Ten Things I Didn’t Learn in 2006

Just as important as what I learned last year is what I didn’t learn – or, more precisely, the things I learned I didn’t know but should.

1. What exactly is the significance of the modularity conjectures?

2. How is culture transmitted?

3. What is the most general form of the Riemann-Roch theorem?

4. What factors contribute to the occupation-controlled wage gap?

5. How can the proof of the extended Riemann hypothesis for function fields be generalized to number fields?

6. What causes some political and social movements to succeed but others to fail?

7. Can every finite group arise as the Galois group of a normal extension of Q?

8. What are the effects of international trade on global politics, especially war?

9. How does Lie theory figure into particle physics, exactly?

10. How can political movements protect themselves from radicalization?

Some of these are well within the realm of human knowledge, but outside mine – namely, 1, 3, 4, 9, and to some extent 8. About the rest, nobody knows that I know of.

31 Responses to Ten Things I Didn’t Learn in 2006

  1. katie says:

    apparently my GEO218 prof knows the answer to #2 considering week #3 of class is entitled “how culture is transmitted.”

  2. whig says:

    Re: #2, Bread making seems to be a good metaphor, and what makes sense to me. Out of bread comes culture, the yeast that leavens.

  3. hujo says:

    Hey some awsome questions i dont speak math but heres my take on one.

    6. What causes some political and social movements to succeed but others to fail?

    Their validity starts it, their necessity, if the ideology is a reflection of the closest thing to truth and addresses the needs of the greater population, aligns with their feelings and experience, it will succeed, however the more valid the cause, the more people will get behind it the faster the changes, the change brings the loss of validity, ushering in the failure of the movement.

    If the movement acquired power then those with it will hold onto power and create the illusion of validity and necessity, in other words lie and manipulate censor scapegoat to support their agenda and hold onto their power, we see it time and time again.

    Operating under corrupt or false ideologies will not address societies needs and will of course create problems therefore creating the necessity to address these problems by creating a movement that’s goal is removing the power and influence from the long dead corrupt movement.

    Like how Feminsm gave birth to mra iwf rwc if ect movements eat themselves or become powers that usually become corrupt and fail by creating an opposing movement that’s ideology now possesses the closest thing to the truth.

  4. SLC says:

    Re application of Lie Algebras and Lie Groups in physics.

    I would recommend a rather old book which I used a million years ago, “Lie Groups for Pedestrians,” by Harry Lipkin.

  5. Cat lover says:

    Regarding #7, try “Groups as Galois Groups: An Introduction” by Helmut Volklein. I just started it, and it looks like an excellent book. What’s been proved (as of ’96) boils down to (1) all solvable groups appear (2) all the sporadic groups appear, except possibly one of the Mathieu groups (3) all the alternating groups appear (4) various partial results concerning groups of Lie type.

    Regarding #3, look at appendix A in Hartshorne’s “Algebraic Geometry” if you haven’t already (but I’m guessing you have). The last form he lists is the most general one I know of.

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