Moving visuals on this page — measured at 0.26% brightness change per frame and zero flashes per second; your reduce motion setting stops them. What moves, and how it was measured
Mathematical plates that draw themselves — prime counts, orbits and lattices rendered live rather than shipped as pictures. It runs continuously while on screen, and it pauses on its own whenever it scrolls out of view.
We measured it rather than guessing: the largest frame-to-frame change in average brightness is 0.26%, and it produces zero flashes per second against the threshold of three set by WCAG 2.3.1. That is well under the limit, and it is not a promise about any individual: if moving images are a problem for you, you should not have to assess ours.
Everything animated on this site honours your system’s reduce motion setting — turn it on in your operating system or browser and these pages stop moving, with nothing else lost. All the mathematics is in the text and the still figures.
The Althöfer Collatz prizes.
Prof. Dr. Ingo Althöfer (Friedrich-Schiller-Universität Jena, Institute of Applied Mathematics — discrete optimization and combinatorial game theory) keeps a standing set of Collatz-family prize problems on his own site: real money, a real deadline of 31 December 2037 across the board, awarded only to the first valid solution.
We picked these on purpose. They are exact, checkable, and defined and judged by someone who is not us — which is the opposite of marking our own work. None of them is claimed as solved.
The specifics of our own work on these prizes are withheld for now. These are Prof. Althöfer’s problems, on his terms, and out of respect for that we are holding back the detail of what we have computed on each one — the proved parts, the measured figures, the charts, the gaps — until he has seen it and is comfortable with its being published here. What stays on this page is only the neutral framing: which prizes exist, that we have entered, and that nothing is claimed as solved. The detail will return once he has approved it, and stay down if he would rather it did.
And a word of plain respect, because it is owed. We are fans of Prof. Althöfer’s work, and we mean the word: the deference on this page is not a formality. These are his problems, posed on his terms, and if he ever asked us to take any of this down, it would be gone the next day, without a word of argument. People like him move mathematics — and the world — quietly, and most of the world never notices they did. He treated one self-taught amateur with patience and genuine kindness, which costs a busy person something and is not forgotten here. To be exact, as everywhere on this site: this is admiration, not a collaboration and not an endorsement — Prof. Althöfer has no involvement in this site, and any error on this page is ours alone.
External competitions and benchmarks — details withheld pending approval
Prof. Dr. Ingo Althöfer (Friedrich-Schiller-Universität Jena, Institute of Applied Mathematics — discrete optimization and combinatorial game theory) keeps a standing set of Collatz-family prize problems on his own site, althofer.de/collatz-prizes.html — real money, a real deadline (31 December 2037 across the board), awarded only to the first valid solution. We picked these as the first real entry here on purpose: exact, checkable, and externally defined by someone else’s terms, not our own scoring.
Althöfer Prize 0 — the stochastic 3n±1 walk (300 Euro) Details withheld
The detail of our work on this prize is withheld pending Prof. Althöfer’s approval. It will return here once he has reviewed it.
Althöfer Prizes 1 (25 Euro) & 2 (50 Euro) — a diverging multiplier, and 9n+1 from n=1 Details withheld
The detail of our work on these prizes is withheld pending Prof. Althöfer’s approval. It will return here once he has reviewed it.
Althöfer Prize 3 — the two-player 3n±1 game (500 Euro, posed July 2023) Details withheld
The detail of our work on this prize is withheld pending Prof. Althöfer’s approval. It will return here once he has reviewed it.
The Main Prize (1,000 Euro)
Not attempted here — stated for completeness, not progress. Prof. Althöfer’s Main Prize is the original Collatz conjecture itself: prove or disprove that every starting n(0) reaches 1 after finitely many steps of the ordinary 3n+1 map. 1,000 Euro, open, same 31 December 2037 deadline as the rest. Nothing on this site claims progress on it, and neither does any prize above.
The terms behind every prize above, stated exactly as Prof. Althöfer lists them: awarded only to the first valid solution received; the 31 December 2037 deadline applies across the board; legal action over a claimed solution is explicitly excluded; and computer-assisted proofs are accepted.