Mathematics

(14)

March 1, 1993

From: Interview by Paul Wellin, Mathematica in Education

What do you think of the state of math and science education in the US right now?

I remember a couple of early experiences interacting with the “computers and education” crowd at conferences. The experiences varied—from me being very pleasantly surprised at how quickly people seemed to be catching on to the potential for this kind of thing, to complete horror at the fact that people like the ones I was seeing were actually teaching young Americans about science or mathematics. Read more

March 1, 1993

From: Interview by Paul Wellin, Mathematica in Education

Why have computer science and mathematics departments diverged so strongly in the recent past?

One of the biggest mistakes of research mathematics in America in the last 50 years has been to let computer science get away. If you look at what was done when computing was young, there was a strong and definite strand of computing that was essentially part of mathematics. The mathematicians rejected it: this was a big mistake. Read more

March 1, 1993

From: Interview by Paul Wellin, Mathematica in Education

Do you think that mathematics and the rest of the sciences will tend to become less distinct, becoming more and more involved in similar computational tasks, albeit on different problems?

With the current system of science in America, I don’t see any mechanism to reduce the rigidity of it. I think it’s a hell of a pity, because more good science and more useful science could be done if there was less rigidity. Over the 15 years or so that I’ve been doing science in America, Read more

June 1, 1996

From: Interview by Stephen Collart, Euromath Bulletin

Some observers see a research crisis in mathematical computation—a dearth of both fundamental and practical advances; others are concerned about a looming funding crisis. How do you see the situation?

Well, I think Wolfram Research has one of the largest—if not the largest—R&D efforts in mathematical computation anywhere. And certainly I’m pretty happy with the stuff we’re getting done—which ends up being both practical and fundamental. I don’t know so much about the academic mathematical computation scene. But I’m a bit surprised you ask about funding. Read more

June 1, 1996

From: Interview by Stephen Collart, Euromath Bulletin

In what areas of mathematics do you see an underdeveloped potential for computational methods? What could be done to encourage developments?

I think the opportunities of computer experiments are absolutely vast. It’s like the situation about three hundred years ago with physics experiments. Even the easy stuff hasn’t been done. I’ve spent some of the past 15 years trying to do a bunch of the easy computer experiments—and I’ve discovered some incredibly interesting things. Read more

April 9, 2005

From: Interview by Andres Hax, Clarín

One of the most stunning aspects of A New Kind of Science—at least for a layman—is the absence of mathematics. In the long term, will your discoveries make mathematics an obsolete tool for scientific inquiry?

Two things are already happening. First, there’s a new kind of basic science emerging—“pure NKS”. It’s like a physics, or a chemistry, or a mathematics, but concerned with systems in the computational world. Second, ideas and results from pure NKS are getting applied to lots of other places. Some of them aren’t science at all. Read more

March 5, 2012

From: Reddit AMA

What got you into mathematics in the first place? What is your favorite piece of mathematics? i.e theorem, proof, fact, construction etc.

Actually, I was first interested in physics… and I learned mathematics as support for that. I’m not sure if it completely counts as mathematics, but I guess it’s the possibility of universal computation. I think that’s the most important thing that’s been discovered in the past century, and perhaps a lot more.

May 14, 2012

From: Reddit AMA

If somebody proved P=NP, what do you think your reaction would be?

I’d be surprised! And then I’d ask just what axiom system (Peano arithmetic, set theory,… ?) was used to do it. I have a suspicion that P?=NP ultimately isn’t a well-defined decidable question. But hopefully we’ll eventually see.

May 14, 2012

From: Reddit AMA

How do you see integration of computational thinking into general math education working? Is it something that every student should be exposed to? How deep does the integration go?

My brother Conrad has an initiative related to this, called Computer-Based Math: https://www.computerbasedmath.org/ I think there are also things to do directly with computation and NKS, without any direct connection to traditional “math”. And yes, I think these are great for all students. Both because it’s a foundation for a lot of things in the world. Read more

February 23, 2016

From: Reddit AMA

What do you think is the most interesting open problem in mathematics?

One that I’m definitely very interested in is really a metaproblem: how much math is doable? Gödel’s Theorem tells us that there are mathematical questions that are undecidable from existing axioms of math… but those questions often seem very artificial, and most working mathematicians merrily proceed without worrying about undecidability. On the other hand, Read more

November 7, 2016

From: Interview by Dingyu Chen, Eton Magazine

Will mathematicians need to learn classical mathematics (algebra, analysis, calculus) in the future if computers can do it for us?

Once one’s made something into a definite calculation, then, yes, one can just get a computer to do it. The challenge is in doing the mathematical thinking or computational thinking to get it to the point where it can be explained to a computer. And that’s the important thing for people to learn to do. Read more

November 7, 2016

From: Interview by Dingyu Chen, Eton Magazine

Hypothetically, if you could choose two fields of math, physics or computing to be magically fully researched, which ones would you choose, and why?

I’d like to know the fundamental theory of physics: what’s underneath space and time and quantum mechanics and all the other things we know in physics today. I’m not sure if you’d quite call it “computing”, but I’d like to know how to capture human concepts in a precise symbolic way that one can compute with. Read more

November 21, 2016

From: Interview by Sarah Lewin, Space.com

If there are some aspects of mathematics that might be common for aliens and humans, would there also be a lot that wouldn’t overlap?

[Take] binary, base 2 numbers. The I Ching, from ancient China, kind of uses those—and there are places where they’d been kind of invented a long time ago, but really nobody cared until modern times, as computers and the whole wave of technology that makes good use of binary numbers. Read more

March 4, 2019

From: Reddit AMA

Why is math so awesome and how can we make it more accessible and easier to teach?

Not really my subject here… But… What’s even more awesome than math IMHO is the whole computational universe… which I think of as a generalization of math. Still, math is basically the single largest intellectual artifact our civilization has built so far. I like teaching it by doing abstract experiments with computers, Read more
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