If you go to a basketball game, it may take you a few minutes to understand the rules, but pretty quickly you will figure out what’s happening. Sure, there might be niche rules here and there that leave you baffled, but you can still follow along. Furthermore, you don’t have to be an expert at basketball in order to enjoy watching others play.
Unfortunately, this isn’t the view people take of mathematics and science. Often, we implicitly assume that we need years and years of school before we can actually make sense of what’s happening. This is particularly true while looking at a proof. Compact notation coupled with strange symbols can leave the whole enterprise of mathematics and science feeling foreign and indecipherable.
As you might imagine, I find this unfortunate. Not because I think everyone should be required to love mathematics and science, but because we get too caught up in having the necessary background to understand a subject. If you go to that basketball game and you have no prior experience with the sport, you can still have a great time even if you don’t understand everything. You might have no idea what happened during certain parts, but overall the experience was positive. Likewise, I think the same can happen with mathematics and science. The crucial point is to not set your expectations too high. If you’re the one crafting an explanation, don’t expect the person to understand everything. Instead, focus on the aspects that they can connect with, even if that isn’t the whole picture.
Notice here that I’m not saying you should mislead them. If they aren’t getting the whole story, tell them that. Make it clear that there’s more to learn. However, I think it’s sad that instead of engaging in this difficult work, we (including myself) retreat to our familiar details that are too difficult for someone with a passing interest to absorb.
My goal is to communicate ideas to others about science and mathematics. If I can’t give the “full” explanation, I need to take it upon myself to offer enough of an interesting explanation that they come for more. Having the necessary background is ideal, but it shouldn’t prevent us from giving explanations to those without the background. It might not be the whole story, but the point is to get them started on a journey of discovery that they will want to continue.
Remember, not everyone is an expert at basketball, and yet millions of people will watch and play. I hope we can find a similar level of engagement in science and mathematics.