Tag Archives: Leibniz



Love, love, love.

It’s too bad I feel like an absolute worthless bag of trash today. Leibniz day is a day to be happy.

BOOSH boosh BOOSH boosh BOOSH I’m gonna go cry for a little while.

Calculus is God

Today I had to go invigilate a MATH 277 final as part of my TA requirements (we each have to invigilate/proctor two final exams; sometimes we get ones we’ve actually been TAs for and sometimes we don’t. This was a case of the latter). It turns out that MATT 277 is University of Calgary’s version of MATH 275, or multivariate calculus. The test involved about 20 or so questions.

Our job as TAs, apart from making everybody sign in on the little attendance sheet, was mainly to just walk around in order to discourage cheating and to help anybody out who raised their hand.

So let me just quickly set the scene for you: a large gym full of 250+ students, a 2-hour exam, and lots and lots of calculus.

I bet you can guess what I was thinking about.

I was thinking about Leibniz!

I was wondering, as I walked down the aisles of seats, watching students write the elongated “s” for integration and the dx/dy (or variations of that) for differentiation, what Leibniz would think if he saw a roomful of people, in 2016, still using some of his original symbols. Like, how ridiculous is that? Calculus has been studied, expanded upon, and extended to a ton of different fields/uses since it was first developed, but we’re still using some of Leibniz’ original symbols.

And what would he think about calculus being taught as basically standard curriculum at universities? What would he think about the tons of different uses of calculus today?

I know I kind of talked about this in a previous post, but I actually think about this quite a bit. Especially today.

Yay calculus! Yay Leibniz!

Which Philosopher would Fare Best in a Present-Day University?

Who do they pick?


Man, I’d get a study group together right away. And by “study group” I mean “just Leibniz and me, somewhere quiet where he can do his genius stuff and I can guard him ‘cause he’s precious.”

I can’t help it, I’m obsessive. Seriously, if I was ever given the option to, say, time travel back to any year (and location) of my choice, I would with zero hesitation pick something involving Leibniz.

Witness the signing of the Declaration of Independence?


See man first create fire?


Observe the dinosaurs?



Leibniz vs. 2015

On occasion (read: every day), I find myself wondering what Leibniz would think of our modern world nowadays. Like, if we were somehow to manage to bring him back to life at age 40 or so and got someone (read: me) to show him around and calm him down when all the new stuff freaked him out, I wonder what he would really think of things.

  • What would he think of modern calculators? His Stepped Reckoner weighed like 80 pounds and could only add, subtract, multiply, and divide. I can buy a palm-sized calculator from the dollar store that can compute any given square root in about the time it takes to blink. And what would he do with a graphing calculator?
  • On the larger scale, what would he think of computers? He may have not come up with the original idea for binary, but he certainly refined it enough so that it could be easy to understand and use. Would he be surprised at how far we’ve come technology-wise just based on binary, or would that be something he may have anticipated?
  • And what would he think about technology in general? Like, I’m sure if we just recreated 40-year-old Leibniz and dropped him into the modern world, he’d likely be VERY freaked out, but barring that—say we were able to calm him down and explain things to him—what would he think of our technology now? I’d bet he’d want to deconstruct EVERYTHING to see how it all works, and it wouldn’t surprise me if he just came up with a few improvements off the top of his head. ‘Cause, you know, Leibniz.
  • How would he feel about the fact that now, in 2015, we still use several of his original symbols in calculus? If I were to show him a college calculus textbook, flip to the first section on integration, and point to his elongated “s” symbol, what would his reaction be? Would he think the textbook was from some previous century? Would he realize that the time he spent thoughtfully considering appropriate and intuitive symbols to describe math was not wasted? I wonder if he’d approve or disapprove of the modern calculus textbook in general.
  • WHAT WOULD HE THINK ABOUT GLASSES? The poor guy was ridiculously near-sighted by the time he was about 20. Reading and writing must have been quite difficult for him. A good pair of specs would allow him to see clearly, both near and far. I wonder what his reaction to that would be.
  • What would he think about his Wikipedia page, or any other brief history of his life/accomplishments? Would he feel proud seeing the long list of accomplishments that he’d achieved during his life? Would he wish he’d had more time to do more things? (Probably.) I wonder if he’d be happy with how people see him nowadays and/or how they interpret his philosophical contributions and his general view of the world.

