I hope that those of you who are not mathematically inclined will allow me to include beautiful equations, and especially beautiful proofs, as examples of art. For example, Euler’s identity, *e** ^{iπ}* + 1 = 0, is considered, by mathematicians at least, to be one of the most beautiful results in the history of the subject. The formula which leads to that identity, also proven by Euler, was described by Richard Feynman as “our jewel”. (As an aside, Feynman’s “Lectures on Physics” have themselves been considered jewels by physicists, although not necessarily by the Cal Tech freshmen for whom they were intended.

Nevertheless, the artistry of Sir Isaac Newton cannot be denied.

Another problem solved by Euler, “The Bridges of Konigsberg”, is an example of a problem that was later studied in a branch of topology called “graph theory”, although that science did not exist until a century or two later. Last week, I was subbing for the calculus teacher at one of the high schools where I work, and she asked me to talk with the kids about this problem, an addition to the class after they had already taken their AP exam. I was able to find a translation of Euler’s 1736 paper on the problem, and spent a week preparing to present the proof to the students. (The teachers for whom I work will testify that no other sub has ever put that amount of dedication into the preparation for a class.) I put together a slide show for the class and am in the process now of making that slide show into a Zoom presentation which I will make available to any of you who might want to see it.

But Euler is not the “artist” who needs to be separated from his “art”. That distinction, for me, belongs to Newton, one of the greatest scientists and mathematicians in the history of the world. Newton, in parallel with Leibniz, developed what we now call “the calculus”. He started out knowing that he needed to invent integral calculus, but to do that, he had to first invent differential calculus. He referred to that latter discipline as the “method of fluxions”, a name that thankfully did not stick, and today we use Leibniz’s notation rather than the cumbersome notation developed by Sir Isaac, but there is no question that Newton deserves most of the credit for the calculus.

Newton’s efforts were not limited to mathematics, however. He also came up with the description of the force of gravity as a universal force existing between any two objects; the fact that white light could be broken up into different colors and then re-assembled into white light; the reason for planets revolving around the sun in elliptical orbits, and many other scientific phenomena. I have two different translations of his “Principia” as well as a biography by James Gleick on my bookshelves

But Newton was a very difficult person, quick to take, and hold, offense over perceived slights, jealous of his discoveries to the point that he often held off on publishing them, and taken to intense battles over intellectual property. Later in his life, he devolved into mysticism and alchemy, at a time when scientific theory was entering its nascency and in need of a champion of his stature.

Nevertheless, the artistry of Sir Isaac Newton cannot be denied. His contributions to the progress of science and math will endure for many more centuries.

**Characterizations**:

*well written*

Jeff, this is a great take on the prompt, and I do believe you’ve well described the relationship between art and science. I knew about the calculus inventions, but being somewhat math challenged never followed the details. In my work as a writer dealing with the sciences, I’ve come across a number of troubling issues. Probably the most famous is about James Watson, who essentially stole critical work from Rosalyn Franklin that enabled his discovery of the structure of DNA. He recently has espoused overtly racist views. Recently there have been many revelations of sexual harassment by famous scientists, and although their achievement aren’t in doubt, I can’t think about them in the same way.

Yes, Franklin did not get the credit she deserved for her X-rays on the DNA molecule, although her contribution was well-enough known that she probably would have shared in the Nobel Prize had she not died before it could be awarded.

There is an apocryphal story that while Watson was teaching at Harvard, he married a Cliffie, and exclaimed to everyone “She’s mine!”, perhaps not recognizing the reaction of many young women at that time to any hint of male claims of ownership.

Very interesting story, Jeff. I think it is fair game to call beautiful equations or proofs “art” but it doesn’t sound like Newton did anything that would have caused people to “cancel” him. I was waiting for sexual transgressions or anti-Semitic or racist views. Sounds like he was just cranky.

Never heard the story about Watson and his Cliffie wife. His comment about her doesn’t seem nearly as troubling as his racist views about IQ and sex drive.

Jeff, I am married to a math major, who often told me how elegant he thought equations were. And my son has a PhD in computational neuroscience. He’s had dinner with “James” a few times (his hostess was a friend) and can attest personally to his unpleasant personality. So your narrative seems compelling to me, though it is way beyond my level of comprehension.

As the mother of a mathematician, I agree that elegant proofs and equations are a form of art. Difficult personalities abound in every field, but that should not be an impediment to learning from them and admiring their genius.

Thanx for the math lesson Jeff, altho it’s all Greek to me! My mom however was a math and art major, and like you she too saw the beauty in numbers, and she was nutty about the prime ones!

Sorry to learn that Newton, although a genius, was not such a nice guy!

I really enjoyed this post, and the appreciation for the beauty in math and science. I struggled greatly over calculus, but was thrilled when I was introduced to the periodic table, relativity, and the genetic code. E = MC2 (squared) is pretty elegant too. If you do have the presentation you made to the high school students, I would love to see it. And to see if I could understand it too 🙂

I will send you the link tomorrow.

Here’s a link to the Zoom presentation I made for future use in teaching the Koenigsberg Bridge Problem:

https://us02web.zoom.us/rec/share/BOMjB7Sohrycqtsh4tOzhItVL4v4PYLemveNOwTV46urfCZbotctS9Etg1EGpxkl.69DTVdNU5W6F9oKM Passcode: +Z2U44^w

Since you are interested in topics, including relativity, I will send a couple of short papers on that topic that I put together several years ago.

I seem to remember that the original form of Einstein’s most famous equation was “delta E = delta m x c^2”, making it clear that an increase in energy would lead to an increase in mass! As for the genetic code, while Watson and Krick discovered the structure of DNA in 1953, and Watson then went to Harvard, while we were there, the actual genetic code was not worked out until a number of years later.

Hi Jeff, I checked out the Zoom on Euler’s proof, and that was really fun. Thanks! I got a little lost on how to find the number of times the letter needed to show up for a solution, but kind of followed the rules on how to get the actual number of times the letter showed up, and I could see whether they matched or not. Very elegant. It would take some practice to be able to apply the rules. Once you know it is possible, is there some way to come up with an actual path as well? Hard to believe Euler would have just doodled his way to that solution. Thanks for the relativity papers–will have to check out too.