I agree with the sentiment you express and thank you for pointing it out.<p>I do think that thinking outsiders should stay out is uncommon in the field of math though.  I am currently a math grad student, and while I am only a grad student what I have seen of the mathematical community makes it seem like it is very open to cross fertilization from other sciences and from amateurs.<p>Admittedly he is historical, but Fermat (professional judge when he did most of his mathematical work) is revered and there are some more recent amateurs that have made genuine contributions.  Much of mathematics is inspired by other fields such as physics.<p>I admit I know some professional mathematicians were tired of finding flaws in amateurs proofs of Fermat's Last Theorem and rebuting supposed refutations of Godel's diagonal proof that the reals are uncountable, but it is very different to be tired of dealing with a constant stream like that than to be hostile towards outsiders in general.<p>From my limited perspective, I think math is one of the fields most open to outsiders and amateurs coming in and making real contributions, both culturally and in the fact that we rarely need expensive experimental setups so the barrier of entry (in terms of money and equipment) is low.