Chapter 17 – How to Read Science and Mathematics (part 1 of 2)


The title of this chapter may be misleading. We do not propose to give you advice about how to read every kind of science and mathematics. We will confine ourselves to discussing only two kinds: the great scientific and mathematical classics of our tradition, on the one hand, and modern scientific popularizations, on the other hand. What we say will often be applicable to the reading of specialized monographs on abstruse and limited subjects, but we cannot help you to read those. There are two reasons for this. One is, simply, that we are not qualified to do it.

The other is this. … Most modern scientists do not care what lay readers think, and so they do not even try to reach them.

Today, science tends to be written by experts for experts. A serous communication on a scientific subject assumes so much specialized knowledge on the part of the reader that it usually cannot be read at all by anyone not learned in the field.

What does the general do in these circumstances? He cannot become expert in all fields. He must fall back, therefore, on scientific popularizations.


Scientists are more concerned than ever before about the nature of the scientific enterprise itself. … Thus we have no hesitation in recommending that you try to read at least some of the great scientific classics of our tradition. In fact, there is really no excuse for not trying to read them.

The most helpful advice we can give you is this. You are required by one of the rules for reading expository works to state, as clearly as you can, the problem that the author has tried to solve. This rule of analytical reading is relevant to all expository works, but it is particularly relevant to works in the fields of science and mathematics.

As a layman, you do not read the classical scientific books to become knowledgeable in their subject matters in a contemporary sense. Instead, you read them to understand the history and philosophy of science. … To follow the strands of scientific development, to trace the ways in which facts, assumptions, principles, and proofs are interrelated, is to engage in the activity of the human reason where it has probably operated with the most success.


By a scientific book, we mean the report of findings or conclusions in some field of research, whether carried on experimentally in a laboratory or by observations of nature in the raw. The scientific problem is always to describe the phenomena as accurately as possible, and to trace the interconnections between different kinds of phenomena.

In the great works of science, there is no oratory or propaganda, though there may be bias in the sense of initial presuppositions. You detect this, and take account of it, by distinguishing what the author assumes from what he establishes through argument. The more “objective” a scientific author is, the more he will explicitly ask you to take this or that for granted. Scientific objectivity is not the absence of initial bias. It is attainted by frank confession of it.  

The leading terms in a scientific work are usually expressed by uncommon or technical words. They are relatively easy to spot, and through them you can readily grasp the propositions. The main propositions are always general ones. Science thus is not chronotopic. Just the opposite; a scientist, unlike a historian, tries to get away from locality in time and place. He tries to say how things are generally, how things generally behave.

There are likely to be two main difficulties in reading a scientific book. One is with respect to the arguments. Science is primarily inductive; that is, its primary arguments are those that establish a general proposition by reference to observable evidence – a single case created by an experiment, or a vast array of cases collected by patient investigation.

This first difficulty arises because, in order to understand the inductive arguments in a scientific book, you must be able to follow the evidence that the scientist reports as their basis. Unfortunately, this is not always possible with nothing but the book in hand. If the book itself fails to enlighten him, the reader has only one recourse, which is to get the necessary special experience for himself at first hand.

Anyone who desires to acquire an understanding of the history of science must not only read the classical texts, but must also become acquainted, through direct experience, with the crucial experiments in that history.

This does not mean that you cannot make a start without going through all the steps described. Take a book like Lavoisier’s Elements of Chemistry, for instance. Published in 1789, the work is no longer considered to be useful as a textbook in chemistry, … Nevertheless, its method was revolutionary at the time, and its conception of a chemical element is still, on the whole, the one that we have in modern times.

He improved chemistry by improving its language, just as Newton, a century before, had improved physics by systematizing and ordering its language – in the process, as you may recall, developing the differential and integral calculus.

Mention of the calculus leads us to consider the second main difficulty in reading scientific books. And that is the problem of mathematics.