Never Forget the Fundamentals

If you have an advanced degree on whatever, it’s sometimes very easy to get cocky and think that the basic knowledge of your area is beneath you. That you have already learned it and that if you ever have to face a problem that involves any of that knowledge, you got it. Because indeed, it’s most likely true, you have learned it and you may not remember all the specifics of it but if you go an look quickly at a book or do a web search everything will magically come back to you.

However, what if you have not book at your disposal? What if suddenly the internet goes down globally? What if I, an PhD student in probability, am in a plane and suddenly a flight attendant screams

• Flight attendant: IS THERE A PROBABILIST ON BOARD?
• Me: I am a probabilist…
• FA: WE HAVE A BAYESIAN EMERGENCY! We need you to solve the following question otherwise the plane will go down!
• Me: Oh no, I do more like SDEs and stuff like that, actually I don’t remember Bayes’ theorem all that well, if somebody has a probability book I am happy to take a look and get cracking though…
• FA: …
• Everyone else: …
• Me: So, no book? Well I tried (sits and accepts everyone’s demise)

Of course, I would be deathly embarrassed by that. But I will soon probably die, so I will get over it.

Naturally the plane crash scenario won’t happen…probably. But it could be that your 14-year-old cousin needs help understanding how to use trigonometric identities for the sum of angles, or that you