How to Read Science and Mathematics

How to Read Science and Mathematics

In today’s world, where the sciences and engineering flourish, most of us inevitably come into contact with books on science and mathematics. From Newton’s laws to the origin of the universe, from quantum mechanics to blockchain, science and technology are everywhere. Because of the nature of these disciplines, reading books on science and mathematics is completely different from reading novels or essays; they must be read according to their own character. So how, exactly, should we read them?

Of course, the scientific and mathematical works discussed here are limited to two forms: first, the great classic works of science and mathematics in our tradition; second, modern popular science writing. These suggestions may also apply to some research papers on deep and specialized topics, though I cannot guarantee that. This is because, until about the end of the nineteenth century, the major scientific works were written for lay readers. After that, however, disciplines began to branch into specialties, and monographs and papers in different fields came to require substantial professional background knowledge to understand. No one can be familiar with every field.

On the other hand, the kind of reading discussed here is not aimed at becoming an expert in a field, but at understanding the questions involved. The history of science is one of the fastest-growing disciplines in academia. In the past, historians of science were often regarded as people who studied history mainly because they lacked the ability to advance real science. That attitude can be summed up by George Bernard Shaw’s famous remark: “He who can, does. He who cannot, teaches.”

Nowadays, one hears much less of this attitude. The field of the history of science has become important, and distinguished scientists study and write about the history of science. None of these books is truly difficult to read. What the reader must do is apply the rules for reading expository works and be very clear about the problem the author is trying to solve. This rule of analytical reading applies to any expository work, and especially to works of science and mathematics.

Pay attention to the author’s initial assumptions, keep them in mind, and distinguish those assumptions from the conclusions reached through argument. The more objective a scientific author is, the more explicitly he will ask you to accept this assumption or that one.

Scientific objectivity does not lie in having no initial bias, but in frankly admitting it. Science is not a chronicle. Scientists are almost the opposite of historians: they seek to free themselves from the limits of time and place. What they want to describe are general phenomena and the general laws by which things change.

When reading scientific works, there are two main difficulties. One concerns argument. Science is basically inductive, and its fundamental arguments are general rules established through investigation and verification—perhaps from a case created by experiment, or perhaps from a series of cases gathered through long observation. Induction is a defining feature of science. There are also other arguments that proceed by deduction. Such arguments are inferred from other theories that have already been proven. In their concern for evidence, science and philosophy are actually not so different.

Mathematics is in fact a language, with its own vocabulary, grammar, and syntax, and beginners must learn these things. Learning a new written language involves the most basic problems of reading.

There are quite a few mathematical difficulties in scientific works, and this is a major obstacle to reading them. There are two sides to this. First, you can often understand some mathematics more clearly than you might imagine at a basic level, and for the parts you do not understand, you can begin with the conclusions alone. Second, if your purpose in reading a mathematics book is to understand mathematics itself, then of course you must really read the mathematics carefully from beginning to end, take notes, and think.