Which of the following will NOT provide patent protection?

Mathematical formulas are not eligible for patent protection because patent law specifically excludes abstract ideas, which includes pure mathematical concepts. A patent is intended to protect inventions that provide a new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof. Mathematical formulas are viewed as fundamental truths that exist independently of human interpretation or application, making them unsuitable for patenting as they do not meet the criteria of being a specific invention or application.

In contrast, new processes, ornamental designs, and plant varieties are all considered patentable subject matter under the right conditions. New processes can be patented as they represent a novel method of doing something. Ornamental designs can receive protection through design patents, which safeguard the unique visual qualities of a product. Plant varieties can be patented under plant patents if they are new and distinct. Therefore, the correct choice for what does not provide patent protection is indeed mathematical formulas.