Love and Math

What Hacker News says

1. lebcaDec 2025
   Second this! And if you want a part memoir part history of this subject as it relates to physics (through Langlands Program) part ode to the beauty of maths, I recommend reading Edward Frenkel's Love & Math:

   https://en.wikipedia.org/wiki/Love_and_Math

   and if you went to school in maths but now have left that world, this book engenders an additional spark of nostalgia and fun due to reading about some of your professors and their (sometimes very difficult) journey in this world.

   Show morethread
2. aquafoxFeb 2024
   If you are into this topic, I recommend "Love and Math" by Edward Frenkel, where he describes his struggles to start an academic career as a jewish mathematician in russia.
   thread
3. jebarkerOct 2023
   Coincidentally I just put down Edward Frenkel's "Love & Math" before opening HN to see this. In particular I was reading the chapter about the early 2000s meetings at IAS using DARPA funding to explore the links between the Langlands Program and physics. Highly recommend the book for those interested in an accessible overview of this area of math.
   thread
4. maze-leOct 2023
   I can also recommend Edward Frenkel's (the guest of this video) book "Love and Math" on the subject. He writes as well as he talks, the book is very approachable, not just for a mathematically literate audience, but also for those who "don't like math". Its about the Langlands Program, but also about his own personal history of becoming a mathematician in the Soviet Union and his experiences with antisemitism during that time. Fascinating Stuff, even though it only barely touches the surface of his research.
   Show morethread
5. AiaAidanMar 2023
   If you're interested in exploring the beauty of symmetry further, and want to dive deeper into the world of math, I highly recommend checking out the book "LOVE and MATH: The Heart of Hidden Reality" by Edward Frenkel.

   Here's a long quote from "LOVE and MATH" that gives a taste of the book:

   "The story of Galois is one of the most romantic and fascinating stories about mathematicians ever told. A child prodigy, he made groundbreaking discoveries very young. And then he died in a duel at the age of twenty. There are different views on what was the reason for the duel, which happened on May 31, 1832: some say there was a woman involved, and some say it was because of his political activities. Certainly, Galois was uncompromising in expressing his political views, and he managed to upset many people during his short life.

   It was literally on the eve of his death that, writing frantically in a candlelit room in the middle of the night, he completed his manuscript outlining his ideas about symmetries of numbers. It was in essence his love letter to humanity in which he shared with us the dazzling discoveries he had made. Indeed, the symmetry groups Galois discovered, which now carry his name, are the wonders of our world, like the Egyptian pyramids or the Hanging Gardens of Babylon. The difference is that we don’t have to travel to another continent or through time to find them. They are right at our fingertips, wherever we are. And it’s not just their beauty that is captivating; so is their high potency for real-world applications.

   ...

   What Galois had done was bring the idea of symmetry, intuitively familiar to us in geometry, to the forefront of number theory. What’s more, he showed symmetry’s amazing power.

   ...

   The general formula for the solutions of the quadratic equations was already known to the Persian mathematician Al-Khwarizmi in the ninth century (the word “algebra” originated from the word “al-jabr,” which appears in the title of his book). Formulas for solutions of the cubic and quartic (degree 4) equations were discovered in the first half of the sixteenth century. Naturally, the next target was a quintic equation (of degree 5). Prior to Galois, many mathematicians had been desperately trying to find a formula for its solutions for almost 300 years, to no avail. But Galois realized that they had been asking the wrong question. Instead, he said, we should focus on the group of symmetries of the number field obtained by adjoining the solutions of this equation to the rational numbers – this is what we now call the Galois group.

   The question of describing the Galois group turns out to be much more tractable than the question of writing an explicit formula for the solutions. One can say something meaningful about this group even without knowing what the solutions are. And from this one can then infer important information about the solutions. In fact, Galois was able to show that a formula for solutions in terms of radicals (that is, square roots, cubic roots, and so on) exists if and only if the corresponding Galois group has a particularly simple structure: is what mathematicians now call a solvable group. For quadratic, cubic, and quartic equations, the Galois groups are always solvable. That’s why solutions of these equations may be written in terms of the radicals. But Galois showed that the group of symmetries of a typical quintic equation (or an equation of a higher degree) is not solvable. This immediately implies that there is no formula for solutions of these equations in terms of radicals.

   ...

   Galois’ work is a great example of the power of a mathematical insight. Galois did not solve the problem of finding a formula for solutions of polynomial equations in the sense in which it was understood. He hacked the problem! He reformulated it, bent and warped it, looked at it in a totally different light. And his brilliant insight has forever changed the way people think about numbers and equations.

   Show morethread
6. gjulianmDec 2022
   I always recommend the book "Love and Math", by Edward Frenkel. The book is fairly approachable I think, and it mixes his own biography with examples of interesting math concepts and connections.

   Funnily enough, Frenkel works in the Langland program that Wiles talks about here, and explains a little bit more about it and why is it interesting.

   Also, I really like this quote from the article

   > Yes, some people are brighter than others but I really believe that most people can really get to quite a good level in mathematics if they're prepared to deal with these more psychological issues of how to handle the situation of being stuck.

   I foud this true in experience. Sometimes people find maths hard at the beginning because it's a different way of thinking, much more abstract, and you don't usually have an intuition when you start. But in the end, most of it is practice. Also, some things only click when you go back to them, or need them for more advanced concepts.

   Show morethread