Math is the series of statements that can be made about things that are true.
Math can't tell you that there are three of [anything that you encounter with your sensory organs], but it can tell you that if there are three of those, you can also say...
In that way, it tells you about the real world while having no connection to any real world. The problem is that as soon as a math-predicted observation fails, we can blame the mistake on our sensory organs - either formatively (when we assigned a particular observation to a particular mathematical entity (like "three"), or conclusively (when we assigned a mathematical result to a sensation.) If a mathematical result consistently fails to apply to any sensation, it ceases to be math - not by disappearing, but by failing to be consistent; if you can't apply a mathematical process to a sensation in a way that enables you to predict a subsequent sensation, there's no way to determine whether the math makes any consistent statement.
Math has to be empirical because it's completely vetted by sensational observations. If a hypothetical god changed some aspect of the underlying physical reality (inclusive of changing some aspect of human sensory organs), the math would change along with it, and things that were math would cease to be math. If you included that god within your mathematics, math becomes the set of all possible maths, which is just the universal set. There's no meaning to a math that says everything about everything.
I guess you can say Platonism is true too, since math is a statement about an underlying reality (because it is discarded when it is not), but it's not a meaningful thing to say. Math that turned out to be correct (and continues to turn out to be correct) is Platonic. Math that was incorrect (or in the future becomes incorrect) is not Platonic. The only way you can determine which math is Platonic and which math is not is through empirical observation, and the degree to which you can be sure that particular math continues to be Platonic is through how well your past observations predict your future observations.
To answer the tweet, people study math because because being able to predict things gives you an advantage in your work.
Math can't tell you that there are three of [anything that you encounter with your sensory organs], but it can tell you that if there are three of those, you can also say...
In that way, it tells you about the real world while having no connection to any real world. The problem is that as soon as a math-predicted observation fails, we can blame the mistake on our sensory organs - either formatively (when we assigned a particular observation to a particular mathematical entity (like "three"), or conclusively (when we assigned a mathematical result to a sensation.) If a mathematical result consistently fails to apply to any sensation, it ceases to be math - not by disappearing, but by failing to be consistent; if you can't apply a mathematical process to a sensation in a way that enables you to predict a subsequent sensation, there's no way to determine whether the math makes any consistent statement.
Math has to be empirical because it's completely vetted by sensational observations. If a hypothetical god changed some aspect of the underlying physical reality (inclusive of changing some aspect of human sensory organs), the math would change along with it, and things that were math would cease to be math. If you included that god within your mathematics, math becomes the set of all possible maths, which is just the universal set. There's no meaning to a math that says everything about everything.
I guess you can say Platonism is true too, since math is a statement about an underlying reality (because it is discarded when it is not), but it's not a meaningful thing to say. Math that turned out to be correct (and continues to turn out to be correct) is Platonic. Math that was incorrect (or in the future becomes incorrect) is not Platonic. The only way you can determine which math is Platonic and which math is not is through empirical observation, and the degree to which you can be sure that particular math continues to be Platonic is through how well your past observations predict your future observations.
To answer the tweet, people study math because because being able to predict things gives you an advantage in your work.