By saying that software isn't patentable because it is simply a collection of mathematical algorithms, you aren't distinguishing between the algorithms that describe the thing and the thing itself.

With software there is no separate thing. The software is the only thing. If there was a separate thing you could identify it.

You can clearly distinguish between, for example, a physics text describing how bricks are affected by gravity, and an actual brick that you can pick up in your hand. The physics text is not patentable completely regardless of how creative it is or how much work went into producing it. The brick may be patentable, e.g. if you make it out of some novel weather-resistant material.

The problem with software patents is that people making texts and not bricks are being accused of infringing patents.

But in reality, much like the photograph, there is a great deal more to software than that; there is thought and creativity involved in "collecting" those algorithms.

Now you're talking about how the software is produced. The end product is still an algorithm. Are you suggesting that if I write a computer program that can produce other computer programs, the programs produced that way should not be able to infringe any patents because they were created deterministically without any human thought or creativity? Patents have no requirement of creativity. Again, the protection for creative works is copyright, and it applies to software as well as it does to photographs and books.

More to the point, analogizing software to several other things that are all indisputably not patentable is a very poor way of arguing that software should be patentable.