What is the highest polynomial degree that has an application in real life, and what is that application? My google search yielded 3rd degree at most.
2026-03-25 12:34:36.1774442076
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Applications of polynomials of a high degree
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The characteristic polynomial of any matrix (though rarely explicitly computed) gives quite a bit of information about that matrix that is incredibly useful in a huge variety of data analysis settings (machine learning, dimensionality reduction, etc.) The degree of this polynomial is the same as the size of the matrix (depending on setting, this can easily be in the multiple thousands, or even larger). Admittedly this is more of a computer science answer than math, but is still relevant.
Practitioners in signal and image processing heavily use the so-called Discrete Fourier Transform, which is a polynomial evaluated on complex variables. Applications in medical imaging abound.
The degree of these polynomials typically reaches the image size, which can be like 4096 or much more.
Other consumers of polynomials are the error correction methods (such as those used in digital communication or CD readers). They are implemented in some types of barcodes, with degrees that reach dozens. If I am right, the QR codes use up to degree 69.