Add spaces: HeattendedtheFourthAll-UnionCongressofMathematiciansoftheUSSRin1961,attendingtheInternationalCongressofMathematiciansinthesameyear.

Answer: He attended the Fourth All-Union Congress of Mathematicians of the USSR in 1961, attending the International Congress of Mathematicians in the same year.

Add spaces: beauty,fat,Japanese,reality,couple

Answer: beauty, fat, Japanese, reality, couple

Add spaces: ThecultureofthewesternUnitedStates,whichmanyconsidertheepitomeofAmerican-ness,isinoriginasynthesisofAngloandHispaniccultureswhichwascreatedinTexasinthedaysoftheTexasRepublicandspreadwiththetrailherdstowhatisnowthewesternUnitedStates(andCanada).

Answer:
The culture of the western United States, which many consider the epitome of American-ness, is in origin a synthesis of Anglo and Hispanic cultures which was created in Texas in the days of the Texas Republic and spread with the trail herds to what is now the western United States (and Canada).