Two cats not getting along

I have two cats that do not get along very well and I always have to keep them separated. One upstairs, one downstairs. One of the cats is a nine year old female who has been here a few years. Whenever she sees the other cat, she does not move at all and hisses and growls. The other is a fourteen year old male who I got last month. He is curious and always tries to approach the female even if she does not want him around her. The female is happy as long as she is left alone, but the curious male always wants to go downstairs and start trouble.

What usually ends up happening is the male chases the female into a corner, and then he simply sits and guards that corner and does not let her out. This is the main problem I am currently having and need help with.

There have been a couple fights before. I'm looking for some advice how to get the cats to be more friendly towards each other so I don't have to separate them all the time.

Are they both spayed/neutered?

If they are, all you can do is let them settle it among themselves. My first male Wawa is obsessed with my girl QT who IMO will never, ever warm up to him. It took several scary confrontations, but now Wawa leaves QT alone most of the time. And whenever he tries anything (he hasn't given up) a look from QT is enough to change his mind.
By the way, they're both nearly as old as your two cats.

Yeah. I don't know what you can do besides let them work it out themselves.

If you can get them eating side by side, maybe that would help. Or, if you can engineer petting both of them at the same time.

They are pretty old for fun and games, but maybe you could figure out some ways of playing with both of them. A couple of catnip mice?

The whole cornering thing is probably the male attempting to establish the dominant role in the house.

Sometimes it can take a while for cats to adjust. I added a new kitten last year and my adult female has just recently decided that he's probably here to stay. As long as they're not injuring each other and both get food, water and litter box access I would let them figure it out.

Cats take time to get used to each other if they are not family. My cats aren't quite as old as yours, a nine year old and five year old. Frank (was 4 then now 9) was really not sure about Max (now 5) when he arrived, and they had few little scraps, no major injuries if any at all. We eventually decided to separate them at night when we couldn't supervise them cos they were still fighting and Max was getting bigger. Now they are perfectly happy to sleep on the same bed together during the day I have even found them washing each other on occasion. Just let them fight it out and they should calm down. Also cats can get very jealous if they think they have layed their claim on something, Max has managed to get it through his head that 'That is Franks chair but he can have his pick of the sofas and the beds are anyones.' So if you cat is sleeping somewhere that the other routinely sleeps, then you might think about putting them somewhere else.

Thanks for the advice everyone, thanks yayi for the gift! =) and yes they are all neutered and everything. I guess I'll try letting them work it out, I'm just afraid that they will fight again and scratch each other's eye or something and I'll have to take it to the vet. Maybe I should try a slow reintroduction?

The male will probably just corner the female again and they will both be sitting near each other, the female unable to move. Once I tried moving the female out of the corner and the male just chased her, probably to corner her again. So I had to get the male away but I was too scared to pick him up because he gets really violent ("redirected aggression" I think you call it?) so I had to put some shoes on and scare him away lol. He scratched my shoes a bunch of times but ran upstairs and I got them separated again. Thankfully none got hurt. Sometimes I think the male just wants some excitement and wants something to scratch at (we do have scratching poles that they use). But that's the situation I'm in. Maybe next time I won't interfere until they actually start fighting.

After a few days together they will get over it most likely. Mine still have bad days with some annoyed hissing, but love each other now. The first couple of weeks were so bad!