I have a decent background in Mathematics and Computer Science .I started learning AI from Andrew Ng's course from one month back. I understand logic and intuition behind everything taught but if someone asks me to write or derive mathematical formulas related to back propagation I will fail to do so. I need to complete object recognition project within 4 months. Am I on right path?
I think the key part of your question is "as a beginner". For all intents and purposes you can create a state of the art (SoTA) model in various fields with no knowledge of the mathematics what so ever.
This means you do not need to understand back-propagation, gradient descent, or even mathematically how each layer works. Respectively you could just know there exists an optimizer and that different layers generally do different things (convolutions are good at picking up local dependencies, fully connected layers are good at picking up connections among your neurons in an expensive manner when you hold no previous assumptions), etc.. Follow some common intuitions and architectures built upon in the field and your ability to model will follow (thanks to the amazing work on opensource ML frameworks -- Looking at you Google and Facebook)! But this is only a stop-gap.
A Newton quote that I'm about to butcher: "If I have seen further it's because I'm standing on the shoulders of giants". In other words he saw further because he didn't just use what people before him did, he utilized it to expand even further. So yes, I think you can finish your object detection project on time with little understanding of the math (look at the Google object detection API, it does wonders and you don't even need to know anything about ML to use it, you just need to have data. But, and this is a big but, if you ever want to extend into a realm that isn't particularly touched upon or push the envelope in any meaningful way, you will probably have to learn the math, learn the basics, learn the foundations.
- Not only is it 100% ok, it's the process.
You may be surprised to know that even mathematicians struggle with mathematics, both the proofs they are working on, and the proofs of their colleagues. Some thinkers are so far ahead of the curve, very few understand what they're stating until generations later.
The main thing is to keep with it.
If you want to bee engineer who work with models as black boxes it could be OK. If you want to be researcher, as the job position or for better understanding of the subject it's not OK. Backporpagation is just basic multivariate calculus. If you straggling with it things like Hessians, regularizers, stochastic processes etc. would cause even more problems. If you want to go research track it could be good idea to take some math courses and prioritize them.