Quicktime does not plya midi songs in any web browser!

I couldn't get any files to load in any browser.
I downloaded some of the files and they refused to play in QuickTime Player or open in QuickTime X.
VLC (free download) did play the files but showed the codec as Windows Media. This is also evident in the file sizes. Typical MIDI files measure in KB's but the files at your link are over a MB in size.

http://free.mididb.com/

Files at this site worked as expected in QuickTime Player.

MIDI files are "computer generated" audio. They can't have any "vocals" because there is no "instrument" for voices.
QuickTime uses an instrument set from Roland.

I couldn't get any files to load in any browser.

As already pointed out, these files are WMA. More importantly, they are in an ASF file container. If you want them to play in your browser and this is the OP's own web site, then the OP should simply rename the files correctly so they will open in QT Player or QT browser plug-in properly. As an example, I have uploaded a re-named file from the original site here.

http://idisk.me.com/jrwalker4-Public/AdrianaMezzadri_-_PrimaveraIluminada.asf/

That's what I'm talking about! But in my case the files are .midi. Now what?

The files are not MIDI files. They are encoded as "Windows Media Audio Std v.2 - DivX audio v2" data in an "ASF (Active Streaming Format)" file container. When QT looks at the files it sees that the file extension (".mid") does not match the file "header/handler" data stored in the file. When this happens, the QT player won't open the file and the QT browser plug-in displays a question mark to tell you that it doesn't know what to do. If you want the files to play correctly on a Mac, then the ".mid" file extension must be changed to ".asf" to avoid confusing QT software.

They are MIDI in file extension (.mid) only. Windows Media Audio is what I find at the site.

A Web browser uses "plug-ins" to help with some file formats. They read the file extension or the page code to help the visitor get the most from the page.
Your link uses the .mid file extension but no HTML code to properly call any browser plug-in so it is up to each visitors settings to help open the files.
The .mid file extension is set to QuickTime for most Mac users. Since the files aren't really MIDI files the QuickTime browser plug-in is called but can't properly play them. This is why the browser displays the icon for QuickTime and a question mark.
Flip4Mac plug-in also uses HTML code to call QuickTime but in this case it can't open the files because of the .mid file extension.

O de sempre, incompatibilidade entre Windows e Mac.

Not really. The Mac player is built around specific standards and adhering to them. Windows media players simply tend to ignore such standards--not caring if the content is in a program stream or a transport stream, if there are timecode breaks or not, don't care whether files are "properly" terminated or not, etc. In this case, whoever posted the files was less than honest about the compression format and the type of file container--in a sense lying to the multimedia player. While Windows players may ignore this discrepancy, QT does not. It is a difference in philosophy, basically, and one which many non-Apple users find disturbing or difficult to understand.

Philosophy with mathematics coexist together?

Of course. If you check, you'll find that many great mathematicians were also noted for their philosophical writings.