Add spaces: Neverputthehotcookwareonanunprotectedsurface.

Answer: Never put the hot cookware on an unprotected surface.

Add spaces: In1905WedderburnprovedthecommutativityoffinitedivisionalgebrasbutgivesmuchinsightintotheinteractionsofDicksoninthiswork.

Answer: In 1905 Wedderburn proved the commutativity of finite division algebras but gives much insight into the interactions of Dickson in this work.

Add spaces: ...hispapersonthree-dimensionalalgebraiccurves(1907)andonpseudosphericalthree-dimensionalspace(1885),wheretheimpossibilityofputtingsuchaspaceintoEuclideanfour-dimensionalspaceandthepossibilityofitsbeingplacedinaEuclideanfive-dimensionalspaceareproved.

Answer:
... his papers on three-dimensional algebraic curves (1907) and on pseudospherical three-dimensional space (1885), where the impossibility of putting such a space into Euclidean four-dimensional space and the possibility of its being placed in a Euclidean five-dimensional space are proved.