Yo, this is super interesting. Infinities!!
Today we had our second test in Complex Variables. The test involved figuring out quite a few Maclaurin series for functions involving i. I’ve been ridiculously busy and thus haven’t had a chance to check out the dude behind the Maclaurin series…until now!
So. A Maclaurin series is simply a Taylor series centered at zero. According to the almighty Wikipedia, this type of series is named after Colin Maclaurin, a Scottish mathematician that lived from 1698 – 1746 (so during Leibniz/Newton time and a little bit after). The reason centered-at-zero Taylor series are named after him is because he used them extensively in his Treatise of Fluxions when describing and characterizing points of inflection, minima, and maxima of smooth functions.
This dude was super smart. He entered college at 11 YEARS OLD and got a Masters degree three years later. He became a professor at age 19 and actually got a personal recommendation from Newton to be appointed deputy to James Gregory, the mathematics prof at Edinburgh, and then once he surpassed Gregory’s position, Newton was so impressed that he actually offered to pay his salary for him.
He also had a crapton of children (well, 7 children, which I guess probably wasn’t a crapton back then) and died of complications from edema.
We started Taylor series proper today, and it’s like the seventh section in a row we’ve spent on series. When our teacher wrote “Taylor Series” on the overhead some guy said, “god, when are the series going to end?”
And without thinking I said, “Never, they’re infinite!” And my teacher looked at me like, “You did not just make that joke.”
Made my day.
Also, happy birthday to Karl Pearson!