Do you capitalise words like 'Liberalism'? [duplicate]

Do you capitalise words like 'Liberalism', 'Communism', 'Socialism'?

I'm presuming that such words are proper nouns because they are the specific names of ideologies. If they are not capitalised, why not?

And if they are capitalised, are words like mathematics capitalised? I am led to believe they are not unless they are the name of a specific course subject like 'Maths 101', but isn't mathematics the proper noun of a specific concept?

The difference in usage depends on whether the "-ism" is related to an established organisation or well-defined movement, or whether it is related to a more informal or organic grouping.

For example: in the UK we have a Conservative party. Thus you can have a Conservative estimate of the state of the economy which is one made and/or promoted by the Conservative party and a conservative estimate of the state of the economy which takes a moderate view of the performance.

These are usually two different things, If the Conservatives are in power the Conservative estimate will be more bullish than the conservative estimate but when they are not in power it will be more pessimistic.

Similarly In the US you can have democratic principles and Democratic principles, the former being the general principles underpinning a democratic state and the latter being the more or less formally expressed principles expressed and promoted by the Democratic Party.

You can also have republican beliefs and Republican beliefs. The former are beliefs held by people who are opposed to hereditary power, particularly monarchy, and the latter are the beliefs formulated, expressed and promoted by the Republican Party.