Interesting things to think about. I also like the idea of him impulsively shunning the fashion of his day in favor of some outfit he saw at H&M or something. He’d go running through the store towards it, shedding clothes and knocking over all the displays along the way.

Everyone else: Leibniz, no!
Me: Leibniz, yes.



You know what the only downside is to LeibnizFest?* Reading the last chapter of that Antognazza biography.

Man, is it sad.

Leibniz did not have a very good time at the end of his life. “Leibniz’s last years were marred by frustration and loneliness,” is the first sentence of that last chapter, and unfortunately it is a very fitting first sentence. First, he’d outlived almost everyone he’d ever communicated with (most of them died in the 1690’s; Leibniz lived until 1716) and thus had very few people to communicate with. Second, he was still trying to recover his reputation after the whole calculus debate with Newton (and actually, I shouldn’t say “after” yet because Newton and his cronies (mostly his cronies) dragged that thing out well past Leibniz’ death). Third, he wanted desperately to keep traveling, but injury, poor health, and prior obligations basically forced him to stay put for a good several years. A quote of his from the bio: “I am shut in my room working and I hardly ever leave it.” This is coming from a man who took on innumerable projects just so that he’d have the excuse to travel and converse with people of different backgrounds and skills, so it’s super sad. And then, of course, there’s the fact that he basically died alone and was given very little recognition for his accomplishments until well after his death.

It’s heartbreaking to me to hear all the crappy things that happened to him in the last five or so years of his life. Someone with such a great mind, such compassion, and such good spirit deserved something better at the end.


To end LeibnizFest on a lighter note, have a look at this Leibniz-centric website that has pretty much everything you could ever want on the amazing polymath. I have it bookmarked. I visit it a few times a week.

It’s a healthy obsession.



*I’m totally calling mid-June to mid-July LeibnizFest now; it’s gone beyond just celebrating on his birthday, let’s be honest.



Awwwwww yeeeeeeeeeeeeah.

Yes, I’m going to read this every June/July until I die.
No, I don’t think that’s a sign of an unhealthy obsession.

Also, I posted this awhile back, but I’m going to post it again because it’s a really good discussion of a good amount of Leibniz’ philosophical viewpoints.


This is by far the best thing I’ve ever found on Tumblr (source).

How to draw Leibniz:


Math Man!

Guess whose birthday* it is today?

Hint 1: He was a Swiss mathematician born in 1667
Hint 2: He tutored l’Hopital in mathematics
Hint 3: Most of his family members were mathematicians as well

Give up?


So why is he awesome?

Not only did he tutor l’Hopital—which eventually led to l’Hopital publishing the first formal book on calculus**–but he also tutored Euler when Euler was young. In fact, he was the one who convinced Euler’s father that he had the makings of a great mathematician, thus steering him away from a life of a pastor.

For a majority of his life, he was in a highly competitive relationship with his equally mathematically talented brother, Jakob. When his brother died of tuberculosis, Bernoulli’s jealousy actually shifted to his son (another mathematician!) and they had a few good disputes about who came up with what papers and ideas.

One super awesome thing about Bernoulli, though, was that he was one of the few who stayed on Leibniz’ side of the whole calculus dispute with Newton. He showed his support by demonstrating several problems that could be solved using Leibniz’ methods, but not Newton’s. Go Bernoulli!



*He was born on July 27th by old style dates; by new style, he was born on August 6th.
**The book was basically all of Bernoulli’s teachings written up formally, which ticked Bernoulli off quite a bit even though l’Hopital mentioned him in the book.

Guess what day it is!!

Yaaaaaaaaay, best day of the year!

Today is Gottfried Leibniz’ 348th birthday, yo.

