Math Foundations from Scratch
The title of this sounded very promising.  Something that actually describes math from scratch needs to exist, but this ain&#x27;t it.  It runs off the rails from the very first sentence, where it asks &quot;What is math?&quot; but doesn&#x27;t actually answer the question except to tell you that it&#x27;s easy.<p>I stopped reading when I got to &quot;Numbers are objects you build to act like the concept of a number.&quot;<p>No no no no no.  No!  Math is the act of inventing sets of <i>rules</i> for <i>manipulating symbols</i> that produce interesting or useful results, or exploring the behavior of sets of rules invented by others.  One of the earliest example of such interesting or useful results is rules for manipulating symbols so that the results correspond to the behavior of physical objects (like sheep, or baskets of grain, or plots of land), and in particular, to their <i>quantity</i> so that by manipulating the right symbols according to the right rules allowed you to make reliable predictions about the behavior of and interactions between quantities of sheep and grain and land.  The symbols that are manipulated according to these rules are called &quot;numerals&quot; and the quantities that they correspond to are called &quot;numbers&quot;.<p>But you can invent other rules for other symbols that produce other useful and interesting behavior, like &quot;sets&quot; and &quot;vectors&quot; and &quot;manifolds&quot; and &quot;fields&quot; and &quot;elliptic curves.&quot;  But it all boils down to inventing sets of rules for manipulating symbols.