TauState isn't a worksheet with a timer. It's a complete training system: a mode for every mood, a lab for every configuration, and statistics that prove the work pays off.
Heads-up: the app's interface is currently German-only. More languages are on the roadmap.
TauState is an intelligent mental-math training app for iPhone and iPad, built for anyone who wants sharper mental arithmetic. It offers 8 game modes and more than 40 operators, spanning the four basic operations, percentages, powers and roots, number theory, and number systems like binary, hexadecimal, and Roman numerals. Difficulty adapts automatically to the player's level, and a fully configurable Lab lets you build custom training sessions around exactly what you want to practise. TauState runs completely offline, with no accounts, no ads, and no tracking, and even its on-device speech recognition never leaves the phone. It's currently free during the TestFlight beta and requires an iPhone or iPad running iOS 18 or later. This website is available in German, English, Spanish, and French, though the app's own interface is German-only for now, with more languages planned.
Play without end, until you stop. Ideal for warming up or for long, unhurried sessions with zero pressure.
A fixed number of problems, start to finish. You know exactly how long the round will take, so you can plan it on purpose.
The countdown is running. Do as much as you can before time runs out, every correct answer counts toward your high score.
A time limit per problem, no catching your breath in between. A hard, fast-paced workout for your head.
A short limit, with bonus time for correct answers. Stay fast and accurate and you extend the round yourself.
Memorise the problems, then answer from memory. Trains more than arithmetic, it trains your memory for numbers too.
Three lives. Every mistake counts until none are left, staying calm beats rushing here.
Build your own mode in the mode builder, from your own rules, time limits and operator combinations.
The Lab lets you shape every detail, operators, number ranges, modifiers. Or just press play and let adaptive difficulty meet you where you are. Every combination can be saved as its own preset and pulled back up any time, for the next run or for one specific weak spot.
Boss problems at the end for extra XP, Ghost Mode makes the task vanish, Mixed Keypad shuffles the keys, Upside-down flips everything 180°, or let chance pull 1–3 modifiers every round. Each modifier trains a different skill, from focus under pressure to spatial thinking when everything suddenly flips.
Accuracy, speed, stars and streaks, rendered in calm, readable charts. A weekly recap and an activity heatmap show the work paying off. No chart overload, just the numbers that actually show where you stand and how far you've come since day one.
A daily challenge, streaks worth protecting, and a heatmap that fills in as you practise, gentle structure that turns calculation into a habit you keep. Like training, consistency here beats the odd perfect run, ten quiet days add up to more than one flawless one.
Forty-plus operators across four worlds: basic arithmetic, advanced math, number theory and number systems. Start gentle, there's always another step up.
Basic arithmetic. Addition, subtraction, multiplication, division, the core where speed is built. This is where you train the automatic reflexes every other operator builds on, from single-digit sums to multi-digit multiplication in your head.
Advanced math. Powers, roots, logarithms, sine & friends, modulo, percentages, fractions, factorials, absolute values. A full toolkit for everything beyond grade school, built the way you'd know it from school or university.
Number theory. Primes, divisibility, digit sums, gcd & lcm, Fibonacci, square numbers. The discipline that shows numbers have their own patterns and rules, far beyond plain calculation.
Number systems. Binary, octal, hexadecimal, Roman, base-4, base-12, including conversion and arithmetic inside the system. Useful from computing fundamentals to a playful look at other ways of counting.
Just speak your answers, recognition runs entirely on the device, offline. Handy for hands-free training, or whenever typing just isn't practical.
The app senses where you are and keeps you right at the edge of growth. Not too easy, not frustrating, just the zone where real learning happens.
Operators, ranges, modifiers, build and save any training configuration. That's how you build your own presets for exactly the weak spot you're working on.
A fresh challenge every day, and a streak you won't want to break. A small, reliable anchor for daily practice.
Six ranks from novice to professor. Every correct answer pays in, progress becomes visible without ever feeling forced.
Dozens of achievements across milestones, combos, streaks and mastery. Small side goals that spice up training without ever getting in the way.
Ten curated colour worlds, from amethyst to midnight, plus sound themes and haptics. Make the app your own without ever distracting from the calculating.
Your complete history as CSV or JSON, your data belongs to you. No vendor lock-in, you can take everything with you, any time.
Free on TestFlight. iPhone and iPad. Private by design.
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