In just a few minutes Section 1 of my Calc I class will begin their re-enactment of the controversy between Isaac Newton and Gottfried Wilhelm Leibniz, and for the first time ever I will bring it to you "live"! (Compare the last iteration of the trial, in which I merely provided a transcript after the fact.)

9:33: Leibniz's lead attorney begins with an opening statement: "Our defendant deserves credit for calculus's development. Newton's statements contain inconsistencies, and he was okay with Leibniz's credit until Leibniz started to gain credit for the discoveries. Moreover, Leibniz's students and colleagues made great strides in furthering mathematics, directly from the work of Liebniz. We challenge Newton's team to present discoveries coming from the work of Newton. We also question Newton's motives in charging Leibniz with plaigiarism."

9:36: Jakob Bernoulli is called to the stand. "We understand that you are familiar with my client, Mr. Leibniz."

"Mr. Leibniz and I have worked side-by-side on this process."

"Can you elaborate on the personal character of my client?"

"He's very friendly, very trustworthy. We've never had any difficulties."

"Can you tell me about any of the other mathematicians you were familiar with at the time?"

"My brother, for one."

"Was it common for you to meet up and share papers, that this was normal and not particular to Leibniz?"

"Yes, it was common."

There is no cross-examination.

9:39: Johann Bernoulli is called to the stand.

"Can you tell us about your relationship with our client?"

"I've worked very close with him and with my brother. We've been working on calculus problems together."

"Is he well-versed in calculus?"

"Yes, definitely."

"Anything else you'd like to add, toward his character?"

"There were problems we were able to work out that he was not able to work out on his own, and he's given us credit. Why would he not do the same with calculus?"

"What's this problem you presented to the Royal Society?"

"It was sent to different mathematicians, including Newton. The answers Newton submitted were different from those that my brother and I submitted. The methods we used came from Leibniz's work."

"So the methods you used, coming from Leibniz, were different from those coming from Newton's work?"

Cross-examination: "Our sources say that I [Newton] solved the problem asked that day, whereas he Bernoulli's solutions came later."

"That is true."

9:43: Ehrenfried Tschirnhaus is called to the stand.

"You met Newton, and later on that year you met Leibniz."

"That is true."

"Did you not share techniques you were familiar with to John Collins and others, and later, when you met Leibniz, he showed you some unpublished papers by Descartes, correct?"

"That may be, but we were both mostly concerned with ethics and other issues at that time."

"But it was common to share material at that time?"

No cross-examination at this time.

9:45: John Collins is called to the stand. "The letters Leibniz had given to you, did they fall into someone else's hands after your death?"

"I don't know."

"Who was the President of the Royal Society at the time the Epistolarum Commercium [sic]?"

"Oldenburg?"

"No, it was Newton. Do you think this may have led to bias?"

"Perhaps."

Cross-examination: "Is it true that you Isaac Barrow?"

"Yes."

"Can you point him out?"

"The man in the green."

"Did he not share Newton's papers with you?"

"Yes."

"Is it possible that Leibniz may have seen these papers?"

"Yes."

"No further questions."

9:50: A historical expert is called to the stand.

"Are you qualified to rule on the personality of one Nicolas Fatio de Duiller?"

"de Duiller knew Newton, and they had exchanged papers. Is there more that you'd like to know?"

"Did they have a personal relationship or a professional one?"

"It cross some borders."

"Can you read this letter from Newton to de Duiller, please?"

[An excerpt of a very personal letter is read.]

"Hmm. That's interesting. It seems this de Duiller may have been romantically involved with Newton?"

["Objection!" "Sustained."]

"Was de Duiller the first to charge Leibniz with plaigiarism?"

"Yes."

"Might his motive have been a personal one?"

"That is possible."

Cross-examination begins: "Where have you gotten your history from?"

"Books."

"Therefore we could assume that you are taking the work of others and 'regurgitating' it, that you are not doing any of the work yourself."

"Well, I've read it all."

"Can we assume, then, that this information is accurate? Were you there?"

["Objection! Was anyone in this room alive when this all took place?"]

"No further questions."

9:57: Leibniz is called to the stand.

"Were you interested in math originally?"

"Not originally."

"It was only after you met Henry Oldenburg that you became interested in math."

"Yes."

"Was it common for you all to meet and have conversations?"

"Yes."

"Was there any secretive exchange? Was there anything going on behind the scenes?"

"No, it was all very open."

"Ideas were discussed in the open?"

"Yes."

"And you saw Newton's letters, right?"

"I saw the letters, but I couldn't understand his notation, so I could get anything from it."

"So you couldn't learn anything from it?"

"No, not really."

Cross-examination begins.

"It's nice to meet you, after hearing so much about you. Have you published any works of your own, before this controversy?"

"Yes, the Acta Eruditorium was published in 1684."

"Did this work contain work on calculus?"

"It had my notation for derivatives in it."

"Was it before or after 1666?"

"It was after."

"And this is after you saw Newton's notes and after you talked to his colleagues?"

"Yes."

"Therefore you published this book after you had spoken with Newton's colleagues and after you had traveled to Britain, and after you had seen Newton's work?"

"That is true."

"No further questions."

10:03: The court recesses for five minutes.

10:10: Newton's attorney makes her opening argument: "Though Leibniz developed notation for calculus, he did not in fact perform any of the work. Although he changed the notation and terminology around, he did not in fact discover any of it. We will show that the facts of the case bear this out."

10:11: John Collins is called to the stand.

"Mr. Collins: you knew Leibniz and Newton."

"I was good friends with both."

"Did you ever feel as though you had wronged Newton?"

"Yes. He didn't know about it until the day he died. But I had taken his work and distributed it, since he was so reluctant to publish it. I showed his work to Leibniz."

