Baking Bread
In this baking the bread example, Ian Stewart addressed the issue between invention and discovery. He stated that although it is important to distinguish the difference between inventing and discovering, he said that everything requires both of them. He then moved on to saying that "Mathematics has an internal structure of logical deduction that allows it to grow in unexpected ways." This means that new ideas can be generated to cover 'holes' in various theories. Also, he said that the origin of mathematics derived from the real world, and that the abstraction of mathematics came from reality itself. So basically, he is emphasizing the fact that mathematics was "always there"
Lottery Illusion
In this section, Stewart compare the Fibonacci numbers with biology. He stated the fact that the number of petals in a flower corresponds to the Fibonacci numbers, may suggests mathematics is inherent in nature. He also said that our minds tend to look for mathematical patterns, which sprang to theories like Newton's Law of Gravity and quantum physics. He then moved on to saying that "Mathematics is our way of understanding certain features of nature. It is a construct of the human mind, but we are part of nature, made from the same kind of matter, existing in the same kinds of space and time as the rest of the Universe." Which further connotes that mathematics is inherent. Stweart then moves onto a bigger picture, in whether aliens (if they exist) have the same kind of maths as us. But he then summarise that mathemtics is different in every enviroment.
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