Caffeine: The Frenemy of Mathematicians
By Alexis Newton
Alexis Newton
As a mathematician, I have a love-hate relationship with coffee — which is to say, caffeine — of longstanding.
The baristas at my habitual Starbucks knew me so well as an undergraduate that they would see me in line and start my order: a grande vanilla sweet cream cold brew.
Now, as a wayward grad student, coffee is my constant companion. It keeps me up to get my homework done (or, more difficult, to stay awake while grading). It fuels the binge-watching of Netflix that follows. It gets my heart pumping at whatever desperate soulless hour I have to get up for class in the morning, and it provides the final ergs of energy to get through that exam.
We won’t even talk about how many marathon cross-country trips, aided by long conversations with friends and my cat complaining from his carrier, that the caffeine in bad drive-through coffee has kept me awake, and alive.
Mathematician Alfred Renyi was quoted as saying that “a mathematician is a machine for turning coffee into theorems.” The quote is often attributed to Renyi’s contemporary. Paul Erdős, who supposedly “had trouble doing mathematics without [coffee], claiming that his mathematical notes became blank pieces of paper that he just stared at, unable to work.”
So, when you indulge in your coffee habit, feel reassured that you are channeling the mathematical greats, and probably on the verge of some world-shaking discovery.
The most important thing I can tell you about caffeine, and your relationship to it, is that for best effect you really don’t want to know how humanity’s miracle drug of choice actually works.
Caffeine, you see, is an adenosine receptor antagonist. Adenosine is what your body starts producing in small amounts just as soon as you wake up. Your adenosine levels — gauged by those adenosine A2A receptors — build slowly throughout the day, and as they do, so does your feeling of fatigue.
That huge Starbucks mug doesn’t stop you from being fatigued, it stops you from feeling fatigued, and therefore you seem sharper and more alert than you otherwise would have.
There are two prices to pay for this miracle. The first is that caffeine does not make all that adenosine go away — it just keeps your body from registering most of it. So when the caffeine wears off — BAM! — the fatigue rushes back in something just attacked your eyelids with a ten-pound weight, pulling them down and shut. More coffee can’t affect the adenosine you’ve already processed, but it can dam the flood … but only a little, and not as effectively as before.
This is the post-caffeine slump.
This is what happens when the caffeine not only wears off, but you’ve reached the point where consuming more coffee only makes you into a more wired, extremely tired person.
Speaking of caffeine wearing off, that’s problem number two.
The average cup of coffee contains about 95 mg of caffeine, but the double-shot Espresso that so many of us favor packs nearly twice that punch (185 mg). And coffee has a half-life in your system of six hours.
So, if you down that double-shot espresso at noon, like I often do, you will still have roughly the equivalent of a regular cup of coffee in your system at 6:00 pm.
More to the point, you will still have what amounts to half a cup of coffee (or, almost as much as a 20-oz. Coke) in your body at midnight.
Which is probably why I watch so many TikToks into the morning hours when I am too dull to keep doing math and too wired to get to sleep.
Note that in this example you only had ONE theoretical cup of coffee all day. I hope that’s more true for you than it is for me.
The good news is that you could kick the caffeine habit. It would take about two weeks, involve some headaches (probably complicated by feelings of homicidal rage), and play hell with what you’ve come to believe are normal sleep patterns.
The bad news is that all of your friends would begin looking at you really funny when you kept ordering herbal tea, and they’d seem to be jerky and talking faster (maybe it would sound like they’d been inhaling helium) as your body slows down to what foolish doctors believe is normal human operation.
Or so I’ve been told. I don’t know for sure because I’ve never even contemplated quitting.
It’s been at least a decade, you see, and while I’m not necessarily any closer to duplicating Erdős’s body of work, it seems too early to give up trying.
Alexis Newton is a third-year Ph.D. student at Emory University studying computational number theory. Outside of the math department, Alexis enjoys reading, writing, and playing with her cat Alfie.