I really like History and this includes the history of Mathematics. Personally, I have dabbled into many old Math works. Since my base knowledge is only up to Calculus 2, I can only appreciate the history of calculus. I have read "Introduction to analysis of the infinite" by Euler, some chapters of "Foundations of Differential Calculus", some passages from "A Treatise on Fluxions" by Collins Maclaurin (particularly on his derivation of the Taylor series), and many papers of Euler, D'Alembert and Lagrange.
I find them, apart from Euler, conceptually difficult to understand. Obviously, they don't rely on concepts that are taught in modern curriculum, and the antiquated notations do not help. For Maclaurin, for example, he relies a lot on geometric concepts, just like Newton.
For example, the origin of the now essential power rule for the integral of a polynomial function, $$\int x^{n} \,dx=\dfrac{x^{n+1}}{n+1}+C$$
is found during the XVII and XVIII century, but they are exceedingly difficult to follow the original line of thoughts, because the method being employed is geometric in nature, the so called the "Method of Indivisibles".
So my question is, do you think the field of History of Mathematics underdeveloped? I personally think so. I have a few reasons for why such is the state of being of the matter:
- It is challenging to re-learn Math concepts and arguments of past mathematicians. Obviously, this increases as the time period recedes into distant past.
- It is unnecessary, because nobody is going to learn much from old and distant Math because new ideas have been developed. People can learn a lot more from compacted version of modern textbooks and modern curricula.
- Along that line of reasoning, mathematicians and students who will become future mathematicians are only interested in solving unsolved problems. Advance in mathematics is about looking forward, not backward. There are no reasons to go back further, except if the history of a mathematical concept or problem is directly related to the problem you are trying to solve.
I think out of all fields of Mathematics, Calculus are studied the most. Apart from this, little are written on the history of Linear Algebra, for example, or Topology. The only book that I have read that is concerned with a fairly modern mathematical concept is "Lebesgue's Theory of Integration: Its Origins and Development" by Thomas Hawkin.
If you look at the field of history of Mathematics, it is a small overlap between History and Mathematics, as a discipline. It is very insignificant because few modern readers are interested in the history of Mathematics as compared to the fields of political history, cultural and economic history.
Do you think there are any values in relearning old Math? Perhaps as a hobby, for modern mathematicians have too many concerns than to learn Math from the past.
Not sure that a lifetime would be enough to read their work.
– Jan 26 '21 at 20:54