This is the most important technical tutorial project that Ciro Santilli has done in his life so far as of 2019.
The scope is insane and unprecedented, and goes beyond Linux kernel-land alone, which is where it started.
It ended up eating every system programming content Ciro had previously written! Including:
so that that repo would better be called "System Programming Cheat". But "Linux Kernel Module Cheat" sounds more hardcore ;-)
Other major things that could be added there as well in the future are:
- github.com/cirosantilli/algorithm-cheat
- computer architecture tutorials with gem5
Due to this project, some have considered Ciro to be (archive):which made Ciro smile, although "Linux kernel documenter God" would have been more precise.
some kind of Linux kernel god.
[ 1.451857] input: AT Translated Set 2 keyboard as /devices/platform/i8042/s1│loading @0xffffffffc0000000: ../kernel_modules-1.0//timer.ko
[ 1.454310] ledtrig-cpu: registered to indicate activity on CPUs │(gdb) b lkmc_timer_callback
[ 1.455621] usbcore: registered new interface driver usbhid │Breakpoint 1 at 0xffffffffc0000000: file /home/ciro/bak/git/linux-kernel-module
[ 1.455811] usbhid: USB HID core driver │-cheat/out/x86_64/buildroot/build/kernel_modules-1.0/./timer.c, line 28.
[ 1.462044] NET: Registered protocol family 10 │(gdb) c
[ 1.467911] Segment Routing with IPv6 │Continuing.
[ 1.468407] sit: IPv6, IPv4 and MPLS over IPv4 tunneling driver │
[ 1.470859] NET: Registered protocol family 17 │Breakpoint 1, lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 1.472017] 9pnet: Installing 9P2000 support │ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 1.475461] sched_clock: Marking stable (1473574872, 0)->(1554017593, -80442)│kernel_modules-1.0/./timer.c:28
[ 1.479419] ALSA device list: │28 {
[ 1.479567] No soundcards found. │(gdb) c
[ 1.619187] ata2.00: ATAPI: QEMU DVD-ROM, 2.5+, max UDMA/100 │Continuing.
[ 1.622954] ata2.00: configured for MWDMA2 │
[ 1.644048] scsi 1:0:0:0: CD-ROM QEMU QEMU DVD-ROM 2.5+ P5│Breakpoint 1, lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 1.741966] tsc: Refined TSC clocksource calibration: 2904.010 MHz │ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 1.742796] clocksource: tsc: mask: 0xffffffffffffffff max_cycles: 0x29dc0f4s│kernel_modules-1.0/./timer.c:28
[ 1.743648] clocksource: Switched to clocksource tsc │28 {
[ 2.072945] input: ImExPS/2 Generic Explorer Mouse as /devices/platform/i8043│(gdb) bt
[ 2.078641] EXT4-fs (vda): couldn't mount as ext3 due to feature incompatibis│#0 lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 2.080350] EXT4-fs (vda): mounting ext2 file system using the ext4 subsystem│ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 2.088978] EXT4-fs (vda): mounted filesystem without journal. Opts: (null) │kernel_modules-1.0/./timer.c:28
[ 2.089872] VFS: Mounted root (ext2 filesystem) readonly on device 254:0. │#1 0xffffffff810ab494 in call_timer_fn (timer=0xffffffffc0002000 <mytimer>,
[ 2.097168] devtmpfs: mounted │ fn=0xffffffffc0000000 <lkmc_timer_callback>) at kernel/time/timer.c:1326
[ 2.126472] Freeing unused kernel memory: 1264K │#2 0xffffffff810ab71f in expire_timers (head=<optimized out>,
[ 2.126706] Write protecting the kernel read-only data: 16384k │ base=<optimized out>) at kernel/time/timer.c:1363
[ 2.129388] Freeing unused kernel memory: 2024K │#3 __run_timers (base=<optimized out>) at kernel/time/timer.c:1666
[ 2.139370] Freeing unused kernel memory: 1284K │#4 run_timer_softirq (h=<optimized out>) at kernel/time/timer.c:1692
[ 2.246231] EXT4-fs (vda): warning: mounting unchecked fs, running e2fsck isd│#5 0xffffffff81a000cc in __do_softirq () at kernel/softirq.c:285
[ 2.259574] EXT4-fs (vda): re-mounted. Opts: block_validity,barrier,user_xatr│#6 0xffffffff810577cc in invoke_softirq () at kernel/softirq.c:365
hello S98 │#7 irq_exit () at kernel/softirq.c:405
│#8 0xffffffff818021ba in exiting_irq () at ./arch/x86/include/asm/apic.h:541
Apr 15 23:59:23 login[49]: root login on 'console' │#9 smp_apic_timer_interrupt (regs=<optimized out>)
hello /root/.profile │ at arch/x86/kernel/apic/apic.c:1052
# insmod /timer.ko │#10 0xffffffff8180190f in apic_timer_interrupt ()
[ 6.791945] timer: loading out-of-tree module taints kernel. │ at arch/x86/entry/entry_64.S:857
# [ 7.821621] 4294894248 │#11 0xffffffff82003df8 in init_thread_union ()
[ 8.851385] 4294894504 │#12 0x0000000000000000 in ?? ()
│(gdb)Examples:
- classification of finite simple groups
- classification of regular polytopes
- classification of closed surfaces, and more generalized generalized Poincaré conjectures
- classification of associative real division algebras
- classification of finite fields
- classification of simple Lie groups
- classification of the wallpaper groups and the space groups
Sponsor Ciro Santilli's work on OurBigBook.com Why you should give money to Ciro Santilli by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16So that he can work full time on OurBigBook.com and revolutionize advanced university-level science, technology, engineering, and mathematics eduction for all ages.
