Mathematical Musings, Memorabilia and Personalities

[xilman]

Originally Posted by devarajkandadai

Maths Conferences In India & Abroad
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There is a vast difference between Maths Conferences in India and those
conducted abroad.

I have just returned from one held in S. India. I had attended one in
Belgium in '96.

In India there is someone to receive you at the airport or Rly Stn. You
are conducted to the venue. Boarding and lodging are free (sponsors
take care of these}.You feel welcome. All the facilities such as
Xeroxing, Internet connections, computing etc are free.

My experience abroad: No one comes to receive you at the Stn. Of
course they give you proper directions as to how to reach the hotel and from
the hotel to the venue.But for everything, even for the coffee during
coffee -breaks, you are required to pay although the list of sponsors
is big. The welcome abroad is COLD.

A.K. Devaraj

Disclaimer: I have never been to a conference in India.

My experiences of conferences in Europe, North America and Australia is slightly different from your Belgian experience, and each were slightly different from each other.

It has been usual to make ones own way from the airport, station, etc, but not inevitable. On several occasions transport has been provided to and from the conference venue.

Board and lodging has never been free for me. Sometimes it has been included as part of the conference fee, but that's not the same as free. Sometimes sponsors subsidise the cost, especially for grad students and the like who have difficulty raising money themselves.

Coffee and other such refreshments is usually free (i.e. provided by sponsors or paid for from the conference fee). At only one, and that in California, was it not the case. Sometimes, but certainly not always, lunch is included. Perhaps half the time it was.

Most conferences I have attended have provided internet-connected machines. At a couple of the conferences I helped set up the network! It is unusual, in my experience, not to have internet connections available somewhere, either directly as part of the conference or by arrangement with the computing services of the host university.

I have never needed to Xerox material at a conference myself, so can't express a personal opinion on that facility.


Paul

[garo]

I am a computer scientist so my experiences with conferences are in that field. I can certainly vouch for a difference between the conference going experience in the US vs. in Europe - particularly continental Europe. However, often one's conference experience is also a function of how large the conference is. I was in Bertinoro, italy in June this year for a workshop of 40 people and we were all treated like kings and queens. It is impossible to do that for a conference with 500 attendees.

That having been said, it is my experience that conferences in Europe do tend to take greater care of attendees than conferences in the United States. I haven't been to a conference in India but my guess is that the experience there will be similar to that of a smallish conference in Europe. And I think that Indians do generally tend to be very hospitable, particularly towards foreign guests.

[Dr Sardonicus]

The sort of thing I have in mind is illustrated by the following:

• Monstrously huge numbers -- critters such as Graham's number, etc whose principal use is being provable upper bounds

• Wilson's Theorem -- that the integer n > 1 is prime if, and only if, n divides (n-1)! + 1.

Useless for determining whether a number of any size is prime, but applicable to proving theoretical results. For example, if p == 1 (mod 4), then x = ((p-1)/2)! satisfies x^2 + 1 == 0 (mod p), thus proving the congruence is solvable.

• The formula for an nxn matrix inverse given by Cramer's rule, A*adj(A) = det(A)I

where I is the nxn identity matrix, det(A) is the determinant of A, and adj(A) is the "adjugate" [formerly called the "adjoint," which term is now generally used to mean the conjugate transpose]. The adjugate is the transpose of the matrix whose entries are the "cofactors" of A, the i,j cofactor being (-1)^(i+j) times the i,j "minor," this being the (n-1)x(n-1) determinant formed by deleting row i and column j from A.

I know, Cramer's rule can be implemented in a computationally sane manner. But a naive application, iterating "expansion by minors" down to 1x1, is hopeless for n of any size.

Yet Cramer's rule has two obvious theoretical applications: one is in proving that an nxn matrix A with integer entries has an inverse with integer entries if, and only if det(A) is +1 or -1. The "only if" part is clear: if A and A^-1 both have integer entries, their determinants are integers with product 1. If you assume det(A) is 1 or -1, then the "adjugate formula" for the inverse shows that A^-1 also has integer entries, proving the "if" part. (If the entries are in a commutative ring R, the result goes through if det(A) is a unit in R.)

Similarly, the formula shows that, if you have an (n-1) x n matrix, and you "fill in" the n-th row with its own cofactors, you get a matrix whose n-th row is orthogonal to each of the first n-1 rows, and whose determinant is the dot product of the n-th row with itself. In the 2x3 case, the "filled in" third row is the "cross product" of the first two rows.

So -- are there any other results out there that might qualify as theoretically interesting, but computationally useless?

[xilman]

Originally Posted by Dr Sardonicus

The sort of thing I have in mind is illustrated by the following:
...
So -- are there any other results out there that might qualify as theoretically interesting, but computationally useless?

String theory.