Re: Self made mathematician

Dunham has a second book that is a little easier to read (I suspect
you'll have no problem with most of "Journey Through Genius"). It is
titled "The Mathematical Universe" and he goes A thru Z thru great
results.

BTW not all mathematical conjectures need be intractable except to
experts. Recently Fermat's "Last Theorm" was solved by Andrew Wiles at
the Institute at Princeton. You may have read about it. You probably
are familiar with the Pythagorean Theorem. For a right triangle

H^2 = S1^2 + S2^2

Where H is the hypoteneuse and S1 and S2 are the lengths of the side.
Familiar example: 3-4-5 because 5^2 =3^2+4^2 (here the "^2" means
square the number, that is 5^2 =5*5 = 25).

Fermat conjectured, for example, that H^3 = S1^3 + S2^3 and in fact H^N
= S1^N + S2^N have no integer solutions for H, S1 and S2. He curiously
wrote in the margin of a document "I have a simple solution but not the
room to write it down..." This conjecture had many false "proofs". I
believe there is a place in the "standard" approach where a certain
assumption that seems fine is wrong.

After centuries, Wiles closeted himself at Princeton for seven years
and then gave a famous talk where at the end he simply said "...and
that establishes Fermat's Last Theorem." It took a good solid year for
specialists to go through his proof - there were a few glitches of no
real importance - and unlike some fields of "science" it such as social
science it is now considered a proven fact.

It is said that Wiles, in his quest, created a body of mathematics that
will keep mathematicians busy for 300 years!

But here's an even easier one to state. Goldbach was a rich man during
the heyday of math a couple centuries ago. He fancied himself a
mathematician but never did much except fund others and bask in their
success. He conjectured that any even integer may be written as the
sum of two prime numbers. Examples:

10 = 3 + 7 (and 5 + 5)

30 = 13 + 17

and so on.

While this has been established by computers for even integers into the
billions, no one has come close to a proof! The utility of a positive
is questionable!

Feel free to e-mail me at gordon.XXXlukXXXesh @nukXXXove.XXXcom

taking out the X's and the space.

Meanwhile, do a google on "twin primes".

Good luck!

Gordon

.

Relevant Pages

  • Re: Andrew Wiles page on Wikipedia
    ... Andrew Wiles is an international expert on the [[Birch and ... He still writes papers on elliptic curves. ... Wiles' loves mathematics and his love of mathematics dates from his ... The conjecture is now a theorem and was ...
    (sci.math)
  • Re: PBZ: Short Proof of Fermats Last Theorem
    ... and a steady flux of attacks against Wiles. ... > “The mathematics of the new physics,” ... there are trillions upon trillions ... > between Escultura and several mathematicians around the World. ...
    (sci.math)
  • Andrew Wiles page on Wikipedia
    ... I am assuming that there are people who know about Andrew Wiles and ... He still writes papers on elliptic curves. ... Wiles' loves mathematics and his love of mathematics dates from his ... The conjecture is now a theorem and was ...
    (sci.math)
  • Re: Prime numbers, counting tells it all
    ... Their word against the mathematics. ... So you've read and understood Andrew Wiles' proof of FLT? ... What Harris has discovered here is that Wikipedia ... And now you are going to explain that the MathWorld ...
    (sci.math)
  • Re: Prime numbers, counting tells it all
    ... Their word against the mathematics. ... So you've read and understood Andrew Wiles' proof of FLT? ... you can't find a contradiction with that ...
    (sci.math)