# Chemiotics: Is math harder than organic chemistry?

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 friend 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.