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\title{Frequently Asked Questions in Mathematics}
\author{The Sci.Math FAQ Team.\\ 
Editor: Alex L\'{o}pez-Ortiz  \bigskip  \\ 
{\it e-mail: alopez-o@unb.ca}}
\date{}


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\begin{document}
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\samepage \begin{teo}[Fermat's Last Theorem]
    There are no positive integers $x$, $y$, $z$, and $n > 2$ such that 
$x^n + y^n = z^n$.
\end{teo}
}

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\samepage \begin{tabular}{|r|r|r|l|} \hline

{Number} & {$p$} & {Year}& {Discoverer} \\  \hline

     1-4 &   2,3,5,7      &             pre-1500 &\\ 
     5   &      13        &                1461 & Anonymous \\ 
     6-7 &      17,19        &             1588 & Cataldi\\ 
     8   &       31          &             1750 & Euler\\ 
     9   &       61          &             1883 & I.M. Pervushin\\ 
    10   &       89          &             1911 & Powers\\ 
    11   &       107         &             1914 & Powers\\ 
    12   &       127         &             1876 & Lucas\\ 
    13-14&       521,607     &             1952 & Robinson\\ 
    15-17&       1279,2203,2281  &         1952 & R. M. Robinson\\ 
    18   &       3217            &         1957 & Riesel\\ 
    19-20&       4253,4423       &         1961 & Hurwitz \& Selfridge \\ 
    21-23&       9689,9941,11213 &         1963 & Gillies\\ 
    24   &       19937           &         1971 & Tuckerman\\ 
    25   &       21701           &         1978 & Noll \& Nickel\\ 
    26   &       23209           &         1979 & Noll\\ 
    27   &       44497           &         1979 & Slowinski \& Nelson\\ 
    28   &       86243           &         1982 & Slowinski\\ 
    29   &       110503          &         1988 & Colquitt \& Welsh\\ 
    30   &       132049          &         1983 & Slowinski\\ 
    31   &       216091          &         1985 & Slowinski\\ 
    32   &       756839          &         1992 & Slowinski \& Gage\\ 
    33  &       859433          &         1994 & Slowinski \& Gage\\ 
    34  &      1257787          &         1996 & Slowinski \& Gage \\ 
    35  &      1398269          &         1996 & Armengaud, Woltman, et. al.\\ 
    36???  &      2976221          &         1996 & Spence, Woltman, et. al.\\ 
\hline    
\end{tabular}
}

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\samepage \OE
}

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\samepage \begin{eqnarray*}x &=& 0.9999\ldots \\ 
    10x &=& 10 \cdot 0.9999\ldots \\ 
    10x &=& 9.9999\ldots \\ 
10x - x &=& 9.9999\ldots - 0.9999\ldots \\ 
     9x &=& 9 \\ 
      x &=& 1 \\ 
\end{eqnarray*}
}

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\samepage \begin{tabular}{|r|l|l|l|r|} \hline

{Year} & {Name} & {Birthplace} & {Country}& {Age} 
 \\  \hline

1936&Ahlfors, Lars     &Helsinki      &Finland  &29\\ 
1936&Douglas, Jesse    &New York, NY   &USA      &39\\ 
1950&Schwartz, Laurent &Paris         &France   &35\\ 
1950&Selberg, Atle     &Langesund     &Norway   &33\\ 
1954&Kodaira, Kunihiko &Tokyo         &Japan    &39\\  
1954&Serre, Jean-Pierre&Bages         &France   &27\\ 
1958&Roth, Klaus       &Breslau       &Germany  &32\\ 
1958&Thom, Rene        &Montbeliard   &France   &35\\ 
1962&Hormander, Lars   &Mjallby       &Sweden   &31\\ 
1962&Milnor, John      &Orange, NJ     &USA      &31\\ 
1966&Atiyah, Michael   &London        &UK       &37\\ 
1966&Cohen, Paul       &Long Branch NJ&USA      &32\\ 
1966&Grothendieck, Alex.&Berlin   &Germany  &38\\ 
1966&Smale, Stephen    &Flint, MI      &USA      &36\\ 
1970&Baker, Alan       &London        &UK       &31\\ 
1970&Hironaka, Heisuke &Yamaguchi-ken &Japan    &39\\ 
1970&Novikov, Serge    &Gorki         &USSR     &32\\ 
1970&Thompson, John    &Ottawa, KA     &USA      &37\\ 
1974&Bombieri, Enrico  &Milan         &Italy    &33\\ 
1974&Mumford, David    &Worth, Sussex &UK       &37\\ 
1978&Deligne, Pierre   &Brussels      &Belgium  &33\\ 
1978&Fefferman, Charles&Washington DC &USA      &29\\ 
1978&Margulis, Gregori &Moscow        &USSR     &32\\ 
1978&Quillen, Daniel   &Orange, NJ     &USA      &38\\ 
1982&Connes, Alain     &Draguignan    &France   &35\\ 
1982&Thurston, William &Washington DC &USA      &35\\ 
1982&Yau, Shing-Tung   &Kwuntung      &China    &33\\ 
1986&Donaldson, Simon  &Cambridge     &UK       &27\\ 
1986&Faltings, Gerd    &1954          &Germany  &32\\ 
1986&Freedman, Michael &Los Angeles &USA      &35\\ 
\hline
\end{tabular}
}

{\newpage
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\samepage \begin{tabular}{|r|l|l|l|r|} \hline

