Physicists and mathematicians have their own notions of 'elegance'. These notions are often tied to mathematical beauty. Paul Dirac was famous for insisting that equations be beautiful. His own Dirac equation is a singular example of beauty; it can literally be written in half a line and yet completely explains the behavior of the electron, taking special relativity into account and predicting antimatter.
Chemistry is much more of an experimental science than physics, so does that mean that notions of elegance would be meaningless in chemistry? Not so at all, although chemists need their own definitions.
Organic synthesis, which is as close to architecture that a science can get, has defined elegance for a long time. Organic chemists will tell you that a complex synthesis is elegant when it can be accomplished in only a few steps, with maximum purity, yield and stereoselectivity, using the most benign reagents under the mildest of conditions. The Nobel laureate John Cornforth said it well: he defined the perfect synthesis as one which could be done by a one-armed operator by pouring down a mixture of chemicals down a drain and collecting the product in one hundred percent yield and stereoselectivity at the other end. Biomimetic reactions particularly lend themselves to definitions of elegance. In such reactions you can usually get a truly elegant cascade of bond formation and breaking that installs several stereochemical centers in one or a few steps. Robert Robinson's synthesis of atropine is a classic example. So is William Johnson's synthesis of progesterone through a stunning biomimetic cascade. I remember both these examples leaving me cold as an undergraduate.
Other kinds of chemists dealing with synthesis would have similar definitions of elegance. But in the age of supramolecular chemistry, elegance is being defined another way, through self-assembly. Traditional organic synthesis deals with the stepwise construction of complex molecules. In much of solid-state and structural chemistry though, simple building blocks self-assemble into some of the most complex chemical architectures and nanomaterials merely by mixing reagents together. A great example concerns the beautiful structures resulting from simply mixing sodium oxalate and calcium chloride under hydrothermal conditions. Solid-state and supramolecular chemists are harkening back to the old days of chemistry, when you got interesting results just by combining simple chemicals together in different proportions.
Whereas an organic chemist would define elegance in the context of yield, stereoselectivity and mild conditions, that definition would not be of much use to a biochemist studying enzymes, since it's child's play for virtually all enzymes to accomplish this goal every single moment of their existence. Carbonic anhydrase, nitrogenase and peroxidase are only three examples of enzymes that nonchalantly go about their business at room temperature with a devastating efficiency that would put an organic chemist to shame. For biochemists, this kind of elegance is passé. Or it's an everyday miracle, depending on how you look at it. For biochemists, signal transduction cascades in which the binding of a single molecule causes a shower of precise protein-binding events involving dozens of biomolecules that usually culminates in genetic expression must seem like a true miracle. The binding of adrenaline to the beta-adrenergic receptor and the ensuing perfectly choreographed symphony of biomolecular music must surely seem elegant.
In other areas of chemistry elegance may be trickier to define. In theoretical chemistry you can use quantum mechanics to describe a chemical system. Given a relatively simple system, it's possible to describe it extremely accurately using high-level basis sets and theory. You can get answers accurate to a dozen decimal places using such techniques. Indeed, in principle, quantum mechanics can describe all of chemistry.
Is it elegant? A first thought may be that it is, since you are using the most fundamental theory available in nature for achieving an unprecedented degree of accuracy. But consider that you can usually get the same result accurate to a lesser number of decimal places (but still quite accurately) using a judiciously parametrized force field. A force field is simply a set of terms describing bond stretching, bending, torsional angles and Van der Waals and electrostatic forces, thrown in with a set of parameters drawn usually from experiment. Given a choice between reams of complex math and days of computer time, and minutes of computer time and a bleedingly simple molecular mechanics equation that you can write on the back of a cocktail napkin (try this out on a girl or boy the next time you are at a party; they will be very impressed), which one would you say is more elegant? Granted, the latter is parametrized with experimental measurements and is not as accurate as the former, but it's still good enough. More importantly, if simplicity is one of the important hallmarks of elegance, then the latter approach is surely more elegant, isn't it?
Ultimately, what matters so much is not elegance but the ability to discover new things. The one thing that sets chemistry apart is its ability to make new stuff that did not exist before. If chemists can find techniques that accomplish this goal more efficiently, they can be forgiven for not thinking too much about elegance.
After all, it was a famous physicist himself who once said, "Matters of elegance should be left to the cobbler and tailor...".
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