The Eagleman Prize in Mathematics and Physics is awarded on a periodic basis to encourage progress on new discoveries.  The prize is awarded to an individual who can provide the best explanation for the novel mathematical relationships provided in each challenge. The winner of each challenge will be declared after selection by a committee of mathematicians and physicists.  The prize carries \$500 US dollars, and is awarded upon majority agreement of the committee.  Under special circumstances the prize may be split among more than one winner. 1st Eagleman Prize challenge The first Eagleman Prize has been awarded to Pascal Wallisch The players in the 2006 challenge were the Golden Ratio (phi, φ), Apery’s constant (ζ(3)), and the masses of neutrons and electrons. φ = 1.6180339887…   [Phi to 2000 decimal places and some history of Phi] ζ(3) = 1.202056903…    The value of Riemann’s zeta function when x=3 is also known as Apery’sconstant   [Apery’s constant] Neutron mass/electron mass = 1838.6836598 ± 1.3x10-6   [list of physics constants] The equation which links them is: The values of these numbers are easily verified.  The relationship between them has to our knowledge never been reported. 2nd Eagleman Prize challenge Keep your eyes on this space for the 2nd Eagleman Prize challenge, to be announced soon. About the prize This prize is meant to spur the hunt for an explanation for the relationship between these numbers. David Eagleman, PhD is a neuroscientist who has pursued mathematical relationships among physical constants and in so doing has stumbled upon some previously unknown findings.  He has chosen to broadcast these relationships – and inspire interest in them – by offering each one sequentially as a challenge for prize money. As with any relationship in mathematics, there is always a risk of reading too deeply into a spurious association – i.e., mere numerology.  There is a non-zero probability of the numbers above sharing a relationship quite accidentally.  Nonetheless, the relationship seems sufficiently surprising and striking that the award is aimed at discovering whether there is a deeper structure.  Johann Balmer, a school teacher, noticed that that four spectral lines of hydrogen fit well to a function involving two integers; upon learning that 12 other spectral lines of hydrogen had been discovered, he quickly verified his formula.  Balmer’s discovery proved an indispensable next step to Niels Bohr’s subsequent description of the atom.  In the best case scenario, this prize humbly hopes to provide the means for a similar possibility.