{Year} & {Name} & {Birthplace} & {Country}& {Age} 
 \\  \hline

1990&Drinfeld, Vladimir&Kharkov       &USSR     &36\\ 
1990&Jones, Vaughan    &Gisborne      &N Zealand&38\\ 
1990&Mori, Shigefumi   &Nagoya        &Japan    &39\\ 
1990&Witten, Edward    &Baltimore     &USA      &38\\ 
1994& Pierre-Louis Lions    & ????  &   France  &   38\\ 
1994&Jean-Chrisophe Yoccoz  &   ????  &   France  &   37\\ 
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1994&Jean Bourgain          &  Oostende  &   Belge   &   40\\ 
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1994&Efim Zelmanov          &   Novosibirsk  &   Russia  &   39\\ 
\hline
\end{tabular}
}

{\newpage
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\samepage \begin{tabular}{|r|l|l|l|} \hline

{Year} & {Name} & {Institution} &{Country}
 \\  \hline

1936&Ahlfors, Lars     &Harvard University         &USA \\ 
1936&Douglas, Jesse    &MIT              &USA \\ 
1950&Schwartz, Laurent &Universite de Nancy       &France \\ 
1950&Selberg, Atle     &Institute for Advanced Study, Princeton&USA \\ 
1954&Kodaira, Kunihiko &Princeton University      &USA \\ 
1954&Serre, Jean-Pierre&College de France&France \\ 
1958&Roth, Klaus       &University of London      &UK \\ 
1958&Thom, Rene        &University of Strasbourg  &France \\ 
1962&Hormander, Lars   &University of Stockholm   &Sweden \\ 
1962&Milnor, John      &Princeton University      &USA \\ 
1954&Serre, Jean-Pierre&College de France&France \\ 
1958&Roth, Klaus       &University of London      &UK \\ 
1958&Thom, Rene        &University of Strasbourg  &France \\ 
1962&Hormander, Lars   &University of Stockholm   &Sweden \\ 
1962&Milnor, John      &Princeton University      &USA \\ 
1966&Atiyah, Michael   &Oxford University         &UK \\ 
1966&Cohen, Paul       &Stanford University       &USA \\ 
1966&Grothendieck, Alex&University of Paris       &France \\ 
1966&Smale, Stephen    &University of California at Berkeley      &USA \\ 
1970&Baker, Alan       &Cambridge University      &UK \\ 
1970&Hironaka, Heisuke &Harvard University        &USA \\ 
1970&Novikov, Serge    &Moscow University         &USSR \\ 
1970&Thompson, John    &University of Chicago     &USA \\ 
1974&Bombieri, Enrico  &Univeristy of Pisa        &Italy \\ 
1974&Mumford, David    &Harvard University        &USA \\ 
1978&Deligne, Pierre   &IHES             &France \\ 
1978&Fefferman, Charles&Princeton University      &USA \\ 
1978&Margulis, Gregori &InstPrblmInfTrans&USSR \\ 
1978&Quillen, Daniel   &MIT              &USA \\ 
1982&Connes, Alain     &IHES             &France \\ 
1982&Thurston, William &Princeton University      &USA \\ 
1982&Yau, Shing-Tung   &Institute for Advanced Study, Princeton              &USA \\ 
1986&Donaldson, Simon  &Oxford University         &UK \\ 
1986&Faltings, Gerd    &Princeton University      &USA \\ 
1986&Freedman, Michael &University of California at San Diego     &USA \\ 
\hline
\end{tabular}
}

{\newpage
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\samepage \begin{tabular}{|r|l|l|l|} \hline

{Year} & {Name} & {Institution} &{Country}
 \\  \hline

1990&Drinfeld, Vladimir&Phys.Inst.Kharkov&USSR \\ 
1990&Jones, Vaughan    &University of California at Berkeley      &USA \\ 
1990&Mori, Shigefumi   &University of Kyoto?      &Japan \\ 
1990&Witten, Edward    &Princeton/Institute for Advanced Study&USA \\ 
1994& Pierre-Louis Lions       &Universite de Paris-Dauphine&France\\ 
  1994& Jean-Chrisophe Yoccoz      &Universite de Paris-Sud&France\\ 
  1994& Jean Bourgain               &Institute for Advanced Study&USA\\ 
  1994& Efim Zelmanov               &University of Wisconsin&USA\\ 
\hline
\end{tabular}
}

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\samepage \begin{teo}[Four Colour Theorem]

    Every planar map with regions of simple borders can be coloured
    with 4 colours in such a way that no two regions sharing a non-zero
    length border have the same colour.
\end{teo}
}

{\newpage
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\samepage \begin{teo}[Four Colour Theorem]
Every loopless planar graph admits a vertex-colouring with at most four 
different colours.
\end{teo}
}

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\samepage \begin{teo}The trisection of the angle by an unmarked ruler and compass alone
is {\em in general} not possible.
\end{teo}
}

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\samepage \begin{figure}\centerline{ \psfig{figure=tri.eps} }

\end{figure}
}

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\samepage \begin{conj}For all positive integers $m$, the program above terminates.
\end{conj}
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\samepage \begin{teo}[Hadwiger-Glur, 1951] Two equal-area polygons $P$,$Q$ are
        equi-decomposable by translations only, iff we have equality of these
        two functions:     $\phi_P() = \phi_Q()$
     \end{teo}
}

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\samepage \begin{teo}There is a finite collection of disjoint open sets in the unit cube
in $R^3$ which can be moved by isometries to a finite collection of
disjoint open sets whose union is dense in the cube of size 2 in $R^3$.
\end{teo}
}

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\samepage \begin{eqnarray*}i[1]&=&0.003077\\ 
       i[2]&=&0.002479\\ 
       i[3]&=&0.002185\\ 
       i[4]&=&0.002118\\ 
       i[5]&=&0.002115\\ 
\end{eqnarray*}
}

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