How Maxwell's Equations (and Quaternions) Led to Vector Analysis

This is the story of best friends Peter Tait and James Clerk Maxwell and how their friendship with William Thomson (aka Lord Kelvin) and Tait's rivalries with Willard Gibbs, Oliver Heaviside, Heinrich Hertz, August Föppl, and Edwin Wilson led to vector analysis.

0:00 Introduction
1:37 Part 1: Tait & Maxwell (1846-1856)
7:25 Part 2: Tait, Hamilton & Quaternions (1854-1867)
17:04 Part 3: Maxwell, His Equations & Quaternions (1856-1879)
25:00 Part 4: Gibbs (1873-1884)
29:18 Part 5: Heaviside (1873-1887)
34:26 Part 6: Hertz changes the game (1887-1890)
38:17 Part 7: War of the Vectors begins (1890-1894)
43:38 Part 8: Tait Loses the War (1894-1901)
51:00 Conclusion

[forrestcharnock]

Now, can you please explain who declared the "magnetic field" to be B and who said it is H?

[lingarajpatnaik]

Kathy, a whole generation of physicists shall be grateful to you for your indepth research in to history of physics. Heavyside is one of my heros. And I learnt so many things from you today! Grateful. Very.

[powerjets]

A brilliant take. A school has lost a physics teacher, but the internet has gained someone inspiring us all with the deeds of those that have changed our world. Some particular favourites in this video.

[josephncraig]

Kathy, this old physicist really enjoys your videos, your spirit, your energy, and your delightful sense of humor! I am particularly drawn to your historical perspective, putting real people behind the names associated with equations. But, simply, your channel is a complete delight, both for its science as well as its humanity.

[suryahitam]

As an engineer who had physics as one of my courses my understanding of vector analysis and electromagnetism would have benefitted enormously from this video. You really do make physics gripping. If this video were a book I would not be able to put it down!

[otiebrown]

Katy,
An incredible history.
Thank you!

[robertbachman]

Just wow. I have been fascinated about the 'vector wars' for a while now. You are an outstanding researcher for sorting through all of this and putting out a memorable presentation. I thought I knew the whole story, but you surprised me at the end. I never knew that Heaviside did not write the modern form of Maxwell's Equations. I look forward to the next video in this series.

PS, I have your book, the Lightning Tamers and highly recommend it.

[FlaminTubbyToast]

As a student training to be a mathematician I find these videos to be truly inspired. I am particularly entertained by the restraint that Kathy shows regarding all important maths. Without a doubt any other professor would have flaunted the convergence and curl out at every turn. This is also quite the case in her early works in this series where i, j, and k would have called out as î, j hat, and k hat.

It gives me much glee to recognize, know, and spot the precursors of the tools I use today. Without which, my work in physics would be particularly impossible.

Kathy Joseph is a fantastic orator and has a fantastic taste in presentation. I have been keen to keep up with each upload.

[GoldenAgeMath]

What an excellent video! I learned more physics history in an hour than I did during my whole degree

[phitsf]

One of my favourite things about physics and maths is the fact it has such a rich history. There are so many characters and the story takes so many twists and turns. Who needs novels when this exists?

[sphakamisozondi]

Wait, Heaviside did not have a college education? And he contribuated to vector calculus?! My level of respect for him went up by a large margin.

[myronplichota]

I nominate this video for a best of 2023 award!

[GlennElert]

I have been involved in physics education and history for a long time now and I have never heard this story told before. I love when your videos teach me something new.

[redknight]

Thanks for talking about this and also talking about Heaviside!!! a great forgotten genius!

[Nakameguro]

Wish I had these videos when I studied electrical engineering decades ago - the historical context of how mathematical physics came to be is fascinating. Subscribed!

[FritsKist]

Words fail to express my joy of your lectures!

[siobhangraham]

I learned all about the maths of these subjects in university, but now to hear about the history and people behind them is fascinating - especially in such a detailed and passionate telling of it! Thank you!

[chrisfuller]

Words cannot express how much I loved this video. What an amazing story and I can't wait to learn more about how relativity caused us to think Maxwell had only 4 equations.

[yutubl]

Wow! Thanks for this very exciting tour through the history of the development of mathematical operators from quaternions to vecor analysis used by Maxwell equations.

[Darthvanger]

Now it makes so much sense!
I was so puzzled reading Maxwell... :)