6 ms·

History of Maths for Beginners

162 points by kreig 2y ago

jaymzcampbell 2y ago
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 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/ConceptsofmodernmathematicsStewart1981 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.
- WillAdams 2y ago
  Famously, take note of Hilbert asking at a conference, "What is a Hilbert space?"
- pvg 2y ago
  An oldie but goldie of the multi-brick/bathroom doorstop variety is Kline's Mathematical Thought from Ancient to Modern Time.
  - bhasi 2y ago
    What does multi brick/bathroom variety mean?
    - pvg 2y ago
      It means it's a big fat book well suited for browsing while on the can. It's a genre.
- teddyh 2y ago
  Also The World of Mathematics (1956) by James R. Newman.
- timthorn 2y ago
  The Cambridge University History of Maths society is a fantastic resource - almost all the lectures are live streamed: https://hom.soc.srcf.net/ https://hom.soc.srcf.net/
  - shanusmagnus 2y ago
    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-TSTSUevxPB- https://drive.google.com/drive/folders/1wkQmFPcrkLM9oJk1G7jF... Contains this banger of a quote: "The Greeks were very poor at using YouTube."
    - timthorn 2y ago
      Next lecture will be delivered later this afternoon :)
andrewinardeer 2y ago
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 https://www.unesco.org/en/days/mathematics
__rito__ 2y ago
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-Volumes/dp/0486409163 https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
godelski 2y ago
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-mathematics/ https://intellectualmathematics.com/opinionated-history-of-m...
- yantrams 2y ago
  Woah thank you for sharing this! Absolutely riveting list of topics.
  - godelski 2y ago
    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 Twitter: https://x.com/viktorblasjo Bluesky: https://bsky.app/profile/viktorblasjo.bsky.social
- allturtles 2y ago
  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-archimedes-good/ 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.
  - godelski 2y ago
    Stick with it. I think you are not quite getting the argument he is making. I don't think he's saying that Galileo didn't do anything meaningful, but he is saying that Galileo is getting more credit than he deserves. > This is why Galileo is the idol of the humanists and the bane of the mathematicians. The philosophers say he invented modern science; the mathematicians that he’s a poor man’s Archimedes. The issue cuts much deeper than merely allotting credit to one century rather than another. Much more than a question of the detailed chronology of obscure scientific facts, it is a question of worldview and how one should approach and understand history. I'm not exactly sure what the problem is. There are plenty of people who were bad at science that also made great contributions. There are also plenty of people who were not great contributors who also were able to establish a big name for themselves. I'll stay out of politics for the most famous current one, but I think I'm safe to point out the age old Woz vs Jobs thing people have talked about. Viktor also does bring Tycho Brahe, which I think people are much more comfortable dunking on now a days. But in his time he lived it up in the limelite. He held many parties and was well known for his intelligence and brilliance, by the public. Brahe was known by all, but now he's just a footnote and an impedance to Kepler. Do you not think it is true that some peoples' stories get embellished? Do you not think it is true that some are greatly so? Do you not think history gets retold to make better stories? Do you not think people who have made great contributions have been ignored? Certainly in the long history all this has happened. Do they not deserve credit? If they do, then the unfortunate reality is that this must be "taken" from those that it was misattributed to. Especially in the progression of knowledge where we over attribute contributions to those that cross some "finish line." Or in the words of Einstein: I stand on the shoulders of giants. > I say that the traditional view of the “Galilean” scientific revolution is not only historically wrong but fundamentally inconsistent with the nature of mathematical thought. When I say Galileo boo, Archimedes yay, my point is not who was the “first” or who should “get credit” for this or that. That’s not so interesting. But Galileo is a window into more important things. What is the relation between mathematics and science? Was mathematics before Galileo a technocratic enterprise? Compartmentalised, limited to certain computational tasks, blind to its own potential? Was mathematics stuck in that ditch until it was liberated by a “conceptual” breakthrough from without, so to speak; from philosophy? Or was mathematics always an expansive, empirically informed, interconnected study of all quantifiable aspects of the world? The latter, of course, if you ask me. In any case, Galileo is ground zero for grappling with these questions. And that is why we study him. Edit: I think there is also a relevant recent HN post as well[0] and I'll point out a comment of mine[1]. The mathematics is a necessary component for the explainability, for the causality. These are the essence of physics and science, and the only language we really have to express them through is the language of math. I am biased though, you can check my comment history as I make similar arguments about our approach to machine learning.[2] And I do think we should understand these things. And in my reply to jebarker you'll find a reason for why I believe understanding the history, in an accurate form, is so important for learning how to move forward. [0] https://news.ycombinator.com/item?id=43344703 https://news.ycombinator.com/item?id=43344703 [1] https://news.ycombinator.com/item?id=43349216 https://news.ycombinator.com/item?id=43349216 [2] https://news.ycombinator.com/item?id=43348954 https://news.ycombinator.com/item?id=43348954
aoki 2y ago
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.”
rottc0dd 2y ago
For calculus history, one of my earliest books I read was "Calculus wars" (https://www.amazon.com/Calculus-Wars-Jason-Socrates-Bardi/dp/1560259922 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-Universe/dp/0358299284 https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Univ...).
amriksohata 2y ago
_By the 9th century A.D., the Indians had made a conceptual leap that ranks as one of the most important mathematical events of all time. They had begun to recognise sunya_ Bit misleading as sunya or zero was invented in india, not recognised, there is a difference.

