When you first study mathematics at undergraduate and early post-grad level there is a sense of being overwhelmed with how on earth anyone figured this out. When you read the messy history of maths, and understand it is an organic, growing field, you feel a little less like an imposter struggling to understand how anyone could've come up with this.
Reading these books (primarily as a software engineer), made me feel better about not immediately getting certain concepts, because it's likely the people these theorems are named after didn't get it either, to begin with. They refined it, they collaborated (like a pull request almost) and eventually everything got very neatly packaged up into a set of theorems. Mathematics is rarely taught in that way, I wish more of the "human" aspect was part of the pedagogical process. I think it might temper some of the fear people have.
"Cambridge University History of Mathematics Society
presents an illegal, immoral, and fattening lecture series,
without the endorsement, approval, or approbation of University authorities on:
HISTORY OF SCIENCE IN ANTIQUITY"
Gives me a warm feeling. Here's one of the lectures to get a flavor:
I cannot recommend enough the podcast Opinionated History of Mathematics by Viktor Blåsjö
What's great about it is that it helps put you in the shoes of the people solving the problems at these times. So it secretly teaches you how to solve problems. He also attacks some of the claims of some historians which are a bit obtuse. The arguments are really well founded and if you're wondering how ancients solved extremely complex math while never inventing the tools you'd think are needed to solve them, then this will answer a lot of that. I think it'll make you see a lot of problems in a different light. It also is just a lot of fun and can be pretty funny.
I took a look and was really turned off by the first episode which is all about dunking on Galileo and what a bad mathematician he was, and generally showing tremendous hostility to anything that isn't math. You can read it for yourself here: https://intellectualmathematics.com/blog/galileo-bad-archime...
The syllogism appears to be:
1. All good science is mathematical
2. Anyone intelligent is very good at math
3. Galileo was not very good at math
4. Therefore Galileo was dumb and did bad science.
For calculus history, one of my earliest books I read was "Calculus wars" (https://www.amazon.com/Calculus-Wars-Jason-Socrates-Bardi/dp...). This also is a essentially book about the Newton and G W Leibneiz. But, it is pretty much a deep dive into life of these two men. Highly recommended.
I laughed when I got to the end of this wall of text, full of “ahistorical fantasies” and “what the fuck moment,” and read: “Despite my negative comment about some points in the book, I would actually recommend it as a reasonably priced, mostly accurate, introduction to the history of mathematics. … A good jumping off point for somebody developing an interest in the discipline.”
When it comes to mathematical concepts- to understand everything broadly, connected to its context, and to understant "what's the point?", nothing tops this book- Mathematics: Its Content, Methods and Meaning (3 Volumes in One) by Aleksandrov, Kolmogorov, and Lavrentev [0].
If you're interested in this sort of stuff I highly recommend Stillwell's "Mathematics and it's History" (https://link.springer.com/book/10.1007/978-1-4419-6053-5) - it's a wonderful mix of quite low level explicit mathematics with contextual history; along with Stewarts "Concept of Mathematics" (https://archive.org/details/ConceptsofmodernmathematicsStewa...).
When you first study mathematics at undergraduate and early post-grad level there is a sense of being overwhelmed with how on earth anyone figured this out. When you read the messy history of maths, and understand it is an organic, growing field, you feel a little less like an imposter struggling to understand how anyone could've come up with this.
Reading these books (primarily as a software engineer), made me feel better about not immediately getting certain concepts, because it's likely the people these theorems are named after didn't get it either, to begin with. They refined it, they collaborated (like a pull request almost) and eventually everything got very neatly packaged up into a set of theorems. Mathematics is rarely taught in that way, I wish more of the "human" aspect was part of the pedagogical process. I think it might temper some of the fear people have.
The Cambridge University History of Maths society is a fantastic resource - almost all the lectures are live streamed: https://hom.soc.srcf.net/
This looks like an absolute delight:
"Cambridge University History of Mathematics Society presents an illegal, immoral, and fattening lecture series, without the endorsement, approval, or approbation of University authorities on: HISTORY OF SCIENCE IN ANTIQUITY"
Gives me a warm feeling. Here's one of the lectures to get a flavor:
https://drive.google.com/drive/folders/1wkQmFPcrkLM9oJk1G7jF...
Contains this banger of a quote:
"The Greeks were very poor at using YouTube."
An oldie but goldie of the multi-brick/bathroom doorstop variety is Kline's Mathematical Thought from Ancient to Modern Time.
What does multi brick/bathroom variety mean?
It means it's a big fat book well suited for browsing while on the can. It's a genre.
Also The World of Mathematics (1956) by James R. Newman.
Famously, take note of Hilbert asking at a conference, "What is a Hilbert space?"
I cannot recommend enough the podcast Opinionated History of Mathematics by Viktor Blåsjö
What's great about it is that it helps put you in the shoes of the people solving the problems at these times. So it secretly teaches you how to solve problems. He also attacks some of the claims of some historians which are a bit obtuse. The arguments are really well founded and if you're wondering how ancients solved extremely complex math while never inventing the tools you'd think are needed to solve them, then this will answer a lot of that. I think it'll make you see a lot of problems in a different light. It also is just a lot of fun and can be pretty funny.
https://intellectualmathematics.com/opinionated-history-of-m...
I took a look and was really turned off by the first episode which is all about dunking on Galileo and what a bad mathematician he was, and generally showing tremendous hostility to anything that isn't math. You can read it for yourself here: https://intellectualmathematics.com/blog/galileo-bad-archime...
The syllogism appears to be:
1. All good science is mathematical
2. Anyone intelligent is very good at math
3. Galileo was not very good at math
4. Therefore Galileo was dumb and did bad science.
Woah thank you for sharing this! Absolutely riveting list of topics.
It is one of my all time favorite podcasts
He's also a nice dude. I reached out to him on Twitter and he happily responds. I'm sure he likes hearing what people think
For calculus history, one of my earliest books I read was "Calculus wars" (https://www.amazon.com/Calculus-Wars-Jason-Socrates-Bardi/dp...). This also is a essentially book about the Newton and G W Leibneiz. But, it is pretty much a deep dive into life of these two men. Highly recommended.
Another great book is "Infinite Powers" by Steven Strogatz (https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Univ...).
Sidenote today (or tomorrow depending where you are), on Friday 14th March the United Nations observes 'International Day of Mathematics'
https://www.unesco.org/en/days/mathematics
I laughed when I got to the end of this wall of text, full of “ahistorical fantasies” and “what the fuck moment,” and read: “Despite my negative comment about some points in the book, I would actually recommend it as a reasonably priced, mostly accurate, introduction to the history of mathematics. … A good jumping off point for somebody developing an interest in the discipline.”
When it comes to mathematical concepts- to understand everything broadly, connected to its context, and to understant "what's the point?", nothing tops this book- Mathematics: Its Content, Methods and Meaning (3 Volumes in One) by Aleksandrov, Kolmogorov, and Lavrentev [0].
[0]: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...