Wavefunction’s crack on the last post “As my uncle (a pharmacist) once put it, “Organic chemistry is just like math…only simpler” prompts me (along with being too lazy to write about positive and negative allosteric modifiers after the long weekend) to put up the following post, which I wrote (under the nom de plume Retread) for “The Skeptical Chymist” 30 months ago (time flies).

The Scandinavian Goddess I had a crush on all through high school could pick up any instrument and play it — piano, clarinet, guitar, saxophone, etc… She didn’t think it was a big deal, it was just the way she was. The Hungarian uprising of ’56 occurred while I was a freshman in college. A classmate, who already knew 12 or so languages, picked up Hungarian in a week or two and went up to Camp Kilmer in New Jersey to act as a translator for the refugees. It was just something he could do. 50+ years later, the 16 year old high school student auditing an upper level college course in abstract algebra I was taking looked up occasionally from his German homework when the lecturer made an obscure point. He blitzed the course and later went on to college.

I don’t think there is anything remotely like that in organic chemistry, although the rumor back then was that Woodward knew all of Beilstein before he hit puberty. Learning organic chemistry always seemed pretty easy and intuitive to me (even now when revisiting it years later). Perhaps it was playing with TinkerToys as a kid. I’ve found math much, much harder.

In organic chemistry you come to know carbon inside out and at least one atom of it is always present, so you can bring everything you already know (which is quite a bit) to the problem at hand. Math isn’t like that at all. You are always bumping up against new definitions, concepts and theorems. Once you get past the plug and chug part of math (use the chain rule n times, integrate by parts m times to find an integral, look for a recursion formula by repeatedly differentiating) you are proving theorems. Here, you must bring everything you know about math to proving the theorem or problem at hand. You may have to create a function, a group, an ideal to solve it, reason by contradiction, think of a counterexample etc., etc…

Is anything like that in organic chemistry? Of course there is. The theorems of organic chemistry are its syntheses. Every reaction you ever heard of comes into play, new ones must be invented, mechanistic pitfalls considered, conditions carefully adjusted etc., etc… You are not asked to synthesize strychnine as a college junior but you start proving theorems in math at that point and never stop. That’s why math is harder (to learn).

So math is harder to learn, but organic chemistry and math are equally hard to do. If we really understood mechanism and reactivity, we could just write out the steps and have a robot perform them. We don’t because our knowledge is very incomplete. In this sense, organic synthesis is actually harder than math, because in math you are starting with a huge background of solidly proven results which are at your disposal. In chemistry you have a similarly huge background, but there is no guarantee that any of it will work on your particular problem. It’s your job to figure out why something which should have worked didn’t do so and a way around it as well. That’s not easy at all.

## Comments

“So math is harder to learn, but organic chemistry and math are equally hard to do”

This is a very good point. The big difference between math and organic chemistry is that in the latter you have to make things work on paper (relatively easy) as well as in practice (hard). In the former you just have to make things work on paper, which is usually hard. Thus, an intelligent student with a general scientific background can understand a graduate level textbook on organometallic chemistry fairly easily, but not a graduate level topology textbook. However, in the former case understanding what’s in the textbook is only the beginning. As you mentioned, in math you get to the hard things pretty soon but in organic chemistry you have to wait till you actually practice them when they get hard.

This also raises the interesting question of why great physicists and mathematicians are usually considered to be smarter than great chemists and biologists by the public. I think the public certainly thinks of physics and math as being the hardest disciplines, and the best practitioners among physicists and mathematicians like Feynman, Einstein, von Neumann etc. have this romanticism attached to them. No such romanticism attaches to Watson, Woodward (assuming people have heard of him) or even Pauling. The very part of chemistry and biology (the actual doing) that is the hard part also fails to impress the public easily. It’s a little sad.

If math is digital, chemistry is analog. Students get taught that, say, low temperature favors the SN2 and higher temperatures favor the E2. One of the hard things to get used to for students dealing with math and physics is that the product ratios aren’t 100/0 and 0/100 at 20 and 80°C; real world situations would be more like 90/10 and 20/80 (or 60/40), as the rate constant for elimination starts increasing. With teaching, I get allergic to using the word “always”, except perhaps in the sentence “there are always exceptions”.

I agree that getting it to work in practice can be hard. One thing I see, particularly with non-organic grad students forced to do synthesis for making ligands or whatever is a lack of intuition about how having multiple unprotected functional groups in your molecule rapidly leads to difficulties with increased reaction complexity. Prayer and hope often isn’t enough to get your acylating agent to selectively go after just one of the amines in your unsymmetrical molecule (despite pleadings of “but I’ll only use one equivalent!”, but there’s a steep learning curve in appreciating that. Hell, I see profs who don’t appreciate that.

As they say, “any science with more than 7 variables is an art”