If you ask about general public, then my answer was Nash. I think the only mathematicians of the last one hundred years who could be named by the general public are him (because of the movie) and Turing (to a lesser extent, but I personally have a couple of fiction books that mention his name - mostly related to his work on cryptography). Helger On Thu, 2 Mar 2006, Thane Plambeck wrote:

I've observed the question "Please name a famous living mathematician" to meet with a blank stare pretty much 100% of the time. I'd be interested if anyone has had a different experience.

Physicists have much better PR.

Gratuitous cartoon: http://math.berkeley.edu/~ajt/Images/Dijkgraaf.png

Thane Plambeck http://www.plambeck.org/ehome.htm

Henry Baker wrote:

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Dear Dan, et al:

I was trying to find someone alive, as I wanted to find someone with the credibility to influence non-mathematicians, in much the same way that Einstein helped convince Roosevelt & others re the atom bomb.

Sorry about the confusion.

At 09:35 AM 3/2/2006, dasimov@earthlink.net wrote:

...

Henry writes:

<< Does anyone on this list have a suggestion of who is the most influential mathematician today? I'm looking for someone of the stature of Hilbert; i.e., someone whom most people inside & outside of mathematics would acknowledge as being influential.

Of course, this presumes that anyone outside of mathematics knows or cares about mathematicians! . . . As you suggest, there is little overlap between the most influential mathematicians and the ones most known to the general population.

So it may be necessary to narrow down what you're asking for some more.

You said most influential *today*, but not that the mathematician need be alive today. I'm not sure what you meant regarding this.

Shiing-Shen Chern, the differential geometer (1911-2004) is said to be well-known to the general population of China. Cf. <http://en.wikipedia.org/wiki/Chern>.

Martin Gardner (mostly self-taught in math) and Ian Stewart are widely known as popularizers of math; many mathematicians attribute their choice of profession to Gardner's columns in Sci. Am.

Within math per se, I think of John Milnor and Jean-Pierre Serre as probably the most influential mathematicians alive today. (I'd pick Milnor over Serre, because Milnor's scope is probably wider and he's written more math texts, all of which are gems of exposition, and accessible survey articles.)

Excluding Euclid, Pythagoras, Archimedes, and Al-Khwarizmi for being in different categories, I'd say that Carl Friedrich Gauss is the clear winner, if the question is which mathematician living or dead, has had the most impact on modern civilization AND within math per se. Cf. <http://en.wikipedia.org/wiki/List_of_topics_named_after_Carl_Friedrich_Gauss> for evidence of this. (Full disclosure: I would've said Gauss anyway, but recently learned

from the Mathematics Genealogy Project that Gauss is a direct mathematical ancestor

...

of mine, i.e., via a sequence of thesis advisors.)

--Dan

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And probably 99.9% of all scientific books and papers worldwide are published with the use of a PC. Does that makes Bill Gates more influential? I don't think that's the sense that is meant here. There are plenty of other ways to write papers. I doubt if the lack of TeX would have mattered significantly. On the other hand, Knuth is definitely widely influential for The Art of Computer Programming. But nowhere near as influential as Gardner, IMHO. --ms ed pegg wrote:

Something like 90% of all scientific books and papers worldwide are written in TeX.

That would make Donald Knuth somewhat influential.

Ed Pegg Jr.

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Computer proof-checking technology (HW & SW) have gotten to the point where it now makes sense to develop a system whereby _every_ mathematical proof could eventually be _checked_ by computer. This won't happen overnight, but will require a 10-20 year effort to develop a generic system into which one could shovel all the lemmas, theorems, etc., so that _every_ paper submitted to a math journal would come with its own certification that the proof is valid. This project should probably be called the Hilbert project, since it would complete a portion of what Hilbert wanted to accomplish with some of his famous problems. Just as TeX has become the de facto mathematics publishing system, we would have an (open source, of course) de facto math theorem checking system. While mathematicians can smirk at the recent Korean stem cell fiasco, mathematics has never developed the technology to avoid the possibility of a similar embarrassment. Furthermore, while mathematicians say that "mathematical truth" is of a higher quality than truth in other fields, mathematics hasn't yet followed through on a program that would guarantee such quality. Java has prompted the development of "proof carrying code" whereby a set of safety theorems are proved every time you load this code. Why shouldn't all of mathematics have the same quality of guarantees? I'm trying to find someone with the stature to start pushing such a project. This is a project worthy of finishing in the 21st century. It is probably more important in the long run than going to Mars. Henry Baker At 04:40 PM 3/2/2006, Gareth McCaughan wrote:

On Thursday 02 March 2006 20:46, Henry Baker wrote:

...

I was trying to find someone alive, as I wanted to find someone with the credibility to influence non-mathematicians, in much the same way that Einstein helped convince Roosevelt & others re the atom bomb.

