First of all, Lewis did have great difficulty with mathematics. After receiving a scholarship to University College, Oxford University, he twice failed the mathematics section of the entrance examination. It is probable that he would never have been admitted to Oxford except that the entrance exam was waived for veterans of WWI. He failed this exam because he had trouble with arithmetical and algebraic manipulation. In Surprised by Joy, he said, I could never have gone very far in any science because on the path of every science the lion Mathematics lies in wait for you. Even in Mathematics, whatever could be done by mere reasoning (as in simple geometry) I did with delight; but the moment calculation came in I was helpless. I grasped the principles but my answers were always wrong. Yet though I never could have been a scientist, I had scientific as well as imaginative impulses, and I loved ratiocination. (p.137). A diary entry when he was twenty-three years old reads, “As an intellectual nightcap have been puzzling over our accounts, which come out to a different figure each time.” (All My Road Before Me, p. 18). Although bad at calculation, he appreciated the benefits of mathematics. As he wrote to a young reader, “I wish I was good at Maths.” And to another, “I am also bad at Maths and it is a continual nuisance to me – I get muddled over my change in shops. I hope you’ll have a better luck and get over the difficulty! It makes life a lot easier.” (C. S. Lewis: Letters to Children, p. 67 and 75).

Lewis attended Wynyard School, a preparatory school that he referred to as Belson and the cruel headmaster as Oldie. “Except at geometry (which he really liked) it might be said that Oldie did not teach at all.” (Surprised by Joy, p. 27-8). One of Oldie’s idiosyncrasies was to make the students do addition problems for long periods of time and then ask how many they had done. Lewis’s brother Warnie solved the problem by doing the same sums each day. Evidently, Jack was too conscientious or too fearful to follow his brother’s example. It is not surprising that with this kind of a regimen, with the constant threat of beatings, that Lewis did not learn, and even hated, elementary mathematics. He later had a much better teacher, William Kirkpatrick although according to Lewis’ biographer and friend, George Sayer, “Kirkpatrick was not good at teaching math and had no insight into Jack’s problems with math, and, rather than sitting by his pupil’s side and working through his problems, he allowed Jack to do too many other things.” (Sayers, p. 116). So at least two of his teachers were not good at teaching elementary mathematics. All educators know how important the quality of early teaching in mathematics is.

However, this is not the whole story. Lewis said, “I can also say that though he [Oldie] taught geometry cruelly, he taught it well. He forced us to reason, and I have been the better for those geometry lessons all my life.” (Surprised by Joy, p 29). Also, Kirkpatrick taught logic well. This proficiency and love of the use of logic in geometry certainly aided Lewis in his apologetic works.

Mathematics is not just calculation and manipulation. In that part of mathematics Lewis had great difficulty all his life. At a higher level, mathematics is governed by reason and imagination, areas in which Lewis excelled. Thus, Lewis was a better mathematician than he has been given credit for. It is possible to be weak in beginning mathematics and still be good at more abstract mathematics. For example, one of the greatest mathematicians of all time, Evariste Galois, twice failed the mathematics part of the entrance examination to the Ecole Polytechnique. I am not at all suggesting that Lewis could have been a great mathematician, but he definitely had more mathematical ability than has been thought.

There are statements that indicate he had a dislike for mathematics. For example he did say, “I read algebra (devil take it)…” (Surprised By Joy, p. 187). And, “I shudder at the subjects you have to take in High School, and some of them I could not even begin to attempt – Algebra and Calculus for example.” (C. S. Lewis: Letters to Children, p. 106). On the other hand, this diary entry, “After supper I read Anthony and Cleopatra – the most intelligible play in the world – clear through like a theorem – and lovely.” (All My Road Before Me, p. 242) show his appreciation of the beauty of a mathematical theorem or proof. Two more quotations show his appreciation for the applicability of mathematics. ““I said this left out the fact that mathematics did conform to experience wherever the nature of the case allowed them to touch it and that this was in fact the reason why we called them true.” (All My Road Before Me, p. 300). “We have recently been reminded how much mathematics, and how good, went to the building of the [Copernican] Model.” (The Discarded Image, p. 103).

He also had an appreciation for mathematicians starting with his mother who “had been a promising mathematician in her youth and a B. A. of Queens College, Belfast.” (Surprised By Joy, p. 4). I believe this passage from Mere Christianity shows his appreciation of mathematicians,

Good tennis players “have a certain tone or quality which is there even when he is not playing, just as a mathematician’s mind has a certain habit and outlook which is there even when he is not doing mathematics. In the same way a man who perseveres in doing just actions gets in the end a certain quality of character. Now it is that quality rather than the particular actions which we mean when we talk of a ‘virtue.’” (p. 80).

