Luck is something that can be defined as something beneficial that happens to us that is not in our direct control. Sort of like walking down the street and finding a $20 bill. The bill was lying there randomly and we were randomly walking there and found it. But it was all math.
Fate is something that pushes us towards a "thing". We choose to ride a bus and when we get off we walk into a person. That person is attractive to us and we exchange numbers. A year later we marry that person. That is Fate. And that is still math.
Fate and Luck are nothing more than the forces of Nature being influenced in such a way that it affects outcomes in our own lives. They are not mystical things at all, but results from computations. We do something that reverberates and that reverberation rebounds upon itself.
To return to the examples, the $20 bill could have been lost by anyone and found by anyone. A cop driving down the road could have found it. It was not our luck. Most likely we were following that path to get to a destination and just happened upon it.
To run into a person and then marry them? This is less Fate than something random. Any person we run into could be a person that we end up with, but for the most part, the people we run into are just random ones. Some can contribute to our lives and others are just background noise.
Is this an example of the Matrix? Maybe. We can never know if that's the actual truth...unless mathematics says so. But until disproved, Fate and Luck do not exist.