The 39 melakhot and the Mishkan

On Shabbat 49b, we are told that three early amora'im, Rabbi Yonatan ben Akhinai, Rabbi Yonatan ben Elazar, and Rabbi Hanina bar Hama, were sitting discussing a very particular case of muktzeh that came up in the mishnah. Then, in classic Talmudic fashion, we are told as an aside that those amora'im also discussed the most fundamental question of our massekhet:

הדור יתבי וקמיבעיא להו: הא דתנן אבות מלאכות ארבעים חסר אחת כנגד מי?

אמר להו רבי חנינא בר חמא: כנגד עבודות המשכן.

אמר להו רבי יונתן ברבי אלעזר כך אמר רבי שמעון ברבי יוסי בן לקוניא: כנגד מלאכה מלאכתו ומלאכת שבתורה - ארבעים חסר אחת.

Why are there thirty-nine categories of forbidden work on Shabbat? What do they represent?

Insulating food Friday evening

The fourth perek of Shabbat (47b–51b) discusses hatmanah, insulating hot food on Shabbat. Materials that add their own heat may not be used. Why not?

Rava establishes on Shabbat 34a–b that there are two rabbinic decrees against hatmanah. One decree applies to insulating materials that add heat, which may not even be used from Friday going into Shabbat. The other decree applies to materials that insulate without adding heat, which may be used on Friday but not once Shabbat starts. The fourth perek then defines which materials add heat and which don't.