"No further questions."

Cross-examination begins.

"What were the contents of the letters you shared with Leibniz?"

"Newton's work."

"Calculus related, or did it concern more infinite series?"

"Is there anything more than your word to support your claim?"

"You have my word, as well as Barrow's and Oldenburg's."

"Other mathematicians saw Newton's work too, though, right?"

"That is the case: I and Barrow saw them, but no one else is claiming that they invented calculus."

"But you are a mathematician, and could have discovered calculus having read those letters, right?"

"Yes, but I wouldn't do that to my friend."

"No further questions."

10:14: Isaac Barrow is called to the stand.

"Would you say that you are the sole person who was allowed to distribute Newton's papers to the outside world?"

"Well, I only shared his work because of his reluctance to publish himself. I shared it with Collins."

"Is it safe to assume that such intellectual news would travel quickly and would seen as a 'bright light' at the time?"

"This is true of Leibniz, as well, who was smart enough to understand Newton's work himself."

Cross-examination begins.

"You worked with tangents, right?"

"And geometric functions."

"Were you familiar with the work of Pierre de Fermat?"

"I don't remember."

"My sources show that you saw another's work and developed further upon it?"

"I don't remember."

"Did Newton himself not elaborate on others' work?"

"Well, Newton invented calculus from other works that were geometric and algebraic and put them together."

"Is it not possible that Leibniz could put together another's ideas and do the same?"

"It is possible."

"Did you lie to Newton?"

"I published behind Newton's back."

"No further questions."

Barrow is questioned on redirect: "I'm gathering that you built on the ideas of other mathematicians?"

"Yes, you could say that."

"When you say 'build on their ideas,' is it not the case that these people were long dead after you used their work?"

"That is true, and I developed many of my own ideas in my travels."

"When did you first meet Newton?"

"When I was Lucasian Professor of Mathematics at Cambridge University."

"So you saw his talents early on?"

"Yes. And I told him to publish early on, but he didn't."

"Later on, you did learn about Leibniz's work?"

"Yes."

"When was that?"

"At least ten years...seventeen years...after Newton's work appeared."

Barrow is finally excused.

10:23: Gottfried Leibniz is called to the stand once more.

"You did see the work of Newton, right?"

"Yes."

"But you did not understand his notation?"

"I didn't get his fluxions, no."

"Did others understand his work?"

"No, others didn't understand it either."

"How can someone become excited about something that person does not understand?"

"It can happen."

"I find that very hard to believe. [There is a brief conference with Newton's colleagues.] Why were you excited about something you couldn't understand?"

"Because I knew that we were working on similar ideas."

"So you were excited about information you couldn't understand and couldn't see a use for?"

"I knew we were both working on calculus at that time."

"Was it called 'calculus' then?"

"No."

[There is a bit of confusion and a couple of objections.]

"No further questions."

There is no cross-examination.

10:26: Isaac Newton is called to the stand.

"Mr. Newton, could you please inform the ladies and gentlemen of the court and jury of your achievements?"

"Even as a young child, I was very intelligent. I made many devices and discoveries."

"So from early on you displayed a keen intellect?"

"Yes, of course."

"Can you tell me about something you published in your adult life?"

"I didn't actually publish on calculus until Opticks in 1704, because I got in a controversy early on with Robert Hooke. I did write letters to colleagues containing my work, and I referred to these letters when publishing Opticks. Leibniz got wind of my ideas and ran with them."

"That must have been hurtful."

"Yes, it was."

"You were knighted by the Queen, right?"

"Yes."

"So it's safe to say that you made meaningful contributions to science?"

"Yes, it is."

Cross-examination begins.

"Can you please read the date of this letter you wrote?"

"October 24, 1676."

"This is before Leibniz's work was published, right?"

"This is true."

[An excerpt is read.]

"By your wording, it would appear you were aware of other people's methods for solving the same kind of problems?"

"But it was all based on my work."

"Do you have proof?"

"Collins and Barrow shared my work with others."

"Leibniz claims there was no calculus in those letters that he was able to understand."

"That's not conceivable: how could Leibniz not understand this work, if he's so smart?"

"But you were aware that other people were doing work in calculus, right?"

"Yes."

Redirect: "There were other mathematicians out there working on these problems that you'd already solved, right?"

"That is correct: Johann Bernoulli's problem, for instance. I solved it in a day, and only years later did Leibniz publish his solution, after he'd seen my work."

From Leibniz's attorney: "How did you submit your answer? Was it not anonymously?"

"I don't recall."

"Was your name on the solution?"

"No, because I was afraid of criticism, after my experience with Robert Hooke."

No further questions.

10:36: Closing arguments begin.

From Leibniz's attorney: "We have shown that a good deal of math came from both Leibniz's colleagues and students, and there was no proof that Newton's calculus played a major role, but rather it was Leibniz's work that formed the basis for these discoveries. We also showed that Newton had motives, personal and professional, for claiming Leibniz was a plaigiarist. We don't feel that Newton's attorneys have proven Leibniz was, beyond reasonable doubt, indeed a plaigiarist."

From Newton's side: "Thank you for your time. I believe that my client has a true and valid case, and that his letters were circulated and recognized long before Leibniz published his work, and that there's no way Leibniz would not have understood the import of these papers. He clearly took this work, changed the notation, and claimed it as his own. Newton, as you've seen, was a brilliant a man, and clearly capable of inventing the calculus."

10:40: Court is adjourned.

## Thursday, October 01, 2009

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Liveblogging *Newton* v. *Leibniz*, Round 1

Posted by DocTurtle at 9:13 AM

Labels: Calculus I, MATH 191

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