"You can patent pretty much anything under the sun that is made by man except laws of nature, physical phenomena, and abstract ideas. These categories are excluded subject matter from the scope of patents."

You believe incorrectly.

http://www.legalmatch.com/law-library/article/what-cant-be-p...

Tell that to the companies that have patented genetic sequences.

No. One can discover mathematics, but mathematics cannot be patented. One can discover an ancient civilization ... and so forth. There are many more examples, and they're not patentable.

One could discover a gene sequence that ... oh, wait.

RSA encryption is pure number theory math and it was patented.