What is the difference between logic and mathematics?

“What is the difference between logic and mathematics?”

While all math was derrived based upon logical premises, I think they are actually very different tools with very different purposes. In fact I would say that math and logic are complementary opposites.

Simply put, Math quantifies while Logic clarifies.

Math provides accurate numericle results, but little intuitive understanding of cause and effect.

Logic provides a greater understanding of cause and effect, but usually only first order estimates of quantitative results.

Math is only useful for matters dealing with numbers, logic is useful for all matters and is basically the creative thought process.

Logic is prone to errors due to intuitive false premise, while math is prone to errors of intuitive false conclusions.

Mathematical formalism is a rigorous step by step process that can only progress forwards.

Logic includes deduction (forward) and induction (backwards) process. Therefore it can solve problems in hindsite such as criminal investigations or trouble shooting problems. It can also solve hidden domains such as reverse engineering an Integrated Circuit.

Math is accumulative where methods can be further developed into more advanced methods and often requires a list of prerequisites, making it more suitable to learn through education and less suitable for learning in a piecmeal fashion. e.g. arithmatic, algebra, calculous, differential equations,…

Logic is less connected to academics and more connected to experience. Since it’s a creative proces and dependant on a wider base of circumstances it must be more flexible. It answers more than how much or how long, but it answers any question, such as why or how it does what it does.

The more math that you need to apply to solve a problem, the more complex the solution will become.

The more logic that you apply towards solving a problem, the more simple the solution will become.

Many problems can be solved by both logic and math. quite often logic may create a shortcut to a very difficult mathematical problem.

example:

Assuming all records are available, what is the average win rate for all poker players that play at a certain stakes in a certain card club when excluding any rake or time charge.

A mathematician will probably not even attempt such a difficult problem even with all available records citing problems with variance and sample size

A logician will tell you it’s 0, any money lost is also money won.