162 points by kreig 2y ago

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 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/ConceptsofmodernmathematicsStewart1981 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.

WillAdams 2y ago
Famously, take note of Hilbert asking at a conference, "What is a Hilbert space?"
pvg 2y ago
An oldie but goldie of the multi-brick/bathroom doorstop variety is Kline's Mathematical Thought from Ancient to Modern Time.
- bhasi 2y ago
  What does multi brick/bathroom variety mean?
  - pvg 2y ago
    It means it's a big fat book well suited for browsing while on the can. It's a genre.
teddyh 2y ago
Also The World of Mathematics (1956) by James R. Newman.
timthorn 2y ago
The Cambridge University History of Maths society is a fantastic resource - almost all the lectures are live streamed: https://hom.soc.srcf.net/ https://hom.soc.srcf.net/
- shanusmagnus 2y ago
  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-TSTSUevxPB- https://drive.google.com/drive/folders/1wkQmFPcrkLM9oJk1G7jF... Contains this banger of a quote: "The Greeks were very poor at using YouTube."
  - timthorn 2y ago
    Next lecture will be delivered later this afternoon :)

andrewinardeer 2y ago

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 https://www.unesco.org/en/days/mathematics

__rito__ 2y ago

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-Volumes/dp/0486409163 https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

godelski 2y ago

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-mathematics/ https://intellectualmathematics.com/opinionated-history-of-m...

yantrams 2y ago
Woah thank you for sharing this! Absolutely riveting list of topics.
- godelski 2y ago
  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 Twitter: https://x.com/viktorblasjo Bluesky: https://bsky.app/profile/viktorblasjo.bsky.social
allturtles 2y ago
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-archimedes-good/ 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.
- godelski 2y ago
  Stick with it. I think you are not quite getting the argument he is making. I don't think he's saying that Galileo didn't do anything meaningful, but he is saying that Galileo is getting more credit than he deserves. > This is why Galileo is the idol of the humanists and the bane of the mathematicians. The philosophers say he invented modern science; the mathematicians that he’s a poor man’s Archimedes. The issue cuts much deeper than merely allotting credit to one century rather than another. Much more than a question of the detailed chronology of obscure scientific facts, it is a question of worldview and how one should approach and understand history. I'm not exactly sure what the problem is. There are plenty of people who were bad at science that also made great contributions. There are also plenty of people who were not great contributors who also were able to establish a big name for themselves. I'll stay out of politics for the most famous current one, but I think I'm safe to point out the age old Woz vs Jobs thing people have talked about. Viktor also does bring Tycho Brahe, which I think people are much more comfortable dunking on now a days. But in his time he lived it up in the limelite. He held many parties and was well known for his intelligence and brilliance, by the public. Brahe was known by all, but now he's just a footnote and an impedance to Kepler. Do you not think it is true that some peoples' stories get embellished? Do you not think it is true that some are greatly so? Do you not think history gets retold to make better stories? Do you not think people who have made great contributions have been ignored? Certainly in the long history all this has happened. Do they not deserve credit? If they do, then the unfortunate reality is that this must be "taken" from those that it was misattributed to. Especially in the progression of knowledge where we over attribute contributions to those that cross some "finish line." Or in the words of Einstein: I stand on the shoulders of giants. > I say that the traditional view of the “Galilean” scientific revolution is not only historically wrong but fundamentally inconsistent with the nature of mathematical thought. When I say Galileo boo, Archimedes yay, my point is not who was the “first” or who should “get credit” for this or that. That’s not so interesting. But Galileo is a window into more important things. What is the relation between mathematics and science? Was mathematics before Galileo a technocratic enterprise? Compartmentalised, limited to certain computational tasks, blind to its own potential? Was mathematics stuck in that ditch until it was liberated by a “conceptual” breakthrough from without, so to speak; from philosophy? Or was mathematics always an expansive, empirically informed, interconnected study of all quantifiable aspects of the world? The latter, of course, if you ask me. In any case, Galileo is ground zero for grappling with these questions. And that is why we study him. Edit: I think there is also a relevant recent HN post as well[0] and I'll point out a comment of mine[1]. The mathematics is a necessary component for the explainability, for the causality. These are the essence of physics and science, and the only language we really have to express them through is the language of math. I am biased though, you can check my comment history as I make similar arguments about our approach to machine learning.[2] And I do think we should understand these things. And in my reply to jebarker you'll find a reason for why I believe understanding the history, in an accurate form, is so important for learning how to move forward. [0] https://news.ycombinator.com/item?id=43344703 https://news.ycombinator.com/item?id=43344703 [1] https://news.ycombinator.com/item?id=43349216 https://news.ycombinator.com/item?id=43349216 [2] https://news.ycombinator.com/item?id=43348954 https://news.ycombinator.com/item?id=43348954

aoki 2y ago

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.”

rottc0dd 2y ago

For calculus history, one of my earliest books I read was "Calculus wars" (https://www.amazon.com/Calculus-Wars-Jason-Socrates-Bardi/dp/1560259922 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-Universe/dp/0358299284 https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Univ...).

amriksohata 2y ago

_By the 9th century A.D., the Indians had made a conceptual leap that ranks as one of the most important mathematical events of all time. They had begun to recognise sunya_ Bit misleading as sunya or zero was invented in india, not recognised, there is a difference.