Donating to Ciro is the most effective donation per dollar that you can make to:
- improve hardcore university-level STEM education for all ages
- help make every child into the next Nobel Prize/Fields Medal/deep tech unicorn co-founder
Ciro's goal in life is to help kids as young as possible to reach, and the push, the frontiers of natural sciences human knowledge, linking it to applications that might be the the next big thing as early as possible. Because nothing is more motivating to students than that feeling of:rather than repeating the same crap that everyone is already learning.
To do this, Ciro wants to work in parallel both on:
- the multi-user website e-learning platform of OurBigBook.com
- creating amazing teaching content that motivates that platform, and that deeply interests Ciro, notably quantum mechanics and its related applications:
- quantum computing
- molecular biology
- condensed matter physics and chemistry
- slightly more theoretical stuff in somewhat related fields of:
- continue to dump his brain/research in areas Ciro has expertise in: software engineering and open source software
Ciro believes that this rare combination of both:produces a virtuous circle, because Ciro:
- proven passion and capability to learn and teach science, technology, engineering, and mathematics subjects
- proven programming skills, including web development
- wants to learn and teach, so he starts to create content
- then he notices the teaching tools are crap
- and since he has the ability to actually improve them, he does
As explained at OurBigBook.com and high flying bird scientist, Ciro is most excited to make contributions at the "missing middle level of specialization" that lies around later undergrad and lower grad education:in a way that is:
But on that middle sweet spot, Ciro believes that something can be done, in such as way that delivers:
- beauty
- power
- in your face, without requiring you to study for a year
- but also giving enough precision to allow you to truly appreciate the beauty of the subjectCiro's programming skills can also be used to create educational, or actually more production-like, simulations and illustrations.
Ciro believes that today's society just keep saying over and over: "STEM is good", "STEM is good", "STEM is good" as a religious mantra, but fails miserably at providing free learning material and interaction opportunities for people to actually learn it at a deep enough level to truly appreciate why "STEM is good". This is what he wants to fix.
The following quote is ripped from Gwern Branwen's Patreon page, and it perfectly synthesizes how Ciro feels as well:
In addition to all of this, financial support also helps Ciro continue his general community support activities:
- writing and updating his amazing Stack Overflow answers: Section "Ciro Santilli's Stack Overflow contributions"
- saving the world from the CCP: Section "Ciro Santilli's campaign for freedom of speech in China"
Yet, all breakthroughs, comes from them, because the people who are crazy enough to believe they can change the world are the ones who actually do ;-)
Sometimes systems of Diophantine equations are considered.
Problems generally involve finding integer solutions to the equations, notably determining if any solution exists, and if infinitely solutions exist.
The general problem is known to be undecidable: Hilbert's tenth problem.
The Pythagorean triples, and its generalization Fermat's last theorem, are the quintessential examples.
A polynomial with multiple input arguments, e.g. with two inputs and :as opposed to a polynomial with a single argument e.g. one with just :
All those dedicated applied mathematicians languages are a waste of society's time, Ciro Santilli sure applied mathematicians are capable of writing a few extra braces in exchange for a sane general purpose language, we should instead just invest in good libraries with fast C bindings for those languages like NumPy where needed, and powerful mainlined integrated development environments.
And when Ciro Santilli see the closed source ones like MATLAB being used, it makes him lose all hope on humanity. Why. As of 2020. Why? In the 1980s, maybe. But in the 2020s?
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