Yes for sure. I am very math-averse (almost failed calculus 1, skated by pre-calc in high school... not my intelligence area) and though I don't have a full time job doing something in AI, I do feel like I can build models that solve real problems (and am doing so in an internship right now).

Probably start with Andrew Ng's Machine Learning course. It has a significant amount of Math in it-- try to understand it, but seriously do not worry about it. Just get the high level concepts, try to get some intuition on machine learning ideas and techniques. You don't need to do the assignments or work too hard on the course (but obviously it's helpful if you do).

Then read these. Don't worry if you're still confused at first. It's fine. Just go through 'em kinda slowly and try to see what's going on.
https://iamtrask.github.io/2015/07/12/basic-python-network/
http://karpathy.github.io/neuralnets/

By now if you're still into it, I highly recommend Chris Olah's blog: http://colah.github.io/
It has some pretty complicated ideas in there, but the articles are illustrated and explained very well so you can get more of a feel for Neural Networks while also getting very excited about them.

Then it's probably time to start really building things. I would use Keras (https://keras.io/) at first, because it's very easy to get cool results without understanding everything under the hood. Do a tutorial or two, it's pretty intuitive and if you've done everything above you should understand more or less what's going on. Then try to find a cool dataset to work with that relates to something you're interested in. If you can't find anything you want to work with, then just use a classic dataset (imagenet is fine, even MNIST when you're just practicing) which will probably be less fun but will still let you learn. With whatever dataset you choose, just implement a simple model on your own without a tutorial (of course, if you get stuck referencing a tutorial is totally fine). Then see if you can tweak your model to get better and better scores. Start reading papers, you can find the newest ones on Twitter from ML researchers (Karpathy, Sutskever, Hinton, LeCunn are some names you could start with, there's probably a Twitter list out there somewhere) and then you can look at the references in those papers to keep finding more and more good ones. Implement any ideas in the paper you think are useful. Often Keras will have functionality to let you implement them easily. If it doesn't, then feel free to dip down into Tensorflow if you feel ready!

From there the world's yours. Find cool data to work with, implement papers to get a baseline measurement, and iterate in any way you can think of. It's very fun :)

The one thing is if you want to get state of the art results or do novel research you might need better hardware. AWS/Google Cloud/Floydhub are all options if you're willing to spend a little money, or you can just keep your expectations low ;)

Wow that turned out to be more of a roadmap than I wanted it to, sorry. The reason you don't need great math skills is that a lot of AI research is very intuitive-- Gradient descent can be internalized as a ball rolling down a hill, Momentum in training neural nets is like momentum in the real world, Neural nets are just manipulating data in high dimensional space... it's all stuff you can visualize instead of use mathematic symbols to depict, but since it's so much easier to write with symbols than it is to create a powerful image, symbols are used often.

To be honest I still usually skip over some equations in papers if they look daunting. Most of the time I don't need to understand them. Most of the time, I can read the abstracts, look at some figures, look at the results, and that's everything I need.