On the bare facts (and I say that from the top rung of Ramsey’s ladder, which I insist is lying flat along the ground), we can see that natural sciences do use maths, when they can.

But none of them could use maths in the first many many centuries of their formation.

Some of them couldn’t even use arithmetic for the longest time.

They do like to use numbers, because numbers are a handy short hand for describing relations, which would otherwise be very clumsy.

For example: “A stick of length in centimeter three quarters of the weight in kilograms of the object to be flung” is clumsy and prone to misunderstanding.

Also it’s hell on the editor if for some reason the proportions needed to be changed at some point in the writing or reviewing process.

In this, mathematics is seen to be a language, the only actually generative human language.

At some point we used latin to communicate science, because it was understood by all members of the scientific elite, thereby handily excluding the rabble.

Now, math has taken much o... show moreOn the bare facts (and I say that from the top rung of Ramsey’s ladder, which I insist is lying flat along the ground), we can see that natural sciences do use maths, when they can.

But none of them could use maths in the first many many centuries of their formation.

Some of them couldn’t even use arithmetic for the longest time.

They do like to use numbers, because numbers are a handy short hand for describing relations, which would otherwise be very clumsy.

For example: “A stick of length in centimeter three quarters of the weight in kilograms of the object to be flung” is clumsy and prone to misunderstanding.

Also it’s hell on the editor if for some reason the proportions needed to be changed at some point in the writing or reviewing process.

In this, mathematics is seen to be a language, the only actually generative human language.

At some point we used latin to communicate science, because it was understood by all members of the scientific elite, thereby handily excluding the rabble.

Now, math has taken much of that role, adding convenience and precision to the two previous reasons.

Often we then run into the problem that the language is more precise than what it is communicating.

Math is a language for communicating relations and relations between relations, in a way that doesn’t tie the brain into knots.

We really have no better tool for that.

The sciences use applied mathematics. Or rather, they apply mathematics.

I can say it in other ways as well:

Mathematics itself isn’t about anything.

Sciences are about something.

This discordance of essence clearly sets aside math from the sciences - something that is not a science, but which happens to be as useful to sciences as the other languages involved in writing down the findings.