The main problem with almost every data scientist I see is exactly that they can not produce real world results when needed. Instead, they live in the personal mental lab in their thoughts and are disconnected from the real world and business goals.
Data science is, indeed, on demand because it's a new discipline and many people are not sure about what exactly they need to do, how and what do they need for that. However, the essence of businesses never changes.
Make it work, not prefect
Data science today for the most businesses around the world is about using ready libraries, same as in software and app development. It's not about wasting time on writing everything yourself from scratch, thus you don't need to be very good at math and know all the ML algorithms.
Languages like Python and libraries like Google TensorFlow or Microsoft Cognitive Toolkit (CNTK) gives you almost anything you need out of the box.
Do not reinvent the wheel
It's fine for the beginner and common everyday usage just to use libraries without much math and algorithm knowledge, but professional and expert in every field, of course, should know the whole domain from the fundamental level.
Always keep learning and practicing. At the end your goal should be to become much better at math and algorithms. It doesn't mean you should be expert in every field, after all everything depends on specific business case and what you will need to implement, but you should be able to build similar tools yourself.
Invest more time into the understanding and seeing bigger picture in the business overall, AI architecture and data science process.
Since this field is very young and you, probably, won't find many insights here, I will share my point of view:
The core essence of data science without which it is impossible is data (knowledge) itself and not just random data, but data which can be used in real world, which can be understood by the machine and used to get business value.
Before the machine learning at the beginning there is always a Knowledge engineering which should answer next questions:
Finally when you have valuable knowledge you may use it for the Machine Learning to start automating your process and getting better results. AI is not a magic switch which you will turn on suddenly one day.
AI is a long, smooth process of transition from manual work to automation
Always start from the goal. Never start from the beginning. Imagine you are already at the end and start going backwards step by step. Now you at the pre-last step and close to final goal. Now you two steps away from goal, now three, etc. Finally you arrived to the beginning point, where you are now and what do you have. When you start from the end, you see full picture and what exactly you will need to do or what is missing. When you start from the beginning, the distance till goal is too big and you won't see many steps between you and your goal.
At the end, not algorithms or libraries will provide a value for many people, but the system altogether, system which has a lot of 1) accessible + 2) valuable + 3) knowledge. This is exactly what "get shit done" in data science means. From the business perspective algorithms can be sacrificed.
Algorithm without data is useless, but data without algorithm is not.
Finally the only correct answer to your question is - both, yet with more focus on finishing tasks. Get things done no matter what and keep practicing, and investing into yourself. Always search for the balance in every part of your life and always prioritize, adapt and change every day based on situation you have only that day and next day do the same.