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According to Popular Science (This article and its images were originally posted on Popular Science September 18, 2018 at 03:53PM.)
What does math look like to mathematicians? It’s very simple. Math looks like language.
A funny language, I’ll admit. It’s dense, terse, and painstaking to read. While I zip through five chapters of a Twilight novel, you might not even turn the page in your math textbook. This language is well suited to telling certain stories (e.g., the relations between curves and equations), and ill-suited to others (e.g., the relations between girls and vampires). As
such, it’s got a peculiar lexicon, full of words that no other tongue includes. For example, even if I could translate a0 + ∑ ∞ n=1 (an cos(nπx/L) + bn sin(nπx/L) into plain English, it wouldn’t make sense to someone unfamiliar with Fourier analysis, any more than Twilight would make sense to someone unfamiliar with teenage hormones.
But math is an ordinary language in at least one way. To achieve comprehension, mathematicians employ strategies familiar to most readers. They form mental images. They paraphrase in their heads. They skim past distracting technicalities. They draw connections between what they’re reading and what they already know. And—strange as it may seem—they engage their emotions, finding pleasure, humor, and squeamish discomfort in their reading material.
Now, this brief chapter can’t teach fluent math any more than it could teach fluent Russian. And just as literary scholars might debate a couplet by Gerard Manley Hopkins or the ambiguous phrasing of an email, so mathematicians will disagree on specifics. Each brings a unique perspective, shaped by a lifetime of experience and associations.
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