...nature is a wonderful realm in which to observe beauty born out of mathematical relationships. The natural world provides seemingly endless patterns underpinned by numbers – if we can recognize them.
Number theory finds unexpected applications in science and engineering, from leaf angles that (almost) universally follow the Fibonacci sequence, to modern encryption techniques based on factoring prime numbers.
Many popular books on mathematics try to be approachable by talking about stock markets or poker odds.Others wax poetic about prime numbers and the mystery of infinity. Cheng’s books lift readers to the rarefied heights of mathematical abstraction by teaching them category theory, which she believes is the most foundational kind of math.
Space exploration requires tremendous precision. Mathematicians have invented ingenious ways to transmit and store information. One surprisingly effective method uses Reed-Solomon codes, which are built on the same basic algebra that students learn in school.
Szemerédi proved that any set comprising a positive fraction of the integers must contain arbitrarily long arithmetic progressions. The result was a landmark in the subfield of mathematics called additive combinatorics.
The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an important idea, but this understanding can quickly slip away without consolidation through practice and repetition.
It’s tough for nonexperts to see mathematics as beautiful in the first place. Beauty is in the eye of the beholder, sure, but it’s also hard to see when the work of art is hidden in darkness, obscured by an impenetrable cloud of symbols and jargon.
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