I love the gentle heat that paprika imparts. Along with its warm colour, paprika can lift a meal to another plane.
There are hundreds of goulash recipes, some have tomato; some have potatoes; some have carrot and celery. Just don't leave out the meat or the paprika.
So you can make goulash how you want (I stand to be corrected by Hungarian readers).
Here's how I made it on Saturday afternoon, as Melbourne was whipped with rain squalls yet again:
Brown onions in butter, dredge cubed veal in flour then brown with the onions, toss in a tablespoon or two of sweet paprika and a little salt and pepper then add a can of tomato puree. Cover with water. Simmer for an hour or two then mix through half a cup of cream and serve with some buttered pasta such as tagliatelle or papardelle; or with mashed potatoes. I used the pasta.
Largely unrelated facts:
Budapest in Hungary once had the largest tramway system in the world. Today, Melbourne's tramway is the world's third or fourth largest depending on who you ask, and the largest outside Europe.
A tram in Budapest.
A tram in Melbourne. This is where I catch the tram to the city. It trundles through Royal Park behind the zoo, emerges onto Flemington Road near the hospitals precinct (RMH, Children's, Women's, Dental), past the Queen Victoria Market (where I bought the veal for the above recipe) and ends up at Flinders Street Railway Station.