re: 2 things
1) The claim is: 'a mathematical proof that ... is impossible' This is the oft-repeated and historically incorrect notion that I am speaking to. If you broaden the issue to the question: Was Newcomb a prolifiec critic of heavier than air flight- then sure, I'm not going to deny that claim. Were many of his criticisms shortsighted? Sure. BUT- there was never any 'mathematical proof' just 'days after kittyhawk'.
2) Please observe this quote: " by which men shall fly long distances through the air". In the broader context:
We have solved the problem of talking between two widely separated cities, and of telegraphing from continent to continent and island to island under all the oceans-- therefore we shall solve the problem of flying. But, as I have already intimated, there is another great fact of progress which should limit this hope. As an almost universal rule we have never solved a problem at which our predecessors have worked in vain, unless through the discovery of some agency of which they have had no conception. The demonstration that no possible combination of known substances, known forms of machinery, and known forms of force can be united in a practicable machine by which men shall fly long distances through the air
On one hand he was less optimistic than he should have been. On the other, he was somewhat correct. Lighter-weight gasoline engines, more informed and precise airfoil design- and most importantly, aluminum aircraft construction were all necessary for practical and economical long-distance 'heavier than air' flight- in the 1901-1906 time frame, these were pretty 'revolutionary' notions. Newcomb was not stupid, nor illiterate. He knew of the contemproary developments and successes...
His main issue was (as he states again and again) practicality and safety. Its clear to me, at least, that he was an advocate of air-ships and that avenue of development. If it were not for the war-inspired development of early powered aircraft, I'm inclined to say he might have had a point. Gas-bag lifting body 'hybrids' are only recently being returned to as an avenue of research. This avenue of exploration ('lighter' than air) never fit the needs for warfare (slow, vulnerable, useless in the cntext of war). Huge amounts of money and talent went into the now 'standard' solution of airfoils, and a lot of very hard problems were solved early. A few notable tragedies capped off what few serious efforts were made (The Ohio and the Hindenburgh)
But this is all neither here nor there. The point is- Newcomb never said 'never' to flight, and certainly not with the apocryphal mathematical proof. Its one of those oogeymen of scientific history, wrongfully attributed to someone who made BIG contributions to statistics, mathematics and astronomy. Far bigger than you or I are likely to muster up in our lives.
DL