^{TM}
Personalized mathematical theorems 
... you could be next!

WHO IS THEORYMINE? (about us!)
About your purchase
About how TheoryMine works
About your purchaseWHAT CAN I BUY FROM THEORYMINE?You can buy new theorems which become yours to name. You will receive a printable certificate in PDF form of the theorem and its discovery (including an outline of the proof). You can then give this away, frame it, sing it, as you like! Also, you can purchase a range of products to go with your theorem, like Tshirts, mouse mats and mugs. All gift items are provided and manufactured by Zazzle. WHAT IS GOING TO HAPPEN WHEN I PURCHASE A THEOREM?If you are not already registered with TheoryMine, you will receive a user name and password to log into the website where you will be able to view the status of your order. WILL I BE ABLE TO PURCHASE EXTRA ITEMS WITH MY THEOREM ONCE I PURCHASED MY THEOREM?Yes. You will be able to purchase additional gift packages (tshirts, mugs and mouse mats) with your theorem once you have received your certificate. You can do so by logging in to your account and click on the "Gift Items Shop " link next to your theorem name. CAN I CHOOSE THE THEOREM I NAME?No. The next theorem that our robot mathematicians discover will be given the name you have chosen. CAN I CHANGE THE NAME OF MY THEOREM AFTER IT HAS BEEN PURCHASED?No. Once a name has been given to a Theorem, that is the name the theorem will have forever. WHAT CAN I CALL A THEOREM?You can call a Theorem whatever you like as long as the name its not inappropriate, libellous, defamatory, blasphemous, obscene, offensive to public morality or an incitement to racial hatred or terrorism. WHICH METHODS OF PAYMENT DO YOU ACCEPT?Payments are carried out on our behalf by PayPal, one of the most popular, secure and established payment gateways. PayPal's pages offer the highest level of security and encryption. Users should be reassured by the internet standard padlock symbol which will be displayed whilst you are entering your card details. We do not hold or see your card details as these are processed directly by PayPal. WHY HASN'T MY THEOREM ARRIVED BY THE DEADLINE YOU PROMISED?Note that if you are not logged into your account when you purchase from our website, your notification email will come to the email address you have registered with PayPal. Please check that email account to see if your notifications emails have arrived. If so, you will also be able to log into the TheoryMine website using the user name and password we have sent you. If your notification email has not arrived by the deadline we specify above or, if it has, but your certificate is not available at "View Certificate" when you log in, then please email us at support@theorymine.co.uk and we will find out what has gone wrong asap. WHY IS MY CERTIFICATE NOT FORMATTED CORRECTLY?Some PDF readers might not support the mathematical characters that appear in the certificate. You might not see these characters when you open the certificate or when you print it. However, if you use Adobe Reader (available for free here) you will not have any of these problems. About how TheoryMine worksWHAT IS A THEORY?From school mathematics you will recall various kinds of numbers: whole numbers, fractions, decimals, etc. You may also have met sets or vectors. These are all examples of mathematical objects. The first thing that TheoryMine does is create new kinds of mathematical object and it can generate an unlimited number of these. In school mathematics you apply functions to numbers, such as addition and subtraction. The second thing that TheoryMine does is create new kinds of functions on these new mathematical objects. TheoryMine can also generate an unlimited number of functions. A Theory is composed of one or more mathematical objects plus some functions on such mathematical objects. WHAT IS A THEOREM?A theorem is a mathematical formula for which we have a proof. Both theorems and proofs are within a theory which consists of a set of axioms. A proof is a sequence of formulae, starting with some axioms and ending with the theorem. Each nonaxiom formula in this sequence follows from the previous formulae in the sequence. All the axioms in TheoryMine theories are recursive definitions. WHAT IS A RECURSIVE DEFINITION?Recursion is a mathematical technique that is much used in computer programs. In a recursive definition, the value of a recursive function is defined in terms of values of the same function applied to smaller inputs. This sounds circular, but because the function's inputs get smaller and smaller the computation eventually stops. TheoryMine also uses recursion to define brand new types of input and output for each theory. These are called recursive objects. WHAT KIND OF THEOREM DOES THEORYMINE DISCOVER?TheoryMine proves properties of functions. For instance, when it comes to addition, it does not matter in which order the numbers are added: 2+3 is equal to 3+2, whereas when it comes to subtraction it does: 23 is not equal to 32. TheoryMine might discover that some of its functions are like addition; giving equal answers whatever the order of the objects to which they are applied. Some functions are inverses of each other, e.g. addition and subtraction: adding a number and then subtracting it, brings you back to where you started. TheoryMine might also discover that some of its new functions are also inverses. The theorems discovered by TheoryMine typically take this simple form. Click here to view an example of a theorem and a detailed explanation. HOW CAN I BE SURE THAT THE PROOF OF MY THEOREM IS CORRECT?The computer programs behind TheoryMine are large and complex and so, like all large complex programs, almost certainly contain bugs However, most of the program merely chooses theories and theorems to prove, and directs their proof. The construction of the proof is handled by a small, well inspected and highly trusted kernel program that only combines axioms and previously proved theorems. It is therefore vanishingly unlikely that any proof it constructs would be faulty. HOW IS IT POSSIBLE TO GENERATE THEOREMS?TheoryMine is based on decades of worldclass research into automated reasoning and artificial intelligence at the Universities of Edinburgh, Cambridge and Munich. It uses the grammars of theories and theorems to generate candidates, filters out the obviously false and uninteresting ones, and then uses automated reasoning to see which of the remainder it can prove. HOW CAN I BE SURE MY THEOREM IS ORIGINAL?The TheoryMine program constructs brand new mathematical theories, that noone has previously developed by using brand new recursive functions and recursive objects. By definition, all theorems of these new theories are themselves brand new. HOW CAN I BE SURE THAT MY THEOREM IS NOT TRIVIALLY TRUE?There are two senses in which your theorem is not trivially true. Firstly, note that some mathematical theories are inconsistent i.e. the axioms contradict each other. In such theories all formulae are theorems, which is clearly undesirable. However, it is a wellestablished mathematical result that theories consisting only of recursive definitions, as TheoryMine's theories are, are inherently consistent. So you can be sure that your theorem is not trivial in this sense. The second sense in which these theorems are not trivially true is that they cannot be directly derived by a simple calculation. In particular, they are not true by simple rewriting from other known theorems, as described in more detail in the answer to the question: IS MY THEOREM INTERESTING?. IS MY THEOREM INTERESTING?TheoryMine applies a series of filters to remove uninteresting theorems before it generates them. On the other hand, don't expect your theorem to earn you the Fields Medal! (the Nobel Prize of Mathematics). In particular, we use the notion of interesting initially developed in Conjecture Synthesis for Inductive Theories (Journal of Automated Reasoning) which was then further developed in SchemeBased Synthesis of Inductive Theories (LNCS, Volume 6437). Technically, this ensures that standard orderings, using known theorems as rewrites, cannot prove the new theorem: that there is no direct symbolic calculational proof of the new theorem. BY WHAT AUTHORITY CAN I ASSIGN A NAME TO MY THEOREM?It is a longstanding tradition in mathematics that the author of a new theorem has the authority to name it. TheoryMine assigns that authority to you. WHY DO YOU CLAIM THAT THEOREMS LAST FOR EVER?A theorem, once proved, stays proved for ever. The reasoning in the proof is deductive, so contains no element of probability or uncertainty. Theorems are abstract objects that are not subject to wear and tear. Even diamonds will be destroyed in the heat death of the universe; theorems won't be. 