At a conference like the HLF—bringing together researchers from across diverse fields—you’re bound to run into a few turf wars.

Mathematician vs. computer scientist.

Mathematician vs. physicist.

Even—in one delicious exchange on Tuesday—mathematician vs. mathematician.

In his morning talk, Sir Andrew Wiles emphasized a fundamental change in his field of number theory over the last half-century: its move from abelian to non-abelian realms.

Afterwards, Michael Atiyah—fellow mathematician and fellow Sir—rose to comment. After praising a “brilliant talk,” he started to redraw the intellectual boundaries.

“The whole idea of doing non-abelian theory permeates not just number theory,” Atiyah said, “but physics and geometry and vast parts of mathematics. What we’re really looking for is an overall unification in some distant future.”

Wiles mostly agreed, then laughed: “We’ve had this discussion before.”

“When I gave a lecture, probably 25 years ago,” Wiles said, “Michael told me that the future of number theory was to be subsumed by physics.”

Wiles smiled at the memory. “I was a little taken aback by this. It wasn’t what I planned for my future.”

But Wiles got the last laugh. “[Physicist] Cumrun Vafa came up to me afterwards,” Wiles explained, “and said, ‘Don’t worry about it. It’s the other way around.’”

This is my last post from the Heidelberg Laureate Forum.
Back to your regularly scheduled bad drawings next week!

Thanks so much for this contact with people that have been only names in articles to me. Somehow your having contact with them brought them closer to me. How fortunate for you to get to be in the same room with them! This was a fun change for your drawingd.

I don’t comprehend the Langlands Program, but am fascinated that it is working to bring unification to broad, disparate fields of mathematics… and then perhaps be applied to fundamental physics as well. Was it discussed or updated at the conference?

Do you have any resources surrounding the connections between non-abelian number theory and physics? I don’t know much about physics, but I love number theory and am very interested in knowing non-mathematics uses of it.

I can not see how number theory can survive on its own apart from theoretical physics. Ultimately the numbers have to apply to *something* to have any value (no pun intended). In physics all theories can be tested, eventually. In mathematics you gotta wait for somebody else to do your proving for you. Sorry, small fish.

Number theory has had no problem surviving, and being one of the most prolific branches of math, for several millenia, even though it had practically no applications until the 20th century. Why would the future be any different? As long as there are interesting problems to research, there’s no reason it should lose momentum. Most math isn’t motivated by applications outside of it.

And even if you needed applications, its applications to cryptography would be enough to keep it afloat anyway.

Thanks so much for this contact with people that have been only names in articles to me. Somehow your having contact with them brought them closer to me. How fortunate for you to get to be in the same room with them! This was a fun change for your drawingd.

I don’t comprehend the Langlands Program, but am fascinated that it is working to bring unification to broad, disparate fields of mathematics… and then perhaps be applied to fundamental physics as well. Was it discussed or updated at the conference?

Yippee! Finally, we return to the funnies!

Do you have any resources surrounding the connections between non-abelian number theory and physics? I don’t know much about physics, but I love number theory and am very interested in knowing non-mathematics uses of it.

Work of Ken Ono, for instance, on mock modular forms has apparently been applied to black hole physics eg http://swc.math.arizona.edu/aws/2013/2013OnoNotes.pdf

thanks! Looks like some dense reading (see what I did there? ^.^ ).

I can not see how number theory can survive on its own apart from theoretical physics. Ultimately the numbers have to apply to *something* to have any value (no pun intended). In physics all theories can be tested, eventually. In mathematics you gotta wait for somebody else to do your proving for you. Sorry, small fish.

Application is secondary… pure mathematics has no issue standing on its own.

Number theory has had no problem surviving, and being one of the most prolific branches of math, for several millenia, even though it had practically no applications until the 20th century. Why would the future be any different? As long as there are interesting problems to research, there’s no reason it should lose momentum. Most math isn’t motivated by applications outside of it.

And even if you needed applications, its applications to cryptography would be enough to keep it afloat anyway.

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