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I am a physicist working in a data scientist role. I was told everywhere that my degree is a very good starting point because I know a lot of math and it is crucial for this job. But other than understanding the math behind the models' calculations I don't use any math. Okay sometimes I need to create principal components or carry out SVD but these are Just algorithms that anyone can look up on the internet.

So honestly I am a bit worried because I might be doing something wrong. Can you please share your experiences? Important note: May be that I don't use deep learning for my job.

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  • $\begingroup$ I did math up to a Ph.D. and have now been doing data science for 15 years. I would say that statistics is far more important than math. Specifically, a feeling and appreciation for randomness and residual variation, and thinking in terms of expectations and higher moments. $\endgroup$ Aug 29 at 13:22
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Having a solid mathematical background is crucial for data science. Someone without solid mathematical background will always use the algorithms as black box models.

Mathematical reasoning is needed when you debug your models but also when you want to come up with a creative solution to a problem at hand. Someone without mathematical background will have a hard time to come up with a solution to a real problem when.

You gave the example of Principal Components Analysis. Without understanding what eigenvalues and eigenvectors are your will always only superficially understand what your results mean. And you will have to explain it to business people in order to convince them that they should use the given algorithm. If you stand there and always say that this is a magical algorithms that is doing something you will not convince the business people to deploy your system.

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Statistical knowledge or statistical thinking is useful or necessary to:

  • Understand, evaluate and pick appropriate metrics to use to evaluate the performance of models.

    You need to understand the real-world cost of prediction errors and how each metric relates to this.

  • Explore and understand the data e.g. to help inform future models or other business decisions or to find and address data errors or anomalies in order to get the best possible performance out of the model.

  • Investigate and address examples that your model performs poorly on beyond just looking at a handful of examples.

  • Compare performance of models appropriately by being able to identify when improvements are likely just noise.

If you never e.g. print out a mean or plot a distribution, then I'd be a bit concerned. Although a lot of the ways in which mathematics helps is not about directly calculating some value or whatever, but more about being able to actually understand what you're doing when you're working with large amounts of data and metrics for that data (i.e. statistics).

It also depends on the domain and on which features you're using. If you're doing e.g. image classification, there probably isn't quite as much room for statistical analysis as there would be if you were just doing a classic prediction problem based on distinct and often independent features.

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No, you don't need mathematics for data science in the same way that you need it for physics. As a data scientist, you won't be integrating a stress-energy tensor, or even solving a differential equation.

What you do need is good quantitative reasoning and critical thinking skills. NotThatGuy's answer gives good examples of things you might think of as "just arithmetic", much more basic than the mathematics courses you've already done, but you'd be surprised at how many people struggle with these things. There will be probably be a bunch of stuff that you do automatically, and don't even realise that you're doing anything special. But these things are second nature to you because of the mathematics training you've had.

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I was educated as a mechanical engineer with minors in CS and math. In my personal experience, knowledge of math can be super useful in signal processing applications, and doing some creative/complex stuff with the data, but as many others have said, I think a good math "feel" is much more impactful than an explicit ability to do the math yourself.

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