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So recently, I was pondering about historical connections of subjects, such as how concepts, ideas and experiments done in history change the course of humanity as they open new doors to exploration and technologies.

Having been to many panel discussions that covered topics from quantum computing to artificial intelligence to genetics and politics, I had this idea on whether something similar can be done in the hsm chat room.

I suspect hsm has enough resources and or userbase to do the task given the majority of questions here are mathematics. This event may also serve to advertise hsm more to attract more users on the significance of paying more attention to how historical developments of a field shaped it into its modern form, and inspire them to search and curate historical archives as they may contain insights that is relevant to present day research

This Meta is made after consulting with Martin Sleziak to first source what the community thought of this one time event

Typical structure of panels

Panels are often 3-5 speakers, each has some expertise in a specific topic and give a seminar or a short talk after briefly introducing themselves (or the host introduced them) . The host will then ask the panelists some prescribed questions, before the Q and A session.

The nice thing about cyberspace is that audience and fellow panelists can ask each other questions directly on the chat, without the need of the mic to move around. Therefore it is expected the panel might end up like an AMA involving multiple people

(footnote: An Ask Me Anything (AMA) is a session where speakers are invited to talk about their work or some topic, and the audience can ask the speaker any questions as the session proceeds.)

Typical panel discussion often range from 1-2 hours.

The idea

The proposed topic is Significant Historical Developments in Mathematics and Future Directions

In order to better fit the chat format, I felt like something like the following structure might be suitable (but there might be better ways to organise it. Let me knew in the comments)

  • Mathematical idea or insight, year (date if it is highly significant), (optional) discoverer(s)
  • Brief description or background of the subject, with relevant degree of details
  • Significance of the idea (e.g. what field is being opened up, what major contributions to mathematics and other science is achieved in the past etc.)
  • Future directions

For example:

  • Complex numbers (Dating back to 75 A.D.)
  • The square root of a negative number is known to crop up frequently throughout history and result in issues on how to deal with it or whether it is sensible. when Girolamo Cardan solves cubics with positive coefficients, solutions with negative square roots popped up, which later summarised by Rafael Bombel to have the general form $r \pm \sqrt{-n}$ and therefore realised that complex numbers are significant in solving cubics. Later in the 16th century, the euler relation $e^{i\theta}=\cos \theta + i \sin \theta$ was contributed by Roger Cotes. Leonhard Euler then gave a general proof of the De Movire theorem. In the 17th century, Caspar Wessel and Jean-Robert Argand independently conceived the Argand plane and hence a geometric representation of the complex numbers. Finally the significance of the study of complex numbers is placed on a firm footing when Friedrich Gauss proved the Fundamental theorem of algebra, thus establishing that all polynomial roots with real coefficients are complex numbers.
  • The opening of the field of complex numbers not only lead to advancements in mathematics such as algebra and geometry, and in physics such as electromagnetism and quantum mechanics, the best contribution of complex number is its uses in engineering sectors and in signal processing, thus one of the pieces that lead to the rise in modern electricity driven technologies.
  • (Unfortunately I am unable to fill in this one cause I am not an expert in complex analysis)

The challenge

Besides the obvious issue of finding panelists and selecting an appropriate time, there are challenges unique in the nature of such talks:

  1. Unlike an ordinary AMA, the host of a panel discussion often need to have some background in the underlying topic. As demonstrated by the example I showed above, I may not be qualified as a good host since my mathematics background is haphazard and full of gaps. While my knowledge base is dense enough to be able to relay questions and continue discussions, it may not be sufficient to get the host Q and A portion going.

Having said that, there are panel hosts that have little to no background on the subject in hand, thus that may not be a significant issue

  1. Finding panelists also poses its own unique challenge due to the topic. As far I am aware, there isn't many regulars who are well versed in the history of mathematics in Mathematics SE. However, given the questions and answers in th hsm site, there might be more qualified users that can be panelists and share about significant parts of mathematical history. As the physics AMA would have informed us, it is often a bit too optimistic to try to look for real life academics and industry personnel to present.

Thoughts and comments

Let me know down in the comments. If you have any recommended speakers, also let us know.

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