Add spaces: ...[Surely]manymathematiciansexperiencedaprofoundfeelingofreliefwhentheyheardofthisresult.

Answer: ... [Surely] many mathematicians experienced a profound feeling of relief when they heard of this result.

Add spaces: TherearetenDisneyPrincessandeachofthemischaracteristicinsomeway.

Answer: There are ten Disney Princess and each of them is characteristic in some way.

Add spaces: Youmustdecidewhatwidthrunnerwilllookbestinyourhallway.

Answer:
You must decide what width runner will look best in your hallway.