2

I am an undergraduate math major student. I believe Euclidean Geometry is one of the most beautiful subjects in math and helps us to improve mathematical intuition. However, there are very few universities that provide Euclidean Geometry courses. Some great mathematicians such as Dieudonné even say that it is wasting time to learn this subject.

Are there still some benefits in modern mathematics to learn that subject? Does anyone have experience that studying the subject actually helped you in research?

metsu
  • 21
  • 4
    IMHO, the interest is mainly pedagogical. Having been trained at an early age to reason on geometrical figures provides a kind of plasticity to the brain that can be very useful for all other parts of mathematics. The best proof is that many great mathematicians of the past - say - 60 years have been distinguished, even winners, in various Olympiads where the ability to manipulate figures is in the forefront. – Jean Marie Sep 19 '21 at 15:37
  • @ JeanMarie Do you mean there are not many advantages for undergraduate students to take some time on this subject? I felt knowing some geometrical definition of shapes(eg, parabola, ellipse, circle of Apollonius) helped me guess ing the shape of some equations in complex numbers. Are there advantages in further subjects in modern mathematics? – metsu Sep 19 '21 at 15:57
  • The study of conics is historically connected to Euclidean Geometry, but most usually it's considered as a (very important) separate set of knowledge (btw, it has been initiated by Apollonius, posterior to Euclides). Indeed conics can be defined by geometric properties but they are at crossroads with analysis, projective geometry, linear algebra, etc. which provide a richness of approaches that leave the "pure geometry" approach unable to cope with all the issues. – Jean Marie Sep 19 '21 at 16:08
  • Yes, Euclidean geometry helps in complex functions theory, when it deals with circles for example, Möbius transformations... – Jean Marie Sep 19 '21 at 16:11
  • 1
    I am glad to hear that. Thank you very much. – metsu Sep 19 '21 at 17:29
  • A youth who had begun to read geometry with Euclid, when he had learnt the first proposition, inquired, "What do I get by learning these things?" So Euclid called a slave and said "Give him threepence, since he must make a gain out of what he learns." Stobaeus, Extracts – Intelligenti pauca Sep 21 '21 at 18:21
  • @ Intelligenti pauca I just realized that you commented to my post. I like Geometry and have fun with learning this. The story is one of my favorite one of Euclid's and the reason I learn math is only because I find it is beautiful. It is my responsibility that I did not really write my question in detail. My main interest is Langland's program and I wanted to ask if learning Euclidean Geometry is good for my career as mathematician or I should concentrate on other stuff like algebra and analysis and set Classic Geometry aside as my hobby. Anyway thank you for your comment!! – metsu Feb 03 '22 at 23:19

0 Answers0