At what point should I no longer include my former professor as a coauthor? I graduated from university somewhat recently with a four year undergraduate degree and during my junior/senior year I worked on a research project with a professor. 

At the beginning of the project (nearly three years ago) he helped me a lot with understanding the background/context of the research, but after so long I was the only one contributing to it (he's an applied mathematician and I'm a computer scientist, and the project is a computer based A.I. so I have been the only one programming it). 

Now that I've graduated and have continued working on the project, and maybe will try to publish within the next year or so, I'm wondering if/how he should be included as an author/contributor? 



Edit: At no point has he ever actually contributed to the project in the form of code. All he's done is mentor me through the concepts, bridging the mathematics and biology/chemistry so that I could understand it and translate into computer code. Additionally, all the code design and approach has been developed by me.
I'll copy and paste my answer from another question earlier today:

Everyone who makes a sufficient contribution to your paper for authorship should be an author on your paper (and no one else).
It doesn't matter what institution they are at nor does anything else: everyone that contributes at a level appropriate for authorship is an author.

Probably the best person to judge this is your former professor. Have a conversation with them about where the project is at and how you see their contributions and ask whether they think it is appropriate if they are an author or if you should be a sole author.