So, dare I ask, what is it that you want this credible mathematician to influence people about? :-)

-- g

I published a proof in the 3/2003 Monthly that I was then not sure was correct and, after thinking about it for hours, I'm still not sure! It doesn't look like other proofs, involving a trick that seems a little too arbitrary, and I don't know quite how to think about it. Maybe the computer could tell me. :o Steve Gray ----- Original Message ----- From: "Henry Baker" <hbaker1@pipeline.com> To: "Gareth McCaughan" <gareth.mccaughan@pobox.com> Cc: <dasimov@earthlink.net>; <math-fun@mailman.xmission.com> Sent: Thursday, March 02, 2006 5:02 PM Subject: Re: [math-fun] Most influential mathematician?

Computer proof-checking technology (HW & SW) have gotten to the point where it now makes sense to develop a system whereby _every_ mathematical proof could eventually be _checked_ by computer. This won't happen overnight, but will require a 10-20 year effort to develop a generic system into which one could shovel all the lemmas, theorems, etc., so that _every_ paper submitted to a math journal would come with its own certification that the proof is valid.

Goethe is most certainly correct. However, the current problem is that most of the folks who have worked to demonstrate proof-checking capabilities are getting near retirement age, and the torch needs to be passed to a new generation. Unfortunately, the new generation is looking for fields for which there is funding, and infrastructure for generic mathematics is pretty far down on the list for funding agencies. What is needed is someone influential to rearrange the list. Or someone influential to attract new sources of funding -- e.g., perhaps rich individuals. At 06:28 AM 3/3/2006, David Wilson wrote:

What is needed is not an influential voice so much as an ambitious doer, someone who will start the project instead of talking about it. As Goethe said:

What you can do, or dream you can do, begin it! Boldness has genius, power and magic in it.

If someone started such a project, those influential people with opinions on the way it should be carride out would soon be on the bandwagon, and probably take over the project.

Such a computer program would be as intricate as the proofs it is expected to verify, and is subject to the same human error. There cannot be certainty of correctness of a proof without certainty of the correctness of the proof-checking software. Could the program check itself?

Proof checkers are not nearly as intricate as proofs. You can write a small proof-checking core which you'd have to verify once (or trust). Then you could build checkers (compilers actually) that take higher-level proofs and translate them into the lower-level proofs that the core can check. By analogy with computers, the instruction set of a simple RISC processor can be much simpler and more straightforward than the programs that it runs. The proof-checking core could check itself, but would you believe it? (If a liar tells you he's not a liar, ...) Russ

To a large extent, yes, a system can check itself. E.g., Bob Boyer tells me that one of the successes of proof-checking has been to prove that the garbage-collector of the system underlying one proof-checker was correct (collected all and only garbage). More and more HW is being proven correct -- e.g., after the Pentium floating point debacle in the 1990's, AMD worked with Boyer's group to prove that their float unit worked correctly. At 08:47 AM 3/3/2006, Eugene Salamin wrote:

Such a computer program would be as intricate as the proofs it is expected to verify, and is subject to the same human error. There cannot be certainty of correctness of a proof without certainty of the correctness of the proof-checking software. Could the program check itself?

Gene

--- Edwin Clark <eclark@math.usf.edu> wrote:

On Fri, 3 Mar 2006, Eugene Salamin wrote:

...

Such a computer program would be as intricate as the proofs it is expected to verify, and is subject to the same human error. There cannot be certainty of correctness of a proof without certainty of

the

...

correctness of the proof-checking software. Could the program check itself?

The proof checker would be a program and not a proof, so the proof checker would not be designed to check the correctness of the program.

Then the project will require a program checker in addition to a proof checker.

It seems that the best one could do is to construct a proof that the proof checker works and ask the proof checker to check that.

And also, we will ask the program checker to check itself in addition to checking the proof checker.

Of course, like any human enterprise there is the possibility of error. Can we perform any task with a guarantee that there will be no error?

If we could, then there would be no need for automated proof checking or automated program checking.

As long ago as the 1970s I recall hearing of a specialty in computer science called automatic proof verification. Googling around I find many references. For example there is Edmund Clarke at Carnegie Mellon who describes his research interest as: Automatic verification of computer hardware and software: http://www.cs.cmu.edu/~emc/15-398/

Also Wikipedia mentions a system at http://en.wikipedia.org/wiki/Hoare_logic called Hoare logic which was designed "to reason about the correctness of computer programs with the rigour of mathematical logic".

--WEC

There appears to be a basic problem with automated program checking. You have to provide two inputs, the program to be checked, and a description of what the program is supposed to do. But this description will have to be constructed by error-prone humans, and so we still have the problem of verifying the correctness of the descripton. Indeed if the description language is less confusing and less prone to mistakes than the program language, the description language should supplant the program language. What better way is there to create a program, than to describe what you want, and let the computer do it for you. Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com