Does a turntable mat make any difference?

The Enlightenment might be out of fashion but empiricism still works. See for yourself—or rather, hear.

Agree on Lee Morgan.

Hi end turntables probably don't have mats because, depending on all the various cartridge and record thicknesses, there would be a myriad of mats that would be 'best'.

For me, at least, it's all about thickness/VTA.

The Funk Firm Achromat is one of the greatest mats available. I have used it on high end Rega P10 and Linn LP12. It DOES a make a significant difference . Bass is tighter and the high notes clearer. The Linn dealer was skeptical and when he heard it he fully agreed that it made a great difference compared to the Linn felt matt. Same for the Rega. On top of it, it reduces static build up. Great product at an affordable price! 

If you're talking about a difference in sound, absolutely not.