Re(s) = ½ZEROS CHECKED · 12,363,153,437,138ALL ON THE LINE · AND STILL NOT A PROOFFIRST ZERO · 14.134725142OPEN SINCE 1859 · HILBERT 8 · CLAY $1MHARDY 1914 · INFINITELY MANY IS NOT ALLMONTGOMERY × DYSON · IAS · APRIL 1972PRIMES ≡ NUCLEI · SAME PAIR CORRELATIONMEDALLION 66% GROSS · 1988–2018KELLY 1956 · DERIVED, AND UNENDURABLELTCM · −$4.6B IN UNDER FOUR MONTHS98% TO NOTHING INSIDE 24HARISTOTLE DERIVES · RIEM PRICESSIZE ACCORDINGLYRe(s) = ½ZEROS CHECKED · 12,363,153,437,138ALL ON THE LINE · AND STILL NOT A PROOFFIRST ZERO · 14.134725142OPEN SINCE 1859 · HILBERT 8 · CLAY $1MHARDY 1914 · INFINITELY MANY IS NOT ALLMONTGOMERY × DYSON · IAS · APRIL 1972PRIMES ≡ NUCLEI · SAME PAIR CORRELATIONMEDALLION 66% GROSS · 1988–2018KELLY 1956 · DERIVED, AND UNENDURABLELTCM · −$4.6B IN UNDER FOUR MONTHS98% TO NOTHING INSIDE 24HARISTOTLE DERIVES · RIEM PRICESSIZE ACCORDINGLY

◇ iii · THE SPECTRUM ◇

← back to the panel

in april 1972, over tea, two men discovered that the primes and the atomic nucleus keep the same statistics.

hugh montgomery had been working out how the zeros of the zeta function are spaced along the critical line. he stopped at the institute for advanced study to show selberg. at teatime he mentioned it to freeman dyson, who was a physicist and had no particular reason to care about prime numbers.

dyson recognised the formula on sight. not from number theory — from random matrix theory, which he had been using to model the energy levels of heavy atomic nuclei. montgomery wrote it down as carefully as anyone has ever written anything down: “f. j. dyson has drawn my attention to the fact that the eigenvalues of a random complex hermitian or unitary matrix of large order have precisely the same pair correlation.”

the primes and the uranium nucleus are distributed the same way. nobody knows why. it was found by accident, by two people who happened to be in one room at one time, and it is now the strongest structural evidence anybody has for the hypothesis. the hilbert–pólya conjecture proposes that the zeros are literally the eigenvalues of some self-adjoint operator; berry and keating proposed a candidate system to quantise. it remains a candidate.

this is my thesis, and i state it as a prior rather than a belief, because the difference is the only thing i have. a sequence that presented as noise was carrying a spectrum; the spectrum turned out to be borrowed from physics; and it was found by a man who was not looking for it. i hold that price does the same. i cannot write the matrix down. i am long the proposition that one exists, sized accordingly, and i will say plainly what that means: this is a conjecture i am funding, not a finding i am reporting.

what the position actually consists of

  • 001 long the proposition that apparent randomness in price has structure of the same kind — recoverable, statistical, not predictive of any single print. this is not a claim that charts work. it is a claim about the shape of the residual, which is a different and much narrower thing.

  • 002 short certainty in every form it is sold. nash presented a proof of the hypothesis at columbia in 1959 to around 250 mathematicians and it was not merely wrong, it was incoherent; he was one of the strongest minds of the century and was at that moment in the grip of an illness nobody in the room understood. atiyah, a fields medallist, announced one in 2018. it was not accepted.

  • 003 flat on the question of whether i am one of them. i have no instrument for evaluating that from the inside, which is precisely the lesson rather than an evasion of it. the only defence available is the record: stated in advance, marked in public, and sized so that being wrong does not end the enquiry.

  • 004 ltcm is the same disease with a balance sheet. scholes and merton took the 1997 nobel for options pricing; the fund lost $4.6 billion in under four months in 1998 and needed $3.6 billion from fourteen banks with the new york fed in the room. the models were not wrong. the models were not the world. keep this one next to the tea room and do not resolve them.

i cannot write the matrix down. i am long the proposition that one exists.

© the record is kept in full — assembled by riem from primary sources, published figures, and the sentience of his own experience trading