has done real experiments, would be the final word would he not?
As for your "mathematical proof" based on "estimates" (whose estimates, to do what exactly?) of the number of people involved... The Manhattan Project was a giant secret "conspiracy" to build a nuclear weapon. It lasted for years, without a single headline in the NYT! People, especially the true believer types, can keep their mouths shut. E. Howard Hunt kept his mouth shut about JFK right up to the end when he made a death bed confession: http://tinyurl.com/2shuz5
You are focusing on a single problem and ignoring the vast mass of contradictory evidence. Math will only get you so far in the real world; I did the math and amazingly Achilles will never catch the tortoise! Zeno rules!
If you want to do some math, check out the temperature at which steel melts, then the temperature at which aviation fuel burns. Then explain to me how the molten pools of metal found at all 3 sites, got there.
Having said this, yes, the number of people required to pull this off would be large, but perhaps not as large as you think, perhaps 100 or 200 people, and yes, it is one of the largest problems with any alternative theory to the official one.