The answers

Wow. I am so impressed with everyone who participated. Particularly with those who managed to tell what landmarks were on the geography shirt. Had I not already known the answers, I don't think I could have recognized the worn-out blobs on the shirt. So good job, everyone.

In case you would like to know the answers, here they are:

1. NYC skyline. (Remember that shirt was made in 1999, so the Twin Towers still existed)
2. St. Basil's at Red Square
3. Leaning Tower of Pisa
4. Statue of Liberty
5. Sydney Opera House
6. Pyramid at Giza
7. Stonehenge
8. Independence Hall
9. Eiffel Tower
10. Gateway Arch in St. Louis
11. Empire State Building
12. Forbidden City
13. Golden Pavilion (Japan)
14. Easter Island
15. Arc de Triomphe
16. Washington Memorial
17. Kinderdijk (I accepted any variation of "windmills in Holland" though)
18. Westminster Abbey
19. Lincoln Memorial
20. Alamo
21. Cristo Redentor in Rio de Janeiro
22. Brandenburg Gate
23. Space Needle
24. Taj Mahal
25. Dome of the Rock
26. Parthenon

For the math shirt, the answers are:

1. Phi is an embedding from Z^n to R^n
2. Moebius Strip
3. The cardinality (order) of the rationals is equal to the cardinality (order) of the naturals, called aleph not.
4. (P implies Q) is equivalent to (not P OR Q)
5. A cube, the 6-sided platonic solid.
6. A two-state Markov model.
7. Trefoil knot.
8. Dodecahedron, 12 sided platonic solid.
9. Sum of the integers from 1 to n.
10. Mandelbrot set.
11. DeMorgan's Law.
12. Taylor series expansion for the exponential function.
13. Navier Stokes Equation.
14. Octahedron, the 8-sided platonic solid.
15. Visual representation of the integral from a to b.
16. nth dihedral group.
17. pi function, the asymptotic density of the primes.
18. Definition of the set of rational numbers.
19. We'll talk about this one.
20. Cauchy integral formula, or winding number
21. Figure 8 knot.
22. Fundamental Theorem of Calculus, or Leibniz rule for integration
23. Tetrahedron, the 4-sided platonic solid
24. Unfolding of the torus onto the plane.
25. 1st isomorphism theorem. (or close enough)
26. Isocahedron.
27. Gamma function, the analytical extension of the factorial function.
28. Euler's formula.
29. Roots of the quadratic equation.
30. The golden ratio, phi, equal to (1+sqrt(5))/2

The geography contest had a clear winner. Congrats Daniel Larsen -- a $5 Amazon gift card is coming your way!
For the math contest, James Dilts beat my dad by just a hair. Congrats James!
For the overall contest, it was again neck and neck, since my dad and James had the same number of geography landmarks right. But since James won math, he again won overall! So a $10 Amazon gift card is coming your way!

As for some of my favorite answers . . .
2.  Храм святого Василия Блаженного, на Красной Площади в Москве. (Which is probably correct. I just can't tell.)
3. Church Office Building
8. Clock tower from back to the future/Um ... there are lots of buildings that look like that, I'm sure. The Ogden Temple?/The church building in the illustration for AoF 11/no idea but it looks like an lds temple
11. Um.  It's a tower.
12. Carousel of happiness.
15. Triumphal arch or pants/arch of malstorm (what is that Spencer?)
16. Shed snake skin.
17. Windmill in Wamego, KS. (Sorry Nathan. I don't even know where Wamego is.)
18. The home of the old woman who lived in a shoe.
19. Shapeless blob on a T-shirt. Yeah. I can see that.
20. Something I'm supposed to remember in San Antonio.
22. Hogle Zoo, elephant cage/Mesa Arizona Temple with flag on top
26. Piranha head on a T-shirt

And then what my uncle said about the math contest:
No, I cannot. But I did find the quadratic formula, my name, a pi(e), a pretzel, an upside-down pretzel, a deformed turtle, a soccer ball, circuit=donut, I co-sign with Theta, and a something that looks like a dreidel. Oh, and it looks like someone started to play hangman.


oh, and about #19 -- I actually am not sure about this one anymore. James said it was "The infinite cover of a circle wedge a circle, or a representation of the simple group generated by two elements" which was the most definitive thing I saw, but I'm still not sure about that. Want to back that up?