4 ms·

An order of magnitude is usually 10. But Erdos only published about twice as many papers as Euler (if this is even a good way to compare their respective output

by wbhart 11y ago

An order of magnitude is usually 10. But Erdos only published about twice as many papers as Euler (if this is even a good way to compare their respective outputs). Also, Erdos was not so much of a theory builder but a problem solver. He also left many unsolved problems, some of which have led to new insights. But he didn't spark the development of new fields of maths in the way that say Grothendieck did.

rjtobin 11y ago
For anyone interested in learning more about this cultural divide within mathematics -- theory building versus problem solving -- Fields medalist Tim Gowers has an interesting article: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf. People I talk to are often surprised to learn that there is quite a bit of snobbery within mathematics on this issue. Mostly people in theory-heavy subjects looking down on areas that revolve more around problem solving. Of course, it's academia, so it surprises me that anyone is surprised that there are turf wars and snobbery.
- Someone 11y ago
  There 's also "Birds and Frogs" that is more positive about the divide, by Freeman Dyson (http://www.ams.org/notices/200902/rtx090200212p.pdf http://www.ams.org/notices/200902/rtx090200212p.pdf) It starts: "Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best friends are birds."
- kzrdude 11y ago
  And then there's the abc conjecture person, whose theory building went so far that nobody can read it? It's this taken to the extreme, isn't it?
j2kun 11y ago
I was not aware that Euler had so many publications. Good point. However, even though I believe Erdos's insights were as deep as Grothendieck's, and that Erdos was as great a mathematician, I don't think I could ever convince an algebraic geometer of it.

by wbhart 11y ago

rjtobin 11y ago

For anyone interested in learning more about this cultural divide within mathematics -- theory building versus problem solving -- Fields medalist Tim Gowers has an interesting article: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf. People I talk to are often surprised to learn that there is quite a bit of snobbery within mathematics on this issue. Mostly people in theory-heavy subjects looking down on areas that revolve more around problem solving. Of course, it's academia, so it surprises me that anyone is surprised that there are turf wars and snobbery.

Someone 11y ago
There 's also "Birds and Frogs" that is more positive about the divide, by Freeman Dyson (http://www.ams.org/notices/200902/rtx090200212p.pdf http://www.ams.org/notices/200902/rtx090200212p.pdf) It starts: "Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best friends are birds."
kzrdude 11y ago
And then there's the abc conjecture person, whose theory building went so far that nobody can read it? It's this taken to the extreme, isn't it?

j2kun 11y ago

I was not aware that Euler had so many publications. Good point. However, even though I believe Erdos's insights were as deep as Grothendieck's, and that Erdos was as great a mathematician, I don't think I could ever convince an algebraic geometer of it.