As I mentioned a week or so ago, I’m re-reading this fantastic bio of him ‘cause it’s important. I know I do this a lot, but let me reiterate just one huge reason why this man is so damn awesome, since it IS his birthday, after all:

Leibniz’ formal schooling was severely lacking any rigorous mathematical training. It focused mainly on Latin, theology, and philosophy. However, due to (among other things) having access to his father’s extensive library, Leibniz developed a curiosity toward mathematics and taught himself quite a bit. However, he was still lacking a lot of knowledge once he got out of school. Here’s an excerpt from the bio regarding his visit to Paris, which was practically the center of all things intellectual in the European continent at the time:

“[In Paris] Leibniz was made painfully aware of the limitations of his mathematical preparation and of his lack of up-to-date knowledge of work in the field; and this soon led to the further realization that, in order to carry his plans forward, he would first need to forge himself new tools. … Thankfully, Leibniz was nothing if not a quick learner: by the end of his Parisian sojourn, in fact, the self-confessed mathematical apprentice had invented the infinitesimal calculus.”

So it took him approximately TEN FREAKING YEARS to go from practically a math novice to inventor of calculus.

That’s so freaking ridiculous.

Happy birthday, Leibniz, you amazing dude. <3



I’ve decided on my tattoo. Behold!



Why an integral sign?

  1. If you know anything about me at all, you know that I love Leibniz. What better way to pay tribute to him in tattoo form than to get a tattoo of his symbol for integration? So it works on the level of Leibniz tribute.
  2. It also works on the level of my liking stats—after all, integration is used quite a bit in many statistical applications/techniques. And since that is the case, it saves me from having to pick a specific statistical formula or expression (which I could never do; I love them all!).
  3. I also just really like this symbol. I thought it was very elegant even before I knew that Leibniz came up with it.

It really does have a lot more meaning to me than I can express here, but I tried, haha. I think I’m going to try and plan it so that I get it done (or mostly done) on July 1st this summer.

‘Cause yeah.







*goes to hyperventilate in the corner*

The New Science


From the site:

“In The New Science, you play the role of one of the great scientists from the scientific revolution in 17th century Europe. You are attempting to publish your remarkable scientific discoveries in order to gain prestige, be seen as the finest mind of your era, and consequently be appointed the first President of the Royal Society.”

And which great scientists can you play as?


This looks really, really interesting. I need this game, yo.

(And a dorkfest of friends to play it with.)

The Six Degrees of Leibniz

I submit that on Wikipedia, you can get from the page of any mathematician to Leibniz’ page in 6 clicks or less (even without clicking through the “Mathematician” or “Mathematics” links that show up in like the first sentence of every mathematician’s Wiki page).

Fun Examples for Fun

Starting mathematician: George Polya
Click 1: Probability Theory
Click 2: Probability
Click 3: Christiaan Huygens
Click 4: Gottfried Leibniz

Starting mathematician: George Boole
Click 1: Differential Equation
Click 2: Derivative
Click 3: Gottfried Leibniz

Starting mathematician: John Venn
Click 1: Set Theory
Click 2: Principia Mathematica
Click 3: Philosophiæ Naturalis Principia Mathematica
Click 4: Gottfried Leibniz

Starting mathematician: Sewall Wright
Click 1: Philosophy
Click 2: Gottfried Leibniz

Starting mathematician: Henri Poincaré
Click 1: Bernhard Riemann
Click 2: Riemann Integral
Click 3: Integral
Click 4: Gottfried Leibniz

Public Service Announcement

A friendly reminder that this man existed and that he was glorious:

Leibniz (2)

You know, in case you forgot.



I’m buying this for myself for Christmas because LEIBNIZ DOLL.


[throws credit card at monitor]

Today is a Blah Factory

Today is the 297th anniversary of Leibniz’ death.

Fittingly, I have had a crap day and don’t feel much like talking.






Edit 2: BINARY!!!!!

Haha, thanks, Google.


Yes. Yes I have.
No shame.

Anyway, completely changing topics…

I mention Achievement Hunter quite a bit on here. There are a few reasons for this.

  1. Listening to them game is like living in the house with the guys again. It’s hilarious.
  2. This sounds super dorky, but they kept me company over the summer. I didn’t have any friends around and they put out YouTube videos at least 5 times a week, so…that was that.
  3. They’re one of the funniest YouTube channels out there, in my opinion. Grown men cussing each other out playing video games is fantastic.

Since starting doing Let’s Plays of Minecraft back in 2012, they’ve done 65 half-hour (or longer) episodes, many featuring the Tower of Pimps.

