matplotlib 3d axes ticks, labels, and LaTeX

The for loop is not necessary, to change the size of your ticks you can use:

    ax.zaxis.set_tick_params(labelsize=10)

How do I adjust the axis ticks to that of my choosing? I.e., how would I get the z-axis to only label 2, 0, and -2, and in the font size that I want? I know how to do this in 2D but not 3D.

You have to change properties of zticks.

Why is the x-axis label distorted, which I wanted to do with this script, but not the z-axis label (gamma)? This does not make sense. I need this axis labeled in the Greek letter. How do I fix this?

You have to disable autorotation for z axis labels. Look at the code below:

import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

mpl.rcParams['legend.fontsize'] = 10

fig = plt.figure()
ax = fig.gca(projection='3d')
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
ax.plot(x, y, z, label='parametric curve')
ax.legend()

ax.set_xlabel('$X$', fontsize=20)
ax.set_ylabel('$Y$')
ax.yaxis._axinfo['label']['space_factor'] = 3.0
# set z ticks and labels
ax.set_zticks([-2, 0, 2])
# change fontsize
for t in ax.zaxis.get_major_ticks(): t.label.set_fontsize(10)
# disable auto rotation
ax.zaxis.set_rotate_label(False) 
ax.set_zlabel('$\gamma$', fontsize=30, rotation = 0)
plt.show()