And it is, at any rate, impossible to prove, that the cogency of mathematical first principles is due to anything more than these circumstances; that the experiences with which they are concerned are among the first which arise in the mind; that they are so incessantly repeated as to justify us, according to the ordinary laws of ideation, in expecting that the associations which they form will be of extreme tenacity; while the fact, that the expectations based upon them are always verified, finishes the process of welding them together.
Thus, if the axioms of mathematics are innate, nature would seem to have taken unnecessary trouble; since the ordinary process of association appears to be amply sufficient to confer upon them all the universality and necessity which they actually possess.
Whatever needless admissions Hume may have made respecting other necessary truths he is quite clear about the axiom of causation, "That whatever event has a beginning must have a cause;" whether and in what sense it is a necessary truth; and, that question being decided, whence it is derived.
With respect to the first question, Hume denies that it is a necessary truth, in the sense that we are unable to conceive the contrary.

The evidence by which he supports this conclusion in the _Inquiry_, however, is not strictly relevant to the issue.
"No object ever discovers, by the qualities which appear to the senses, either the cause which produced it, or the effects which will arise from it; nor can our reason, unassisted by experience, ever draw any inference concerning real existence and matter of fact."-- (IV.p.

35.) Abundant illustrations are given of this assertion, which indeed cannot be seriously doubted; but it does not follow that, because we are totally unable to say what cause preceded, or what effect will succeed, any event, we do not necessarily suppose that the event had a cause and will be succeeded by an effect.

The scientific investigator who notes a new phenomenon may be utterly ignorant of its cause, but he will, without hesitation, seek for that cause.

If you ask him why he does so, he will probably say that it must have had a cause; and thereby imply that his belief in causation is a necessary belief.
In the _Treatise_ Hume indeed takes the bull by the horns: " ...