This quality of mind that the mathematician shares with some scientists is commented on in an essay in God in the Dock:

That the continued application of scientific methods breeds a temper of mind unfavourable to the miraculous, may well be the case, but even here there would seem to be some difference among the sciences. Certainly, if we think, not of the miraculous in particular, but of religion in general there is such a difference. Mathematicians, astronomers and physicists are often religious, even mystical; biologists much less often; economists and psychologists very seldom indeed. It is as their subject matter comes nearer to man himself that their anti-religious bias hardens. (p. 135).

That he understood the mathematical method is shown by the following statement:

Unless you accept these [principles from the Tao] without question as being to the world of action what axioms are to the world of theory, you can have no practical principles whatever. You cannot reach them as conclusions: they are premises. … If nothing is self-evident, nothing can be proved. Similarly if nothing is obligatory for its own sake, nothing is obligatory at all. (The Abolition of Man, p. 40).

His appreciation for pure mathematics is shown in the following statements. "Human intellect is incurably abstract. Pure mathematics is the type of successful thought.” (God in the Dock, p. 65). “Egyptian and Babylonian Mathematics were practical and social, pursued in the service of Agriculture and Magic. But the free Greek Mathematics mattered to us more.” (The Four Loves, p. 69).

Another aspect of mathematics that Lewis appreciated was its permanence. In this regard, he compares mathematics to morality and religion.

Wherever there is real progress in knowledge, there is some knowledge that is not superseded. Indeed the very possibility of progress demands that there should be an unchanging element…. I take it we should all agree to find this sort of unchanging element in the simple rules of mathematics. I would add to these the primary principles of morality…. As regards material reality, we are now being forced to the conclusion that we know nothing about it save its mathematics…. Like mathematics, religion can grow from within, or decay…. But, like mathematics, it remains simply itself, capable of being applied to any new theory of the material universe and outmoded by none.” (God in the Dock, p. 45-7).

Many have accused Lewis of being opposed to science. In reply to J. B. S. Haldane’s charge that That Hideous Strength showed anti science bias, Lewis pointed out that the only good character and the only natural scientist in the evil National Institute for Coordinated Experiments (N.I.C.E.) is a physical chemist.

The good scientist is put in precisely to show that ‘scientists’ as such are not the target. To make the point clearer, he leaves my N.I.C.E. because he finds he was wrong in his original belief that’ it had something to do with science.’ (p. 83). To make it clearer yet, my principal character, the man almost irresistibly attracted by the N.I.C.E. is described (p. 226) as one whose ‘education had been neither scientific nor classical – merely ‘Modern’… Lest even this should not be enough, the hero…is made to say that the sciences are ‘good and innocent in themselves; (p. 248) though evil ‘scientism’ is creeping into them… If anyone ought to feel himself libeled by this book it is not the scientist but the civil servant. (Of Other Worlds, p. 78).

Lewis goes on to say that if any one now attempts to take over the world he would do it under the guise of science. In other words science would be used to disguise their real intent. “Technocracy is the form to which a planned society must tend. Now I dread specialists in power because they are specialists speaking outside their special subjects. Let scientists tell us about sciences.” (God in the Dock, p. 315). Lewis then acknowledges that it is another of his books that could more easily be misunderstood to show anti science bias but he explains what it is really against.

If any of my romances could be plausibly accused of being a libel on scientists it would be Out of the Silent Planet. It certainly is an attack, if not on scientists, yet on something which might be called ‘scientism’ - a certain outlook on the world which is causally connected with the popularization of the sciences, though it is much less common among real scientists than among their readers. It is, in a word, the belief that the supreme moral end is the perpetuation of our own species, and that this is to be pursued even if, in the process of being fitted for survival, our species has to be stripped of all those things for which we value it – of pity, of happiness, and of freedom. (Of Other Worlds, p. 76-77).

Here the charge of an anti technology bias on Lewis’ part could be defended but even here we must be careful to understand his view. He did say, “Their labour-saving devices multiply drudgery; … And as for permanence – consider how quickly all machines are broken and obliterated”. (The Pilgrim’s Regress, p.187). He preferred buttons to zippers because a button could be easily replaced while a zipper could not. He never learned to type, in fact, wrote with a dip pen, several levels behind the then current level of writing technology. However, “’I agree Technology is per se neutral,’ Lewis wrote to Arthur C. Clarke in 1943: ‘but a race devoted to the increase of its own power by technology with complete indifference to ethics does seem to me a cancer in the Universe.’” (Aeschliman, p. 61). Also, he comments on “the advance, and increasing application, of science. As a means to the ends I care for, this is neutral. We shall grow able to cure, and to produce, more diseases, to alleviate, and to inflict, more pains, to husband, or to waste, the resources of the planet more extensively.” (God in the Dock, p. 312).

