Field of Science

Woodward on the difference between mathematics and chemistry

When I was studying organic chemistry in college, my uncle who was a pharmacist and who had studied the subject himself used to say that "organic chemistry is just like mathematics, only simpler". There was more than a shred of truth in this statement. The logic inherent in the theorems of math is mirrored in the precise logic of reactivity and structure in organic chemistry. At one point in college my interests deviated toward physics and math.

But I wisely realized the allure of chemistry, not only because I thought my abilities were more suited for this discipline but because chemistry presented some special features; for instance, while logic may apply in both math and chemistry, in chemistry you could find exceptions (as James has nicely documented) and the whole concept of absolute 'truth' was much more provisional. At the same time there were models of great predictive power and elegance, such as the Woodward-Hoffmann rules. This strange mix of rigor and empiricism inherent in chemistry really captivated me. Mathematicians may be drawn to the rock-solid certainty of mathematical truths, but for me, the more complex nature of chemical reality made it seem much more human.

Yesterday I was reading R B Woodward's fabulous Cope Lecture in which he documents his interest and growth in chemistry. Woodward was such an extraordinary intellect that he could have probably had an outstanding career in any discipline. In fact he says that he was tempted by mathematics at one point but then recognized the unique nature of chemistry. He gives two reasons which I think do as fine a job of capturing the essence and allure of chemistry as any other. The first reason would probably be appreciated by all of us who were drawn to the subject. The second reason sums up the nature of science itself, what Richard Feynman called "imagination in a straitjacket". In chemistry, ideas have to answer to reality.

Here's the master speaking (the italics and capitals are his):
"The fact is that I have always been very fond of mathematics- for one short period, I even toyed with the possibility of abandoning chemistry in its favour. I enjoyed immensely both its conceptual and formal beauties, and the precision and elegance of its relationships and transformations. Why then did I not succumb to its charms? For two reasons, I believe:

FIRST, because by and large, mathematics lacks the sensuous elements which play so large a role in my attraction to chemistry. I love crystals, the beauty of their form- and their formation; liquids, dormant, distilling, sloshing!; the fumes; the odors- good and bad; the rainbow of colours; the gleaming vessels, of every size, shape and purpose. Much as I might think about chemistry, it would not exist for me without these physical, visual, tangible, sensuous things.

SECOND, while in mathematics, presumably one's imagination may run riot without limit, in chemistry, one's ideas, however beautiful, logical, elegant, imaginative they may be in their own right, are simply without value unless they are actually applicable to the one physical environment we have- in short, they are only good if they work! I personally very much enjoy the very special challenge which this physical restraint on fantasy presents"
To which we can only say, "Amen!".


  1. Great post! Thanks.

  2. while logic may apply in both math and chemistry, in chemistry you could find exceptions (as James has nicely documented)

    The examples posted by James are not "exceptions" to the rule, they illustrate the the "rule" is not as simple as one would like. While these may be annoying to the undergraduate who is having trouble memorizing reactivity patterns, they illustrate the need for complete understanding.

  3. True, that was just an analogy. The point was that 'truth' is murkier, which also makes the whole thing more interesting. A better exception may be to the statement that "alkali metals form positive ions" or "electron withdrawing groups direct meta substitution".


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