Well check out the latest Minecraft update:

Pretty cool! Congrats, guys. And seriously, check them out (if excessive cursing doesn’t bother you, haha).

This One is Tumblr’s Fault, I Swear

Someone I follow posted this awesome link to Newton’s notebooks stored in the Cambridge Digital Library (link link link!).

Now that I’ve got access to both Newton’s notes and Leibniz’ notes (thanks to checking out Dr. Wolfram’s awesome post on Leibniz’ archives), you can probably guess how freaking excited I am.

So. Graphology in itself is pretty much pseudoscience, but it’s still interesting to compare the writing styles of these two geniuses, just to see if any similarities/differences stand out. That’s allowed, right? (Screw it, I’m doing it anyway.)

A lot of Newton’s notes were written in English ‘cause…duh…he was an Englishman. From what I’ve read about Leibniz, I think he could read and write in English but not nearly as fluently as in several other languages; most of his work was in Latin, the rest in French and German. So I couldn’t find a good English excerpt from both. So let’s do Latin, just for the sake of keeping the language consistent.

Here’s a Newton page:


Look at his writing, it’s so neat! I’m no handwriting analyst or anything like that, but it looks like this section of Newton’s notes was written slowly and deliberately as if he’s just sitting there going, “yeah, I got this.” There are a few things crossed out, of course, but it looks like he took the time to carefully scratch them out and then just kept going. Slow but steady. And his numbers are so clear, too, holy crap.

The above is just a screenshot of a semi-magnified page; on the actual Cambridge site you can zoom in further and make out the English notes he made in the margin. If you look at a lot of other pages in this section of notes, Newton really seems to keep things very organized, even if it looks like he’s making scratch calculations in some parts.

And then there’s Leibniz:


I was planning to do both samples in Latin like I just said above, but I’m snatching pictures of Leibniz’ notes from Dr. Wolfram’s post on him so there aren’t nearly as many choices as with Newton. So I figured a more appropriate comparison would be pages written by both men that contained both words and numbers. I believe Leibniz’ page is written in French, but I seriously can only make out like three words here.

I’m not sure if it’s just because of different writing tools or different ink/paper, but Leibniz looks like he pressed fairly hard (or at least as hard as you could with a quill). Also, in contrast to Newton, it looks to me like Leibniz wrote pretty rapidly. Newton’s corrections were either neat single cross-outs or carefully scribbled out so the mistake couldn’t be read. All of Leibniz’ corrections look like, “no time for error must keep writing!” *scratchscratchscratch* “ONWARD!” Even his numbers look rushed (look, it’s binary!). It almost looks like he used this page for just those calculations but then wrote around them, continuing from a previous page.

On some of the other pages Leibniz really manages to get a lot on a single page. We’re talking ITTY BITTY scrawl, a consequence of his becoming very near-sided in his 20s and it only getting worse as he got older. I’m actually not sure how good (or bad) Newton’s vision was. Of course he did stick a darning needle back behind his eye and wiggled it around (optics experiment), so…

Anyway. Just an interesting thing to see the differences/similarities in their styles.

Holy Crapples

Oh my god.

There’s an article on Leibniz on Uncyclopedia.

The whole thing is a Leibniz/Newton slashfest.

  • “He was born with extremely long and poofy hair, which he wore to bed every night and named ‘Poof.'”
  • “The mathematician Isaac Newton fell in love with Leibniz when he discovered this divine hair, nicknaming him ‘Gotthair.'”
  • “He enjoyed sex, tapdancing, walking his headdress, keeping frogs in his pocket, drinking, and keeping frogs in his headdress.”
  • “Newton fell desperately in love with Leibniz, and ferociously stalked him. Leibniz, however, was not interested in Newton’s inferior and less poofy hair.”
  • “Leibniz’s troubles of giving us this divine truth was due to the threat of Netwon’s sex drive. Leibniz was never able to sit down long enough to write more than a couple of pages before Newton found him again.”
  • “Leibniz and Poof relentlessly attempted to avoid Newton’s calculus seduction, which began the series of violent battles known as the Calculus Wars.”
  • “It has been theorized that Leibniz’s unique ability to rise from the dead is attributable to Poof’s power level being over 9,000!”