WordPress going mental, creating core.xxxx files

A few days ago I noticed very oddly I’d went over my Disk Usage limit- I discovered this was due to something creating lots of core.(a number) files in my WordPress directory, varying in size, from 0kb to VERY LARGE. Soon after my WordPress website started to not work at all at times, and at other times just to display the page “weirdly”.

Anyway, whats happening? – I contacted my host already and they say it’s a problem with WordPress

Thanks