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Comment by hiAndrewQuinn | Hacker News Reader

Seconded. Math does nothing for you by default but it makes almost everything else easier, to the point of making the impossible possible.

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I have found several points in my career where taking the extra time to learn math fundamentals (particularly linear algebra) has paid off when learning something more high level. People often say that the math in machine learning doesn't matter and you can staple python libraries together but I've made convincing arguments in product design meetings based on how the mathematics of certain algorithms lends itself to our particular use case and how it helps scalability

Thirded. I just got back from a customer visit. They were trying to do something where the back of the napkin math said it would take a couple dozen CPU years to solve. I recognized a simple (in the math world) transformation we could do and the could run the whole problem in under 10 min.

Coding the transform isn’t trivial, so we’ll get some contract dollars to solve it, but it will still be done faster than the naive approach.

These are pretty sophisticated customers, but they don’t have a deep math background. Without that you wouldn’t find the “obvious” solution.

If you can recall it, do you remember the math problem in question? And could you loosely explain how you transformed it?(just with general concepts or keywords for my own curiosity. I love math, and seeing how different problems can relate to each other in unexpected ways. For example, when the sum of two quadratic roots gives the width of a given rectangle. Like this problem: A rectangle has an area of 32ft² . Its width is 4ft less than its length. What is the width? A = l(w) and 32 = l(l - 4). I’ll spare you the work shown, but l = 8 and l = -4. … (8) + (-4) = 4 = w

Roughly it can be viewed as a change of coordinates and then recognizing the symmetry. Say you had a 2D function of x and y and transformed it to r and theta and then noticed that it was independent of theta. You go from an 2D problem to a 1D one.

In this case we’re transforming a 7D problem into a sum of a discrete set of 2D problems. With more algebra we could get it down to a 1D problem but that would take more human work that wouldn’t be paid off later in CPU time. If their project ends up scaling and the 1D transformation makes sense, we’ll do it.

What field of mathematics is this?

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