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Becoming a successful data scientist without knowledge and acumen in mathematics or statistics is highly improbable as these are the fundamental blocks of data science. All statistical models, optimization algorithms, machine learning algorithms, classification techniques etc. are based out of mathematical and statistical concepts specifically linear algebra. Although tools such as Python & R has pre-defined commands to cater to these functionalities; still a data scientist needs to understand the basics of these concepts.
With literally zero? No. It’s going to take at least a good bit of probability and algebra. But, I’ll deviate from some others and say that a base level of math skills can be fine. There are many kinds of data scientist. Without a strong math background you wont be developing new statistical techniques, but most of us don’t do that anyway. At least half of data science is programming applied to practical data problems, and you don’t need math to code. Logic and skill, yes, but most programmers aren’t math geniuses and neither are most data scientists.