>>No, you do not need to know what a “p” value is...

I go to that first. The p value answers the question "How likely is it that the effect seen is from noise?". It ranges from 0 to 1 (multiply by 100 if you'd rather think about it in percentages - I certainly started out that way).

I use it as a quick filter to decide if it's worth my time to dig through the rest. How would you feel if you spent hours understanding a study and later realized that it had a 50-50 chance of just being noise? 80%? 90?

>>...or any of the math involved

Agreed that you don't need to know the math behind how it was calculated. If it's in a legit journal you can expect they've checked that for you. But the p value is there to help you.