pandas.isnull() (also pd.isna(), in newer versions) checks for missing values in both numeric and string/object arrays. From the documentation, it checks for:

NaN in numeric arrays, None/NaN in object arrays

Quick example:

import pandas as pd
import numpy as np
s = pd.Series(['apple', np.nan, 'banana'])
pd.isnull(s)
Out[9]: 
0    False
1     True
2    False
dtype: bool

The idea of using numpy.nan to represent missing values is something that pandas introduced, which is why pandas has the tools to deal with it.

Datetimes too (if you use pd.NaT you won't need to specify the dtype)

In [24]: s = Series([Timestamp('20130101'),np.nan,Timestamp('20130102 9:30')],dtype='M8[ns]')

In [25]: s
Out[25]: 
0   2013-01-01 00:00:00
1                   NaT
2   2013-01-02 09:30:00
dtype: datetime64[ns]``

In [26]: pd.isnull(s)
Out[26]: 
0    False
1     True
2    False
dtype: bool

Your first problem is that math.isnan() does not accept string values as input. You can try and see math.isnan('any string').

Because you are in the pandas dataframe already, you are better off to use Pandas to handle your case. For example:

df.dropna()           # column-wise nan drop
df.dropna(axis=1)     # row-wise nan drop

Note that there are very useful arguments for additional convenience in dropna(), so do check those out from the doctring or corresponding manual entries.

As a word of advice for along the journey, when you work with pandas, it's good to keep in mind that often whatever you want to do, is easier to do just within native pandas functionality. Because Pandas is kind of a gold standard for this type of work, generally speaking whatever you are thinking you want to do (if it makes sense) the Pandas community had already thought of (and implemented) it.

Just use both:

>>> names=['Pat','Sam', np.nan, 'Tom', '']
>>> for idx,name in enumerate(names):
...     if name == '' or pd.isnull(name):
...         print(idx)
...
2
4

However, realize that:

>>> pd.isnull(None)
True

So if you want to check specifically for NaN and not None, use math.isnan (while guarding against passing non-float values to math.isnan:

>>> import math
>>> for idx,name in enumerate(names):
...     if name == '' or (isinstance(name, float) and  math.isnan(name)):
...         print(idx)
...
2
4

Use the pandas method isnull to test:

Use with AIIn [45]:

df = pd.DataFrame({'words':['from', 'fairest', 'creatures' ,'we' ,'desire', 'increase' ,nan ,'that' ,'thereby']})
df
Out[45]:
       words
0       from
1    fairest
2  creatures
3         we
4     desire
5   increase
6        NaN
7       that
8    thereby
In [46]:

pd.isnull(df['words'])
Out[46]:
0    False
1    False
2    False
3    False
4    False
5    False
6     True
7    False
8    False
Name: words, dtype: bool

Use math.isnan:

>>> import math
>>> x = float('nan')
>>> math.isnan(x)
True

Methods for this already exist, particularly because of the weird properties of NaNs. One of them can be found in the math library, math.isnan and numpy already has a method implemented for this as well, numpy.isnan. They both deal with all three kinds of NaNs shown in your code (but the numpy version is vectorized):

import math
import numpy as np

list(map(math.isnan, [float("nan"), math.nan, np.nan]))
# [True, True, True]

np.isnan([float("nan"), math.nan, np.nan]) 
# array([ True,  True,  True])

If you are using pandas, pandas.isna is also interesting because it considers None and pandas.NaT (Not a Time) as missing values as well:

import pandas as pd

pd.isna([float("nan"), math.nan, np.nan, None, pd.NaT])
# array([ True,  True,  True,  True,  True])

Your code has a potential flaw, it does not return True only for NaNs (although it does return True for all NaNs), but for all objects which are not equal to themselves. In particular, it will think any instance of this class is NaN (probably true, but not necessarily):

class A:
    def __equal__(self, other):
        return False

You could add your variables which you'd like to interpret as NaN to na_values argument of the pd.read_csv:

df = pd.read_csv('your_file.csv', na_values=['NAN'])

Also you could find some information in that answer.

All default NA values from na-values:

The default NaN recognized values are ['-1.#IND', '1.#QNAN', '1.#IND', '-1.#QNAN', '#N/A','N/A', 'NA', '#NA', 'NULL', 'NaN', '-NaN', 'nan', '-nan']. Although a 0-length string '' is not included in the default NaN values list, it is still treated as a missing value.