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Comment by noud | Hacker News Reader

Professional mathematician (but in business, not academia). I hold a PhD in mathematical physics. Below the list of books that taught me the most. However, these books are often not directly related to my current work. Also, I don't think they will be useful for everyone, as some of them are strong specialized books. These books mostly taught me to think like a mathematician. One of the strongest skills I learned as a mathematician is to dive deep into a topic and learn almost everything that you can learn about it (going from 80% of knowledge to 99.9%). I "read" these books completely several times in my career.

* Atiyah, Macdonald - Introduction to Commutative Algebra.

* Bourbaki (in French).

* Gasper, Rahman - Basic Hypergeometric Functions.

* Hasti et al - Elements Of Statistical Learning.

* Rudin - Real & Complex Analysis.

* Thomas, Thomas - Elements of Information Theory.

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Do you feel challenged as a mathematician in industry? Are there jobs that are challenging? As interesting as just learning a new topic? Just curious.

With challenging you probably mean mathematically challenging, right? There are many jobs that are challenging with respect to soft skills (project managing, team leads, directors, ...).

It's hard to find a job that's mathematically more challenging than an academic job. But I believe that there are enough jobs that give you the opportunity to make them mathematically challenging. But you need to take the initiative. Good soft skills and presentation skills help. For example, at my company one of our product lines has over 10 million products per year. These 10 million products can be grouped in 50k "unique" items. It makes no sense that there are so many "unique" items. This is like going to the supermarket for milk and you have to choose between 50k different brands of milk. Without explicit requests from management, I designed a distance metric between these "unique" items (using domain knowledge), which allowed me to apply several manifold learning techniques (in particular, t-SNE and UMAP). (Re)Learning several mathematical techniques along the way. In this way I have an easy to understand 2d picture that can explain in detail which "unique" items are actually unique and which ones are "pretty similar". These "pretty similar" products can be reduced to one unique item. Next to just-doing-my-job tasks, taking these type of mathematical challenging initiatives have always worked out for me and are appreciated by my company.

Summarized, in industry, you should look for a job that gives you the freedom to make it challenging. When you found a challenging task, start applying all the mathematical techniques you know, and try to learn new techniques along the way.

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