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Mathematics of Machine Learning
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We’ve come a long way from the start: we’ve studied propositions, logical connectives, predicates, quantifiers, and all the formal logic. This was to be able to talk about mathematics. However, ultimately, we want to do mathematics.
As the only exact science, mathematics is built on top of definitions, theorems, and proofs. We precisely define objects, formulate conjectures about them, then prove those with mathematically correct arguments. You can think of mathematics as a colossal building made of propositions, implications, and modus ponens. If one theorem fails, all others that build upon it fail too.
In other fields of science, the modus operandi is to hypothesize, experiment, and validate. However, experiments are not enough in mathematics. For instance, think about the famous Fermat numbers, that is, numbers of the form Fn := 22n + 1. Fermat conjectured them all to be prime numbers, as F0, F1, F2, F3, and F4 are primes...