Lewis was aware of a tendency to apply science in ways that caused more problems that they solved. Today consider the problem of what to do with radioactive wastes. He even compared applied science to magic.

There is something which unites magic and applied science while separating both from the ‘wisdom’ of earlier ages. For the wise men of old the cardinal problem had been how to conform the soul to reality, and the solution had been knowledge, self-discipline, and virtue. For magic and applied science alike the problem is how to subdue reality to the wishes of men: the solution is a technique; and both, in the practice of this technique, are ready to do things hitherto regarded as disgusting and impious such as digging up and mutilating the dead. (The Abolition of Man, p. 77).

He even went so far as to say. “The evil reality of lawless applied science (which is Magic’s son and heir) is actually reducing large tracts of Nature to disorder and sterility at this very moment.” (Miracles, p. 179.

Lewis understood that the theories, models, or pictures that science uses are not reality but only useful to give us some glimpse or understanding of reality but that behind it all is mathematics. “If you start investigating the nature of matter, you will not find anything like what imagination has always supposed matter to be. You will get mathematics.” (Letters to Malcolm, p. 107). “The walls, they say, are matter. That is, as the physicists will try to tell me, something totally unimaginable, only mathematically describable, existing in a curved space, charge with appalling energies. If I could penetrate far enough into that mystery I should perhaps finally reach what is sheerly real.” (Letters to Malcolm, p. 104-5)

In discussing theories of the atonement he compares them to scientific theories.:

What [scientists] do when they want to explain the atom, or something of that sort, is to give you a description out of which you can make a mental picture. But then they warn you that this picture is not that the scientists actually believe. What the scientists believe is a mathematical formula. The pictures are there only to help you to understand the formula. They are not really true in the way the formula is; they do not give you the real thing but only something more or less like it. They are only meant to help, and if they do not help you can drop them. The thing itself cannot be pictured, it can only be expressed mathematically. (Mere Christianity, p. 54).

Earlier it was noted that Lewis believed that mathematicians and physicists were more likely to be religious that most other scholars. He even has his fictitious devil, Screwtape; advise another devil of the “danger” of science when tempting his human patient.

Above all, do not attempt to use science (I mean, the real sciences) as a defence against Christianity. They will positively encourage him to think about realities he can’t touch ands see. There have been sad cases among physicists. If he must dabble in science, keep him on economics and sociology; don’t let him get away from that invaluable ‘real life’. But the best of all is to let him read no science but to give him a grand general idea that he knows it all and that everything he happens to have picked up in casual talk and reading is ‘the results of modern investigation.’ (Screwtape Letters, p.14.

To summarize: Lewis had difficulty with and disliked arithmetic and elementary algebra but loved the logical structure of geometry. He appreciated the beauty of mathematics and understood the nature of higher mathematics and its relation to reality. He had realistic doubts about technology and scientism or the belief that the perpetuation of our species was the highest value. He used mathematics and science to illustrate spiritual ideas. Also, he appreciated the value of the disciplines of mathematics and science. Remember that this paper does not show his extensive use of space dimensions in his fiction and in his Christian writings. Therefore, to say that Lewis was poor at mathematics and simply leave it at that is to fail to appreciate his highly creative literary use of higher mathematics and his use to illustrate Christian principles.

I would like to end this paper on a lighter note concerning Lewis’ understanding of mathematics education, even in the United States. In Mere Christianity, in the chapter “Is Christianity Hard or Easy” he wrote,

Teachers will tell you that the laziest boy in the class is the one who works hardest in the end. They mean this. If you give two boys, say, a proposition in geometry to do, the one who is prepared to take trouble will try to understand it. The lazy boy will try to learn it by heart because, for the moment, that needs less effort. But six months later, when they are preparing for an exam, that lazy boy is doing hours and hours of miserable drudgery over things the other boy understands, and positively enjoys, in a few minutes. Laziness means more work in the long run. (p. 197).

Then in a letter to one of his young American readers,
But beware of the Maths. master who over-marks the work. Generous marking is nice for the moment, but it can lead to disappointments when, later, one comes up against the real thing. American university teachers have told me that most of their freshmen come from schools where the standard was far too low and therefore think themselves far better than they really are. This means that they lose heart (and their tempers too) when told, as they have to be told, their real level. (C. S. Lewis: Letters to Children, p. 83-4.